Math Level K TG

Teacher's Guide

Level K

TEACHER'S GUIDE

Lighthouse Math

Program Directors

Mrs. Zehava Kraitenberg, M.S. Curriculum Advisor, Elementary School Principal

Jane Chamberlain Master of Education in Curriculum and Instruction

Credits

Curriculum Writers

Jane Chamberlain Middle School Math Instructor M.Ed. in Curriculum and Instruction

Susannah Maria Malarkey 4th Grade Instructor

M.A. in Teaching K-8

Karen Williams 5th Grade Instructor

PhD of Education in Curriculum and Instruction

Karen Legreid Math Interventionist K-5

M.A. in Curriculum and Instruction

Mizuho Shiomi 3rd Grade Instructor

M.A. of Arts in Education K-8

Joy Aragones 4th Grade Instructor

M.A. in Education Technology

Chelsea Ruocco 6th Grade Instructor

M.A. in Childhood Education 1-6

Kelly Boehme

1st Grade Instructor

M.Ed. in Elementary Education K-6

Jennifer Ramos-Martinez Curriculum Specialist

M.A. in Curriculum and Instruction

Rebecca Kay-Lewis 5th Grade Instructor

M.Ed. in Elementary Education K-6, 5-8 Math

Sarah Thorman 2nd/3rd Grade Instructor

B.S. Liberal Arts and Sciences (Psychology) Post-Baccalaureate Teacher Certification (Grades K-6)

Francine S. Foote 5th and 6th Grade Instructor

M.A. in Instruction and Curriculum

Review Team

Zehava Kraitenberg M.S. Curriculum Advisor

Elementary School Principal

Layout & Design

Akiva Leitner Project Manager Kevanyc.com

Jane Chamberlain Middle School Math

Instructor M.Ed. in Curriculum and Instruction

Yehuda Gartenhaus M.A. Elementary School Principal

Branko Pejovic/Chris Dunn Layout Directors

©Copyright 2023 Lighthouse Curriculum Inc. All rights reserved.

Lighthouse Math Teacher's Guide Level K • ISBN 978-1-955773-47-8

Elizabeth Szoc 4th Grade Instructor

B.A. in Elementary Education

Luke Bote

K-12 Instructor

M.Ed.. in Leadership

Molly Fernholz

K-6 Instructor

B.A. in Education

Joanna Bell

7th - 12th Grade Instructor

B.S. in Integrated Math Education

Mechi Weizer Curriculum Advisor Elementary School Principal

Issac Flores Illustration Director

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Content developed in collaboration with The Reimagined Classroom

Contact Lighthouse Curriculum:

By calling: 718.285.7100, or emailing: info@lighthousecurriculum.com For more information visit www.lighthousecurriculum.com

Introduction and overview of skills at the beginning of each chapter

Vocabulary words with checkboxes students can check off as they go through the lessons

Clearly coded lessons: blue for the lesson page, red for the exercise page

Let’s learn! helps introduce the concept

Try it together! provides guided practice as a class

Practice provides plenty of problems to practice the skill

Tabs on the top of each page allow you to find chapters and lessons easily

Teacher notes give tips and ideas to guide teachers during the lesson

Icons provide clear, visual instructions to help students understand the directions The Microphone directs the teacher to say a specific instruction

About the Curriculum

The program builds in review and new concepts throughout each level as students step up through mastery of skills. By providing foundational skills and practice, students retain information. The stepwise approach is consistent as students work through 16 chapters comprising eight lessons of review, new skills, guided practice and problem-solving. All lessons include step-by-step instructions for clarity, giving all teachers the tools for success.

Custom illustrations provide a vibrant learning experience. Illustrations complement math questions by including information directly tied to and used to solve the problem. The books are formatted in a way that each grade level can be completed successfully by the culmination of the school year. Lighthouse Math gives teachers the tools they need to teach and gives students everything they need to learn.

Table of Contents. A quick reference for skills and topics found in each chapter

How to use the student book

y The book is “all in one” and can easily be used without extra resources

y Easy to read numbers and spaces for student writing

y Custom images to assist in learning concepts

In Chapter 1, we will learn about primary colors, secondary colors, and sort by comparing objects in size.

Intro to the chapter

y Provides an overview of skills covered in the chapter with images and easy to read bullet points

y Vocabulary

 Listed with checkboxes on the chapter intro page  Students and teachers can check off the vocabulary as they learn and use it

Each chapter has 4 lessons made up of 4 color-coded pages: (See page inserts for each left and right)

y Learning page (blue) provides daily review, guided lesson, and problems to complete together as a class

y Exercise page (red) provides practice problems for students to do independently or in groups, for class discussion, daily work, or homework

About the Program

Direct Instruction (Let’s learn)

y Custom made visuals and images directly linked to content

y Students are immediately engaged with a problem-solving task that promotes mathematical reasoning skills. These tasks allow for multiple points of entry, varied solution strategies, and provide opportunities for meaningful mathematical discussions

Guided Practice

(Try it together/ Learn and Connect)

y Provides for a gradual release of responsibility in solving the problems from the teacher onto the students

Hands-on partner and group activities

y Engages students in a productive struggle with the lesson concepts

y Provides students with an opportunity to construct arguments and critique the reasoning of their peers

Independent Practice (Daily review, Practice)

y Provides students with plenty of opportunities for repetition, which builds fluency and helps them relate mathematical procedures to conceptual understanding. The teacher is able to differentiate to meet the needs of the class and of individual students

Problem-Solving Skills (Challenge, Word problems)

y Students apply skills to real-world problem-solving situations

y Allows for extensions of learning and applications opportunities

y Provides students opportunities to engage in mathematical discussion and sharing

Game-Based Learning

y Allows for students to learn and connect in a different way, which leads to further retention

y Research shows that games provide an environment for learning and engaging with the concepts in multiple ways

y Games can provide a mind-body connection, reach students at all levels, open up conversations and communication about mathematics, and keep students motivated

Formative Assessment

y Quick assessments at the end of each lesson allow teachers to see evidence of student thinking, evaluate progress toward the learning goals, and adjust their instruction accordingly

Summative Assessment

y Chapter assessments directly linked to the lessons to test mastery of skills

y Consistent in length and format that includes a variety of problems

y Teacher notes and sample problems to help guide students through instructions

Common Errors

y Notes and examples for teachers about common errors or what to look for when guiding students through a lesson

Differentiated Instruction

y Extra practice and support to help both struggling learners and early finishers

Spiral Review

y Daily review and warm-up activities provide a quick check of skills

y Important arithmetic skills are reinforced and reviewed throughout the levels

y All levels begin with a comprehensive review of foundational skills

Begin the lesson with direct instruction.

Read the problem together and discuss the model or image provided.

Use icons to assist with learning how to follow instructions independently.

Interact with the visual model to find important information and apply it to the lesson or problem.

Direct instruction for teachers to read to assist with

Help Flash and figure out problems together.

Continue practice or assign problems for independent work

A large number of problems to allow for differentiated instruction and practice. Choose odd number problems to complete first, or choose some problems to assign.

page 20.

Refer to notes to find tips and lesson ideas for teacher guidance

How to use the Teacher Guide

y Use the teacher guide to complement the student workbook.

y The exact version of student pages is shown with a green answer key.

y Easy to use, consistent, and color-coded sections

y Guide students through the workbook with extra activities, pre-requisite skills, and game-based learning.

y Differentiate with additional tips for both struggling learners and early finishers.

Start off the class with review, mental math, or short activity so students can practice some math skills right away. A quick set of independent or class problems that include pre-requisite skills or warm-up activity

Prepare your lesson.

y Use objectives to guide you through the main idea.

y Quick reference and extra tips for vocabulary covered in the lesson

y Materials list helps you be prepared to lead activities and be ready with resources.

objects and ask students to help sort by color. Students will raise their hands to say which color the object is. Place the objects on each paper or next to it.

Guiding Questions

1. Are all of the blue objects the exact same? Why or why not? [They are not the exact same because some are dark blue and some are light blue.]

2. Why is it important to know your colors? [It helps to describe them and sort them into groups.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section and tell students you will be matching paint color with the same color object. Ask students, “Which color are we looking for in the first paint color?” [red] Direct students to circle with a pencil the red pail. Now have students tell you what color they are working with next. [blue] Circle what is blue. Say, “The pail is blue.” Ask students what is the last color they will be looking for today. [yellow] What is yellow in this line? Tell students to point to the crayon and next point to the star. Say, “The star is yellow, so circle the

Use an activity or teacher prompts to get your students reading the book and answering questions together. Questions and dialogue for discussions are provided with answers to help guide the lesson. Prepare and lead group or partner activities to help reinforce the concepts

Copy of the student book pages with answers available for quick answer checks and corrections

Easy to find references to help differentiate your class.

Tips and ideas to assist learners who may need more support

Early Finishers

Students

Challenge and Explore

Give

Do you have students who complete the work more quickly? Find activities or ideas to provide these students with useful work or sharing to reinforce concepts without just adding extra problems.

Common Errors

Help guide students through problemsolving or challenge questions Extend the thought process by providing discussion points or writing about math so you can learn about how your students are thinking. Share and present ideas to hit upon performance learning and communication. This can also be used as a formative assessment for some of your advanced learners.

Guide students to work in their student books

Start with a problem together or help with another step-by-step guide. Find examples of work or tips for reading directions, showing work and labeling answers correctly.

Be on the lookout for common errors to help prevent mistakes or point out best practices.

Every lesson comes with a quick assessment This can be an exit ticket or quick check to see what your students learned that day. It can even be used as a short quiz or recorded to help you show progress and understanding. This allows you to determine whether your students are ready to move on or need more review. It can also help you determine homework or classwork assignments.

Counting from 0 to 10 with pennies

Chapter 1

Counting from 0 to 10 with pennies

In Chapter 1, we will learn about primary colors, secondary colors, and sort by comparing objects in size.

• Identify the primary colors: red, blue, and yellow

• Sort items based on primary colors

• Identify the secondary colors: purple, green, and orange

• Sort items based on secondary colors

• Describe objects based on length

• Identify and draw objects of di erent lengths

• Complete patterns based on object length

• Describe the length of objects

• Classify objects as shorter or longer Vocabulary Words

Level K Chapter 1-1

Objective and Learning Goals

y Identify a color as a primary color.

y Recognize the words: red, blue, and yellow.

y Identify and sort items based on primary colors.

Vocabulary

y Primary colors - colors used to create all of the other colors: red, blue and yellow

Materials

y 5 red, 5 blue, and 5 yellow objects (Pre-Lesson)

y Red, blue, and yellow construction paper (Pre-Lesson)

y Blank paper (Activities)

y Small red, blue, and yellow objects (Struggling Learners)

y 5 varying small red objects per student (Challenge)

Pre-Lesson Warm-up Guiding Questions

Gather together 5 red objects, 5 blue objects, and 5 yellow objects. Make sure to find objects of varying shades of reds, blues, and yellows, if possible. These objects can be anything in the classroom (blocks, counters, balls, markers, etc.). Place a red, blue, and yellow piece of construction paper on the floor. Have students sit on the floor so that the papers are visible to all students. Point to each piece of construction paper and have the students call out that color (red, blue, and yellow). Then, hold up each of the objects and ask students to help sort by color. Students will raise their hands to say which color the object is. Place the objects on each paper or next to it.

Guiding Questions

1. Are all of the blue objects the exact same? Why or why not? [They are not the exact same because some are dark blue and some are light blue.]

2. Why is it important to know your colors? [It helps to describe them and sort them into groups.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section and tell students you will be matching paint color with the same color object. Ask students, “Which color are we looking for in the first paint color?” [red] Direct students to circle with a pencil the red pail. Now have students tell you what color they are working with next. [blue] Circle what is blue. Say, “The pail is blue.” Ask students what is the last color they will be looking for today. [yellow] What is yellow in this line? Tell students to point to the crayon and next point to the star. Say, “The star is yellow, so circle the star. Now we are going to practice looking at the spelling of these color words. Draw a line from the red circle to the word red. Spell the word red with me as I say it aloud.” Have students point to each letter as you spell the color word.

Activities

Pass out a blank piece of paper to students. Direct students to take out a red, blue, and yellow crayon. Model for them. At the top of their paper, draw a red, blue, and yellow circle spaced evenly apart. Take students on a color hunt. As they walk around the classroom, have students draw an item for each color in the correct color column.

Apply and Develop Skills

Continue working through the Try it Together and Independent Practice. Remind students to look for the color that matches the paint.

Struggling Learners

Provide students with a bucket of objects (all either red, blue, or yellow). Place red, blue, or yellow construction paper pieces in front of the students. Have the students sort the objects by matching the object to the paper. Holding the objects right next the paper helps the students see which color it matches.

Early Finishers

Students can continue going on a color hunt inside the classroom for more objects. Students will draw or write the object they find in the classroom on their previous chart.

Challenge and Explore

Give each student five objects that are all a shade of red. Tell students to put the objects in order from darkest to lightest.

Ask students:

1. How did you compare the objects? [By placing the objects right next to each other in order to see which was darker or lighter.]

Assess

Give each student an object (either red, blue, or yellow). Have the student sort their object by placing it on the construction papers (red, blue, and yellow) previously used.

Common Errors

Students may think that a color has to be an exact match. Make sure to show variation in reds, blues, and yellows so that students can see that each color can have a dark and a light shade.

Level K Chapter 1-2

Objective and Learning Goals

y Identify a color as a secondary color.

y Identify and sort colors into purple, green, and orange groups.

y Identify and sort objects into black and white groups.

Vocabulary

y Secondary colors - colors resulting from mixing two primary colors (orange, green, and purple)

Materials

y Water

y 3 clear cups (Pre-Lesson)

y Food coloring in red, blue, and yellow (Pre-Lesson)

y 2 different colors of modeling clay (red, blue, and yellow)/ student (Activities)

y Paper

y Crayons

y Orange, purple, and green small objects (Struggling Learners)

y White modeling clay (Early Finishers)

Pre-Lesson Warm-up Guiding Questions

Gather 3 cups of water in clear glasses and have the red, yellow, and blue food coloring ready to use. Ask students: What are the primary colors? [red, blue, and yellow] Mix blue and yellow together in 1 water cup, red and yellow together in another water cup and red and blue together in the last water cup.

Guiding Questions

1. What happened when the two colors were mixed in the water? [They made a new color]

2. How can new colors be made? [by mixing primary colors together]

Tell students that the primary colors can be mixed together in different ways to make new colors called secondary colors. Finally, show students a black and white object and identify that these colors are opposites. Ask students: What other objects do you know that are black? White? [Answers may vary]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section and tell students you will be matching the paint color to the object. Ask students: Which color are we looking for with this paint? [purple] Direct students to circle the purple object. Walk around to check student work. Repeat for the Try it Together section.

Activities

Pass out primary color modeling clay to students. Give each student two different primary colors (either red and blue, yellow and red, or blue and yellow). Tell students to mix their clay together. (Teach students how to fold in and knead the clay together). Ask students: What do you notice happening to the clay as you mix it? [the color is changing] After all of the students have mixed their clay, ask students to share their results with the class and identify the new color they made as either green, purple, or orange.

Apply and Develop Skills (Practice)

Continue working through the rest of the Try it Together and independent practice. Remind students to look for the secondary color that matches the paint.

Struggling Learners

Provide students with a bucket of objects (all either orange, green, or purple). Place orange, green, and purple construction paper pieces in front of the students. Have the students sort the objects by matching the object to the paper. Holding the objects right next to the paper helps the students to see which color it matches.

Early Finishers

Students can continue exploring their clay by adding white clay to it. They can see how adding more or less white affects the color of their clay. They can also add in other colors to see the results of more than two colors combined together.

Challenge and Explore

Go on a hunt in the classroom for primary colors versus secondary colors. Students should take along a piece of paper and draw or write down objects they find that are primary colors and secondary colors. Share the results as a class. On a chart or the board, keep track of how many objects were primary colors and how many were secondary colors with the whole group. Draw tallies, circles or write the number to keep track of the total primary and secondary colors found.

Discuss the results by asking the following questions:

1. Were there more primary or secondary colored objects?

[answers may vary]

2. Which objects were easier to identify? Why? [answers may vary]

Assess

Tell students to use crayons to draw 1 commonly found object that is purple, 1 object that is green, and 1 object that is orange on a piece of paper. (For example, students can draw purple grapes, green grass, and an orange piece of fruit.)

Common Errors

Students may think that all colors are primary colors. Make sure students can identify and sort objects into primary and secondary colors. Creating a chart to show the two different categories can be helpful for students to reference.

Objective and Learning Goals

y Understand and use the words short, medium, and long to describe object length.

y Identify and draw objects of different lengths.

y Recognize and complete patterns based on object length.

Vocabulary

y Short - describes the length or height of an object that is smaller than others

y Medium - refers to an object’s size or length that is between short and long

y Long - describes an object that is bigger or longer than others

Materials

y Pencils

y Paper

y Rulers

y Printouts of objects of different lengths

Pre-Lesson Warm-up Guiding Questions

Start the lesson by introducing the vocabulary words. Use common classroom items to demonstrate short, medium, and long. Have students identify the size of other items around the classroom.

Guiding Questions

1. What does it mean when something is short? [It means that it’s not very long from one end to the other. It is smaller in length or height compared to other objects.]

2. How is a medium object different from a short or long one? [A medium object is in between a short and a long object in terms of its size or length. It is not as short as the short object, and it is not as long as the long object.]

3. Can you arrange these objects in order from short to long? [Yes, arranging objects from short to long means placing them in a way that their lengths or sizes increase. We start with the shortest object, followed by the object of medium length, and finally, the longest object.]

Introduce the Lesson (Try it Together)

Explain the words, short, medium, and long, using classroom objects. Draw a pattern of caterpillars in growing lengths from short to long on the board, labeling each one. Model an example problem by drawing a short and medium line and tracing a long line. Ask students to describe the lines and the pattern they notice.

Activity

Provide students with images showing a short line and a medium line with space for them to draw a long line. Words are written under each image to help them recognize the pattern. Repeat this activity three times with different images, encouraging students to use a ruler for precision.

Struggling Learners

Encourage students to use physical objects and visual aids to understand the concepts of short, medium, and long. Provide additional practice in identifying and drawing objects of varying sizes. Some students might confuse short and long, especially when translating these concepts into drawing. Reinforce the meaning of these terms with visual aids and repeated practice. Some students may have difficulty understanding patterns. Use clear, simple examples and gradually increase complexity as their understanding grows.

Early Finishers

Have students create their own patterns using the concepts of short, medium, and long. They can then exchange their patterns with a partner to solve.

Challenge and Explore

Ask students to apply the concept to real-life situations, for instance, arranging their books or pencils in order of size. They could also extend patterns to include more steps, or create more complex patterns.

Discuss the results by asking the following questions:

1. Can you think of something around you that is short, something that is medium-sized, and something that is long? [Short - My pencil. Medium - My book. Long - The classroom ruler.]

2. Imagine you have three pieces of string: one is short, one is medium-length, and one is long. Can you put these in order from shortest to longest? How did you decide which one goes where? [First is the short string, then the medium one, and the longest is last. I know because the short string is the smallest, the medium string is bigger than the short one but smaller than the long one, and the long string is the biggest of all.]

Assess

Circle the word that describes something that is not long and not short.

Options: Short, Medium, Long

Draw three lines below: one should be short, one should be medium, and one should be long. Label each line with the correct word.

Common Errors

Some students may not understand that the pattern is based on length. Be explicit about this, and reinforce it throughout the lesson.

Level K Chapter 1-4

Objective and Learning Goals

y Describe the length of objects.

y Correctly identify which object is shorter.

y Correctly identify which object is longer.

Vocabulary

y Which - question word used when comparing

y Shorter - object with less length

y Longer - object with more length

y Compare - observing 2 or more different things

Materials

y Pencils

y Rope or string

y Linking cubes

y Dry-erase board

y Dry-erase markers

Pre-Lesson Warm-up Guiding Questions

Have students stand up. Give them 20 seconds to find a partner. Ask them to decide who is shorter and who is taller. First, have the shorter partner raise their hand. Then have the taller partner raise their hand. Repeat one or two more times with different partners.

Ask for volunteers to hold two different strings. Ask the group to decide which one is shorter. Instead of saying taller, introduce the vocabulary word longer. Explain that when we are talking about length, we use short and long. When we are comparing two things, we use shorter and longer.

Guiding Questions

1. Were you always the shorter partner? [answers vary, most should say no, sometimes they were shorter and sometimes they were taller]

2. When you look at just one person, can you say they are taller or shorter? [no, you have to compare them to another person or thing]

3. If I say student 1 is short, does that tell me about student 2? [no, you have to say student 1 is shorter than student 2]

Introduce the Lesson (Try it Together)

We will be comparing different objects and deciding if something is longer or shorter than something else. Notice we need to have at least two objects to compare them. Hold up two pencils. Say: Look at these two pencils I am holding. One of the pencils is longer than the other. Which one is longer? [students will call out which pencil is longer]. What word can I use to compare the other pencil in my hand to this one? [shorter] Very good. This pencil is shorter than the other pencil. [Hold up the shorter pencil.] Look at the Let’s Learn section. Flash is pointing to the crayons. Read what he says: This crayon is longer. Have students point to the longer crayon, then trace the circle around it. Now move on to Glow. Which caterpillar is shorter? Trace the circle around the shorter caterpillar. Continue on to the Try it Together section. Read the instructions aloud and have students first circle the objects that are longer in problems 1 and 2 and then the objects that are shorter in problems 3 and 4.

Struggling Learners

Use items in the class or in real life to help struggling learners. Use the string again to model what is longer, then ask students to look at another example and find the longer set of linking cubes. Try again until they understand the concept of longer. Then repeat the same thing with shorter. Use the same examples the second time to help students understand that each pair will have one that is longer and one that is shorter.

Early Finishers

With a partner, use linking cubes to create two different lengths. Then the partner has to say which one is longer and which one is shorter.

Students can play “I spy” with objects around the room using longer or shorter as the hint. For example, “I spy something shorter than my pencil.” The partner has to guess objects from around the room.

Challenge and Explore

Line up three pencils or pieces of string. Ask students to make statements about each object. For example, the red pencil is shorter than the green pencil. The red pencil is longer than the blue pencil. See how many different statements they can make.

Discuss the results by asking the following questions:

1. Is there one that is shorter than both of the others? [yes, one object is shorter than object 2 and object 3] 2. Is there one that is longer than both of the others? [yes, one object is shorter than object 2 and object 3]

Assess

Students find two objects from around the room and put them on their desk. Ask them to hold up or point to the longer one first, then hold up or point to the shorter one.

Common Errors

Students may assume that something large is always longer. In the examples, compare two unlike things. One should be wider but shorter, and one should be smaller but longer. For example, a balloon and a string. Make sure they know that the string is longer even though it is slimmer.

Chapter 2

In Chapter 2, we will recognize basic shapes, compare shapes, and learn about patterns.

• Name basic shapes: square, circle, rectangle, and triangle

• Recognize shapes in di erent sizes and orientations

• Identify properties of shapes: sides and vertices

• Find basic shapes in the real world

• Describe positions of shapes

• Draw patterns using primary and secondary colors

• Identify shape and color patterns

Vocabulary Words

Level K Chapter 2-1

Objective and Learning Goals

y Name basic shapes: square, circle, rectangle, triangle.

y Recognize basic shapes regardless of size or orientation.

y Identify properties of shapes, such as sides and vertices.

y Identify basic shapes in real world situations.

Vocabulary

y Square – shape with four equal sides and four vertices

y Rectangle – shape with two sets of equal sides and four vertices

y Triangle – shape with three sides and three vertices

y Circle – shape with a curved edge

y Vertices – points where sides connect and create a corner

y Side – the line that connects two vertices together

Materials

y Chart paper

y Cutout of each shape

y Pattern blocks (triangle, circle, square, rectangle)

y Crayons or markers of blue, yellow, red, and green

y Brown paper bags with shapes inside

Pre-Lesson Warm-up Guiding Questions

Make an anchor chart with 4 columns titled SHAPE, SIDES, VERTICES, and EXAMPLE. In the SHAPE column, draw a square, rectangle, circle, and triangle. Leave the other columns blank. Show students a cutout of a square. Ask if anyone knows the name of the shape. It is a square. Ask students, while tracing the sides with your finger, “What do you notice about the sides of the square?” [there are four, they are straight, they are equal] Touch the corner. Tell students, “This is the corner of my shape. It has a special name: VERTEX or VERTICES.” Have students repeat the word. “How many VERTICES does the square have?” [4] “What are some real world examples of SQUARES?” [answers will vary: napkin, window pane, cheese slice] Record student information on the chart paper. Repeat process for each shape.

Guiding Questions

1. How are rectangles and squares alike? How are they different? [both have 4 sides and 4 vertices. A square has four equal sides. A rectangle has 2 short sides and 2 long sides.] 2. How is a circle different from the other shapes? [It has 0 sides and 0 vertices.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section. Have students trace the sides of each shape and say the name of the shape. Have students touch the vertices on the triangle. How many vertices? [3] Touch each vertex on the square. How many vertices? [4] Look at the circle. How many vertices? [0] Now the rectangle. How many vertices? [4] Using the colors yellow, red, blue, and green, have students trace each shape in the matching color. Look at the Try it Together section. Ask which shape it is. Count together the number of shapes and trace the number in the lines.

Acivities

Pass out a brown paper bag with a triangle, square, circle, and rectangle inside to student pairs. Each partner takes a turn reaching inside the bag and grabbing a shape. Before pulling the shape out of the bag, partner 1 must feel the shape and describe it to partner 2. Descriptions should only be about the features of the shapes, like sides and corners, not the name of the shape. Real-world examples can be given as well. Then, partner 2 must guess what shape is being described by the clues given. Students then switch roles.

2 3 1

Apply and Develop Skills (Practice)

Give instructions for the practice pages. Have students trace each shape and encourage them to say the name of it. Have students color each shape based on the key in the instructions. Remind students that shapes can have a different orientation (be tilted) or a different size, but if they share properties of sides and vertices, they are the same shape. Remind students that shapes can be found in the real world. Draw a line from the shape to the real world picture.

Struggling Learners

Provide students with a handful of pattern blocks. Tell students to sort the shapes. (Allow students to choose how to sort the shapes.) Ask students: How did you sort the shapes and why? Continue allowing students to regroup the shapes with different reasons for their sorting. After a few times, tell students to sort by the number of sides and then vertices. Then, identify the name of each group of shapes (rectangle, square, circle, and triangle) based on the number of sides.

Early Finishers

Have students count the number of each shape on the practice page that they colored. Encourage them to practice writing their numbers 1-3 as they count each shape. For an extra challenge, they can count the total number of shapes they colored.

Challenge and Explore

Go outside and have students draw a rectangle, square, circle and triangle that they find in real life. (For example, students may draw a building and label it “rectangle.”) Come back to the classroom and make a class bar graph for the amount of each shape found in real life.

Tell students to draw each shape and say the name of each shape. Ask them how many sides each shape has. Assess

Common Errors

Students may think that squares and rectangles are the same shape. Remind them that squares have 4 equal sides. Rectangles have two sides that are longer.

Level K Chapter 2-2

Objective and Learning Goals

y Identify circles, squares, trianglse and rectangles by looking at sides and corners or vertices.

y Describe positions of shapes (before, behind, above, below, next to).

Vocabulary

y Side - the line that connects two vertices together

y Vertices/Corners - where two sides meet Materials

y Construction paper cut out of circle, square, triangle, and rectangle to be used on whiteboard (Pre-Lesson)

y Painter’s tape

y 25 different size and color shapes to use for floor sorting game (Activity)

y 4 bins/baskets (Struggling Learners)

y Variety of shapes in colors and sizes (Early Finishers)

y Shape cards with multiple copies of each shape (Challenge)

Pre-Lesson Warm-up Guiding Questions

Tell students that they will explore the world of shapes by being able to recognize and compare shapes like circles, squares, triangles and rectangles. Show models of these shapes. Ask students to compare.

Guiding Questions

1. What do you notice about the circle? [The sides are curved and there are no corners.]

2. What do you notice about the square? [There are four sides and four corners/vertices. All sides are the same size.] Compare a triangle with a rectangle and note the differences. Shapes can be compared based on size and position, too. Place a circle on the whiteboard and put a triangle underneath it. Say that the triangle is under the circle or the circle is above the triangle. These are positional words.

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section and talk about the shapes. Read the headings aloud in the chart so students know what to be looking for. What is the first shape you see? [circle] Have students use their finger to follow the outside of the circle. Say the shape name and color. How many sides and vertices does a circle have? [There are no straight sides and no corners, so we write 0.] Trace the zeros. Move down the chart, noting each shape’s color, number of sides, and corners/vertices. Continue tracing the shape while saying its name. Ask what they notice about the triangle before tracing the numbers in the columns. Do the same with the square and rectangle. Compare the similarities and differences between the two shapes. [Number of sides and vertices are the same, but the lengths of the sides are different.] Trace the numbers.

Activities

0 0 3 3

4 4

4 4

Complete a floor shape, sorting activity with 25 pre-cut different size paper shapes in varying colors. Create a sorting grid on the floor using painter’s tape. Grid needs to be large enough for students to stand inside it. Students will be moving in and out of grid. Provide each student with a shape and confirm shape identification. Next, begin sorting. Make sure floor grid is labeled for “CIRCLE, SQUARE, TRIANGLE, and RECTANGLE.” One at a time, have students move to the correct grid square. When 2 or more of the same shape enter the grid, ask students to make comparisons. Sizes and colors may be different, but number of sides and vertices would be the same. Continue making comparisons while sorting, noting shape attributes.

Apply and Develop Skills (Practice)

Follow the microphone to give students directions.

Struggling Learners

In a small group, show one size of colored shapes: circle, square, triangles and rectangle. Have two of each shape in different colors. With four bins in front of the group, model where each shape should be sorted based on the picture of the shape on the bin. Ask students why would you place the circle in the bin with a circle labeled on it. Discuss the attribute of the shape. A circle is round and has no sides or corners. Continue to model the sorting of the rest of the shapes and discuss shape attributes with sides and corners. Reinforce these math vocabulary terms.

Early Finishers

Provide students with a mixture of different sized and colored shapes: circle, square, triangle, and rectangle. Ask students to sort into 4 piles based on shape. Ask students why they put certain shapes together. As they sort, can they find shapes that are similar to put in the same pile? For an additional challenge, add a diamond to the group and ask students where that shape should be sorted. Discuss the reasoning.

Challenge and Explore

Provide students with patterned shapes on the classroom whiteboard (i.e. circle, square, circle, square….). Ask student volunteer to come up and draw what comes next in the pattern. Provide a few more examples on the whiteboard for volunteers to solve.

Prepare a set of shapes for pairs of students to work at their desk together. Shapes could be drawn on index cards or cut out of construction paper. Introduce a few other shapes into the patterns, such as a diamond, star, or pentagon. One student creates the pattern, and one student guesses what comes next.

Assess

Hold up a picture of a circle, square, triangle, and rectangle (one at a time) and ask what shape it is. Create a classroom chart with 4 shape images in 4 separate columns. Provide students different sized and colored shapes to come up to the chart and place their shape into the correct shape column.

Common Errors

Students may focus on the size and color of a shape and not the shape attributes, like sides and corners or angles. Students may not be able to describe or use the correct vocabulary when describing shapes. Students may also confuse a square and rectangle and not recognize the difference in the side lengths.

Level K Chapter 2-3

Objective and Learning Goals

y Identify and draw the next color in a pattern.

y Identify primary and secondary colors.

Vocabulary

y Pattern – items that repeat in a specific order

Materials

y Chart paper

y 10 of each -yellow/green/blue beads per student (Activities)

y 5 red beads per student (Activities)

y 2 pipe cleaners per student (Activities)

y Note cards (Struggling Learners)

y Linking cubes (Struggling Learners)

y Extra beads (Early Finishers)

y Extra pipe cleaners (Early Finishers)

y Crayons

Pre-Lesson Warm-up Guiding Questions

Tell students they will be practicing color patterns. Show students the following example of a pattern on an anchor chart. The pattern should be alternating blue and red circles. Point to each circle and have students say the color. Now ask students: What color would come next? [blue] Repeat with two more patterns: OOOO ____ and OOOOOO

Guiding Questions

1. What happened with the colors in each example? [The colors kept repeating.]

2. Did the colors ever change order? [No, the order always stayed the same.]

3. What does it mean for the colors to be in a pattern? [The colors repeat in a specific order.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section, and as a class, point to the colored squares and say the colors together. Ask students, “What color comes next?” [blue] Tell students to get a blue crayon and draw a blue square. Continue saying shape names and colors. Have students circle the next shape. Move on to the Try it Together section and have students look at number one. As a class, point to each rectangle and say the color. Ask students: What is the next color in the pattern?[blue] Repeat for the remaining patterns. Remind students to say the patterns aloud in order to determine which color comes next. Circle one of the three choices. Finish coloring in the caterpillar based on the patterns.

Activities

Provide each student with 2 pipe cleaners and 10 blue beads, 10 yellow beads, 10 green beads, and 5 red beads. Tell students to make 2 different patterns on the their pipe cleaners. Place the beads on the pipe cleaner in this order: blue, yellow, blue, yellow. Continue making the pattern with their blue and yellow beads. Check that students are alternating colors. Repeat this process for beads in this order: green, green, red, green, green, red. Continue the pattern.

Apply and Develop Skills (Practice)

Complete the section on what comes next. Say the shape name and color aloud. Next, review answer options on the right-hand side of the page. Which shape fits best? The last page of independent practice requires choosing the correct color to come next. Students need to be prepared with crayons to complete this activity.

Struggling Learners

Provide students with a note card with colored squares drawn on it (blue, red, blue, red, blue, red). Have students use linking cubes to make the pattern on the card. Tell students to match up their linking cubes with the colors on the note card. Then, ask students: What color linking cube would you pick to go next? [blue] Tell students to continue the pattern with their linking cubes. Repeat the note cards with the following patterns: red, green, red, green; and yellow, red, red, yellow, red, red.

Early Finishers

Provide students with more pipe cleaners and colored beads. Students will create their own patterns to make bracelets for themselves. They can use the beads in any color pattern they choose.

Challenge and Explore

Read and discuss the following word problem as a class: The teacher passed out markers in a pattern. First, she passed out a red marker to Joe. Next, she passed out a yellow marker to Tim. Third, she passed out a red marker to Sam. Charlie is waiting for his marker.

Ask Students:

1. What color marker will Charlie get? [yellow]

2. How do you know? [The pattern is red, yellow, red, yellow.]

Assess

Tell students to draw their own pattern using red and blue crayons on a note card. Have them explain their pattern and say which 2 colors will come next.

Common Errors

Students may think that a color pattern is just repeating the same colors in ABAB format. Make sure to show students other patterns, like the ABCABC pattern or AABAAB. Patterns can have multiple colors in repeating orders.

Level K Chapter 2-4

Objective and Learning Goals

y Students will identify shape and color patterns.

y Students will continue shape and color patterns.

Vocabulary

y Repeating pattern – objects that continue in the same order

Materials

y Triangles and squares cut out of construction paper for Warm Up. Triangles should be cut in two different colors.

y Linking cubes, blocks, coins and crayons for early finishers to create their own pattern

y Linking cubes for the Challenge and Explore activity

Pre-Lesson Warm-up Guiding Questions

The teacher should put the triangles and squares that were cut out on the board in a repeating pattern. The teacher should use triangles that are all the same color (for example, red triangle, green square, red triangle, green square). The teacher should ask, “What shape comes next?” [Red Triangle] Now, the teacher should use shapes to make a new pattern that uses triangles of different colors (for example, red triangle, blue triangle, green square, red triangle, blue triangle, green square, red triangle). The teacher should ask, “What shape comes next?” [Blue Triangle] Depending on your class, you could repeat this activity by adding another square color. You also could add a different shape (circle, arrow) in the pattern.

Guiding Questions

1. What makes each of these examples a pattern? [Answers will vary but should include that the colors and shapes repeat in a specific order.]

2. How is the second pattern different from the first pattern? [Answers will vary but could include there are two different colors of triangles, there are more shapes]

Look at the Let’s Learn section as a class and have students point to the first shape. Ask students to name the shape and tell the color of the shape [green triangle]. Repeat this process with the following shapes. When you get to the end of the pattern, ask, “What shape comes next?” [green triangle] Have students use their green crayons to draw and color the next shape.

Introduce the Lesson (Try it Together)

In Try it Together, have students put their finger on the first shape. Have students name the color as well as the shape [blue circle]. Continue through number one by naming each shape and its color. When you get to the end of the pattern, ask students, “What shape comes next?” [red square] Students should circle the square. Repeat this process for numbers 2 and 3. Walk around to be sure students are pointing to each shape when it’s named.

Struggling Learners

Struggling learners may need to look at the pattern in 2 parts. First, students may need to point to each shape and name the color. Then, students should point to the shapes again and name the shape. Finally, students can put the color and shape together to determine what comes next in the pattern.

Early Finishers

Students can use objects in the classroom (linking cubes, crayons, blocks, coins) to make a repeating pattern. Other students in the class should look at the pattern and continue it.

Challenge and Explore

The teacher can show students an increasing or decreasing pattern. For example, 1 red cube, 2 blue cubes, 3 green cubes. The teacher should explain that the next item in this pattern would be 4 yellow cubes. After this, the teacher could show a decreasing pattern or have students make their own increasing or decreasing patterns.

Assess

Make several patterns with cubes.

1. red cube, blue cube, red cube [blue cube] 2. green cube, green cube, yellow cube, green cube, green cube [yellow cube]

Ask students to complete the pattern by adding the next cube.

Common Errors

Students may pay attention to only the color or the shape. Remind students to say both the color and the shape when they point to each shape.

Chapter 3

In Chapter 3, we will practice understanding and writing numbers 0 to 5.

• Recognize numbers 0 to 5 in picture, word, and number form

• Write numbers 0 to 5

• Count numbers 0 to 5

• Represent a number of objects with numbers 0 to 5

• Assign number values to objects while counting

0 1 2 3 4 5

Objective and Learning Goals

y Recognize the numbers one and zero in picture, word, and number form.

y Write the numbers one (1) and zero (0).

y Count the numbers one and zero.

Vocabulary

y Zero - shows that there is no amount

Materials

y 10 note cards (Activities)

y Anchor charts

y Five frames (Struggling Learners)

y Sticky notes (Early Finishers)

y Plastic bears (Struggling Learners)

y Paper

y Pencils

Pre-Lesson Warm-up Guiding Questions

Write the number 0 largely on one anchor chart and the number 1 on the other anchor chart. Ask students: What are some ways to show the number zero? [Sample answers: Show no fingers, the word zero, 2-2=0, etc.] Write student responses around the zero on the anchor chart. Next ask students: What are some ways to show the number one? [Sample answers: 1 finger, the word one, 1+0=1, 1 star, 1 apple, 1 tally, etc.] Write student responses around the one on the anchor chart.

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section. Have students count the amount of apples together. Look at the bowl and ask how many apples are in the first bowl. [Zero] How many apples are in the second bowl: zero or one? [one] Have students use their pencils to trace the number underneath each bowl. Move down to the empty bowl and ask how many apples are in the bowl. [zero] Trace zero. In the Try it Together section, have students look at problem #1. Do they see any pictures? [no] So, if there are no pictures, does this show 0 or 1? [0] Continue asking how the pictures shown represent a number.

Activities

How

and write. 0 0 0 1 1

Make 10 different note cards with different representations of the numbers zero and one. Label the note cards with the letters A-J. See the chart for note card examples.

A. Number word: zero

B. Blank note card

C. 1 star drawn

D. Number word: one

E. 1 finger drawn

F. Blank note card G. 1 circle drawn H. 1 square drawn I. Blank note card J. Number word: zero

Provide students with a worksheet divided into 10 equal sized boxes. Each box will be titled: A - J. Hide the note cards around the room. Students walk around the room to find the note card. Once they find a note card, they locate the letter on the card, determine if the card is a “0” or “1”, and write that number in the corresponding letter box on the worksheet. They then return the card back to the hiding space so other students can find it.

Apply and Develop Skills (Practice)

Learn the concept of a five frame. Draw a model of a five frame on a whiteboard, inserting only one object. Explain how using a five frame helps us to count. Ask how many objects are in the frame. Remove the object and ask how many are in frame. Work together on five frame questions while modeling on the whiteboard.

Struggling Learners

Provide students with a five frame. Ask students to put 1 bear in their five frame. Now ask students to take the 1 bear away. What is left in the five frame? [nothing or zero] Explain that when there is nothing, this shows the number zero, 0.

Early Finishers

Give students sticky notes and challenge them to add more representations of the numbers zero and one to the anchor chart created at the beginning of the lesson.

Challenge and Explore

Read the following problem: Mickey had no toys. His friend shared a toy with Mickey. How many toys does Mickey have now? [1] How many toys did Mickey have at first? [0] Discuss with students how zero and nothing are the same concept.

Assess

Students will draw a picture of one of something on a sticky note and add it to the the “one” anchor chart.

Provide students with a blank five frame and a few objects. Ask students to show 1 and 0 on their five frame using objects of their choice.

Common Errors

Students may not realize that zero is a number even though it is nothing. Remind students that a number describes how many of something.

Objective and Learning Goals

y Recognize the numbers 2 and 3 in the picture, word, and number form.

y Write the numbers two, 2, and three, 3.

y Count the numbers two and three.

Vocabulary

y Counting - naming numbers one by one in order

Materials

y 10 note cards (Activities)

y 12 note cards (Early Finishers)

y 2 Anchor charts

y Five frames (Struggling Learners /Apply and Develop)

y Plastic bears (Struggling Learners)

y Dry-erase board, Dr-erase markers

y Painter’s tape (Apply and Develop)

Pre-Lesson Warm-up Guiding Questions

Write the number two, 2, large on one anchor chart and the number three, 3, on the other anchor chart. Ask students: What are some ways to show the number two? [Sample answers may include: two fingers, the word two, 1+1=2, 2 tallies, etc.] Write student responses around the anchor chart for the number two. Next ask the students: What are some ways to show the number three? [Sample answers may include: three fingers, the word three, 1+2=3, 3 stars, 3 tallies, etc.] Write student responses around the number on the anchor chart.

Guiding Questions

1. Which number, 2 or 3, is greater or more? [three]

2. How do you know that three is more than two? [It has one more in value.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section as a class. Ask students: Which shows 2 apples? [Students point to the first set of apples.] Which shows 3 apples? [Students point to the second set of apples.] Count aloud the number of apples, point with your finger, and trace the number. Move on to the Try it Together section and have students look at problem #1. Count and point to the sports balls as a class. Circle the answer. Ask students: How many sports balls are there? [2] Remind students to point and count as they finish the rest of the section by circling the numbers.

Activities

Make 10 different note cards with different representations of the numbers two and three. Hold up each note card and have students write the number on a dry-erase board. The first student to write the number correctly wins. Keep playing, using all 10 note cards.

Number word: two

Two tallies

Three stars drawn

Two hearts drawn

Two pennies drawn Number word: two

Two fingers drawn Three tallies

Two pennies drawn Number word: three

Apply and Develop Skills (Practice)

Look at the concept of the five frame again. Make a five frame on the floor using painter’s tape large enough for students to stand inside each square. Remind students that a five frame helps us count. Ask for two students to come stand inside the five frame. How many students are in the frame? [2] Have them take a seat, and ask three students to stand inside the five frame. How many are inside now? [3] Work together on the five frame questions, helping to make a connection between the physical object and the corresponding number. If time allows, challenge students by using the floor five frame to show different numbers (0-3).

Struggling Learners

Provide students with a five frame. Tell students to put two bears in their five frame. Next, give students a new five frame and tell students to put three bears in their second five frame. Ask students: Which five frame has more? [the five frame with three bears] How do you know? [Answers may include: There are more spaces filled. There are fewer empty spaces.] Continue by telling students a number (two or three) and telling them to show that many bears in their five frame.

Early Finishers

Give students 12 blank note cards. Student draw or write different representations of the number two on six separate note cards (example: two circles, the word “two”, 2, etc.). Then, they will draw or write different representations of the number three on the remaining six separate note cards. After writing on the cards, students will flip all of the cards face down. Finally, they will flip over two cards at a time to see if they find a match. Two cards must represent the number two, or two cards must represent the number three.

Challenge and Explore

Tell students to count aloud from 0 to 3. Discuss the order of counting with students. Show a model of a five frame with 0 and add one at a time while counting. Ask the following questions: Why does zero come first when counting up? [It is the least value.] Why does three come after two when counting up? [Three is more than two.] Does the order of the numbers change when we count? [The order stays the same because the value does not change.]

Assess

Tell students to draw a picture of two or three of something on a sticky note and add it to the correct anchor chart for the numbers two or three. Provide each student with a blank five frame and set of counters or plastic bears. Ask students to show the value on the five frame depending on what number you call out to the class.

Common Errors

Students may not realize that zero is a number even though it is nothing. Remind students that a number describes how many of something. Students may also struggle to keep track of counting. To help them keep track, students can cross off objects as they count aloud.

Objective and Learning Goals

y Recognize the numbers four and five in picture, word, and number form.

y Write the numbers four, 4, and five, 5.

y Count the numbers four and five.

Vocabulary

y Counting - naming numbers one by one in order

Materials

y Anchor charts

y Five frame (Struggling Learners)

y Bears (Struggling Learners)

y Blank chart (Early Finishers)

y Dice (Early Finishers)

y Linking cubes (Early Finishers)

y 1 brown paper bag/student (Challenge)

Pre-Lesson Warm-up Guiding Questions

Write the number four, 4, large on one anchor chart and the number five, 5, on the other anchor chart. What are some ways to show the number four? [Sample answers may include: four fingers, the word four, 2+2=4, four tallies, etc.]

Write student responses around the anchor chart for the number four. Next, ask the students: What are some ways to show the number five? [Sample answers may include: five fingers, the word five, 3+2=5, 5 stars, 5 tallies, etc.] Write student responses around the number five anchor chart.

Guiding Questions

1. Why is it important to practice counting to 5? [Answers may include: In order to count objects quickly; to be able to add; to be able to subtract, etc.]

2. How can making groups of objects help with counting? For example, if I grouped objects in groups of 5, how would this help to count? [By making groups of 5, it helps to skip count by 5.]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section as a class. Ask students: Which shows 4 apples? [Students point to the first set of apples.] Which shows 5 apples? [Students point to the second set of apples.] Count aloud the number of apples, point with your finger, then trace the number. Move on to the Try it Together section and have students look at problem #1. Count and point to the number of squares. Cross off each square. How many squares are there? [4] Remind students to cross off while counting the rest of the section.

Activities

Make number cards for numbers 1-5. Hold up the number card 4. Tell students to stand up and get into groups of 4. There can be no more or less than 4 per group. If a student does not have a group, they must be seated. Go around to each group and have students as a class count how many are in each group. Repeat for the rest of the cards. Students who don’t have a group can lead the counting. Extensions could be how many groups the class can make with a certain number.

Apply and Develop Skills (Practice)

Continue working through the Try it Together. Remind students to point as they count in order to keep track.

Struggling Learners

Provide students with a five frame. Tell students to put 4 bears in their five frame. Next, give students a new five frame and tell them to put 5 bears in their second five frame. Ask students: Which five frame has more? [The five frame with 5 bears has more.] How do you know? [Answers may include: All of the spaces are full.] Ask students: How does a five frame help us count? [Answers may include: It shows numbers organized to count quickly.] Continue by telling students a number (four or five) and telling them to show that many bears in their five frame.

Early Finishers

Give students a chart on a piece of paper (like below), a single die, and linking cubes. Tell students to roll the die, build the number shown with the linking cubes, and place the cube stack on top of the number of their chart. For example, if the student rolls a 2, they will stack 2 linking cubes and put the stack on a 2 on the chart. Students will play until all spaces on the board are covered. If a student rolls a six, they can pick from the board which number they want to create with their linking cubes.

Challenge and Explore

Give each student a brown paper bag and tell them to collect items. They can collect any items they want but cannot pick more than 5. Return to the classroom and have students share their brown bag items and count them as a class. Ask students: Was anyone able to collect 5 of the same item?

Assess

Tell students to show 4 of something from their desk. Items can include 4 crayons, 4 markers, 4 pieces of paper, etc. Walk around to check the groups. Repeat for the number 5.

Common Errors

Make sure students are counting and keeping track. Students may count a group of objects without keeping track, which may cause them to count 5 every time. Five is number that students are used to counting to from memory. Crossing off objects or pointing to objects as they count out loud will assist students in keeping track.

Objective and Learning Goals

y Students will write the digits 0-5.

y Students will represent a number of objects with numbers 0-5.

y Students will accurately assign number values to objects while counting.

Vocabulary

y How many - a question phrase asking you to count the number of something

Materials

y Five frame printables or reusable manipulatives

y Dry-erase markers

y Counting blocks or pieces

y Dry-erase board (teacher)

Pre-Lesson Warm-up Guiding Questions

Start with a whole class review of the memory tricks to remember writing numbers (Round and back on the railroad track. Two. Two. Two; Around the tree, around the tree, that is the way to make a three; Go down and around and then you stop. Finish the five with a line on top.; etc.) using stuffed animals, balls, or other objects in the room.

Provide each student with 5 or more manipulative counting blocks (or, for increased engagement, try snacks like pretzels, crackers, or fruit snacks). Using the Five Frame space, ask students to fill in one, then two, up to five. Each time you call out a new number, have students write the number with a dryerase marker on their table or whiteboard. Then ask them to start removing them one at a time, again writing the numbers as they go. From five, go to four, down to zero. (If you’re using snacks, you can allow students to eat one of them when they are removing numbers).

Guiding Questions

1. How many do you have when your whole frame is full? [5]

2. When we start counting, what number should we start with? [0 or 1]

3. When you have no objects, how many do you have? [0 objects]

4. How do you remember how to write the number (0-5)? [answers will vary depending on rhyme and number]

Introduce the Lesson (Try it Together)

Flash says we can count from 0 to 5! Let’s Learn! Have students touch, circle, check, or cross off each animal as you count to reinforce number correspondence. Look at the first box. How many do you see? None! What number shows us nothing or none? [0] Draw a line to the 0 and trace it. Have students follow the line to match the pictures to the number for the dogs and cats. Trace each number. Then ask students to count the frogs. How many frogs are there? [1] Find the number 1. Draw a line to match. Do the same process for the turtles and fish. Continue on to the Try it Together section. Have students count the objects, trace the numbers, then write each number two times.

3 3 1 4 2 5 3 3 1 1 1 4 4 4 2 2 2 5 5 5

Struggling Learners

Learners struggling to write numbers might need more practice tracing the lines of the numbers or using a model as a reference for writing the number. Have students trace with a pencil, marker, or manipulative objects (beans, buttons, etc.).

Learners struggling with number sense can use a five frame to help them finish their practice pages. They can also benefit from a five frame that has the numbers written in it to build their memory for what number goes with each object.

Early Finishers

Early finishers can work in pairs to play Silent Codes. Using number flash cards, they take the first three cards, and that is the code they have to share with their partner. They have to communicate the code to each other using only their counting pieces. For example, if the code is 2,4,3, they will place counting pieces in a group or line of 2, a group or line of 4, and a group or line of 3. The partner must write the code with a dry-erase marker. If they get it correct, the first partner will give them the secret code (thumbs up, smile, touch your nose, etc.) and switch roles. Early finishers familiar with numbers up to 10 can play the game up to 10.

Challenge and Explore

Instead of counting up from 0 to 5 or counting down from 5 to 0, ask students to write and count the numbers in a random order.

Guiding Questions

1. What is the first step when you hear a number called? [Answers may vary, start at zero, count up]

2. Is four closer to one or five? How do you know? [five; answers will vary]

Assess

Place 5 objects on the table or draw 5 shapes on a piece of paper. Ask students to write the numbers assigned to the object as they count from 0-5. They should write on a paper to keep as a recorded formative assessment.

Common Errors

Students may flip numbers so they are mirrors of what they should be. Remind students to start their numbers closer to the left side of the paper. Students may start numbers too close to the bottom line or too close to the top line. Remind students to stretch their numbers from the top all the way to the bottom.

Chapter 4

In Chapter 4, we will learn to count to 5 using shapes, five frames, and tally marks.

• Identify and count shapes up to 5

• Use a five frame to count up to 5

• Identify and quickly recognize numbers using pennies

• Recognize and draw tally marks to represent numbers from 0 to 5

• Introduce the concept of the value of a penny

• Combine di erent objects to make 5 in all

1 2 3 4

Vocabulary Words

Objective and Learning Goals

y Understand the relationship between numbers 0-5 and quantities.

y Answer “how many?” questions about the objects they see based on their shape.

Vocabulary

y Count - to discover how many objects there are

y Triangle - a shape with three sides and three vertices

y Square - a shape with four equal sides and four vertices

y Circle - a shape with a curved edge

y Rectangle - a shape with two sets of equal sides and four vertices

Materials

y Pencil

y Whiteboard and markers

y Wooden pattern blocks of different shapes

Pre-Lesson Warm-up Guiding Questions

Start by reviewing shapes with students. Tell students that you will play a game of “I Spy,” and start by saying, “I spy a circle.” Have students guess, and each time they guess, gather or draw the objects they identify. Do this until the object is guessed or until five objects have been guessed. Then count how many objects were guessed before getting it right. Continue this game with triangles and rectangles.

Guiding Questions

1. How many circles did we guess before getting it correct? [between 1 and 5]

2. How do you know there are [#] that we guessed? [answers vary; you can point to or pick up each one]

3. What can we do to help us count correctly? [answers vary; use our pointer finger, cross off each object, put a dot next to each object, move each object to a different place]

Introduce the Lesson (Try it Together)

There are different ways we can keep track of how we count. One way is to point at each object. Let’s try it. Flash wants to know how many triangles there are. Use your finger to point to each triangle as we count together. 1…2…3…4. There are 4 triangles. Trace the number 4. Another way is to circle each object. Look at the next picture and trace the circle around each triangle as we count them. Count aloud as you circle, then trace the number 5. There are 5 triangles. One more way we can count is to color the object as we count. Take out a crayon. Color and count the circles. Trace each number with your crayon as we count together. There are 4 circles. Move to the Try it Together section. Slowly read each instruction aloud to students. Encourage students to point, circle, or color the objects as they count.

Struggling Learners

Struggling learners may need support with shape identification or counting. For learners struggling with shapes, use pattern blocks and give directions like “find the triangle” while making the shape with your hands or drawing it nearby. For learners struggling with counting, use the pattern blocks to move each item they have counted to another part of the table. Each time the student moves a shape, they should say the assigned number. When they have all been moved, line them up and have the student count them again to make sure they get the same number.

Early Finishers

Early finishers can use the pattern blocks to create problems with a partner. Take turns creating their own problems for their partner. One person lays out a mix of shapes and asks their partner to count a certain shape. When the partner gets it right, they switch.

Challenge and Explore

Tell students they can use their pattern blocks to help them with the challenge problem. Say that John has 2 circles and 3 squares, and Jack has 3 circles and 1 triangle. Who has more shapes? Who has more circles?

Discuss the results:

1. How did you know John has more shapes? [put 2 circles and 3 squares in one area and count them; he has 5; other answers may vary]

2. Can Jack have more circles if John has more shapes? Why? [yes, because circles are one type of shape.]

Assess

Using the pattern blocks or another options with a mix of squares, circles, triangles, and rectangles, ask the student to count the number of one of the shapes. Include at least 5 of that shape in your mix to ensure that they can count accurately to 5.

Common Errors

Students without strong number sense skills may struggle to combine counting with differentiating shapes.

Students may struggle to identify the difference between shapes, especially rectangles and squares.

Level K Chapter 4-2

Objective and Learning Goals

y Quickly identify a number using pennies.

y Use a five frame as a tool to quickly identify a number between 0 and 5.

y Identify a number between 0 and 5 without counting up from 0 or 1.

Vocabulary

y Penny - a coin that has the value of 1 cent in the U.S.

y Five frame - a rectangle split into 5 spaces; tool used to count up to 5

y Value - how much a coin is worth

Materials

y Coin purse

y Pennies

y Large five frame

y Paper plates or large-scale printed pennies

y Whiteboard

y Dry-erase markers

y Individual student five frames

y Dice

Pre-Lesson Warm-up Guiding Questions

Start by brainstorming different things in our environment that are important to count. Take out a coin purse and shake it. Ask students what they think is inside. Empty some of the different coins in the purse. Hold up a penny and ask them if they know what kind of coin it is.

Guiding Questions

1. Why would we use coins to help us count? [answers vary]

2. Do you know how much value a penny has? [1 cent]

Introduce the Lesson (Try it Together)

Teacher can use a large-scale five frame to display on the wall or a whiteboard using cardboard, tape, or another material. Choose 5 students to hold 5 large penny printouts or paper plates. Align the students near the board and ask the first 3 to hold up their pennies in the five frame. Ask the class how many pennies there are. Ask them how many spaces are open. Repeat as many times as you would like with different combinations of pennies/student volunteers.

Activity

Using pennies and five frames at their workstations, ask students to fill in their own five frame with different numbers between 0-5. Start by rolling a die and calling out a number. If you choose, you can make it a competition to see which table group can get the correct answer first or have students pair up and practice calling numbers for a partner.

1 2 3 4 4 2 5

Struggling Learners

For struggling learners, call a small group to the back table. Use a model of a five frame and have them use their own five frame and pennies. Model for them or work with them to count from 0-5 with the five frame. For each counting, ask them how many squares have a penny in them and how many are blank. Once you have done the activity in order, try to show students a five frame with a random number and ask them to tell you the number (see if they can do so without counting).

Early Finishers

Students can work with a partner or group of 3 to play speed frame. Have one person fill a frame with pennies, and the other partner or partners have to race to see how quickly they can identify the number shown. For an added challenge, have students remove the five frame.

Challenge and Explore

Read the following challenge problem to students: John wants to buy a piece of chewing gum that costs 5 pennies. He empties his pockets and puts his change on the table and sees this (display 3 pennies). Does he have enough to buy the gum?

Discuss the results by asking the following questions: 1. What tool or strategy can we use to help us figure out this problem? [the five frame; strategies may vary] 2. Why can’t he buy the gum? Explain. [answers vary; 3 is less than 5]

Assess

Have students use their individual five frames and pennies at their tables. Tell students to show 3 on their five frame. When they have completed this, ask everyone to put another penny on their frame. Ask students to show on their fingers how many they have now. Repeat the structure of the activity as necessary.

Common Errors

Students may struggle to recognize a number without counting up from 1. Students may count the empty space instead of the pennies. Point to the pennies to count when beginning to practice, to demonstrate one to one correspondence, and then move toward instant recognition.

Level K Chapter 4-3

Objective and Learning Goals

y Identify and draw tally marks corresponding to the numbers 0 to 5.

y Recognize the concept of tally marks.

y Match a group of objects to its corresponding tally mark representation and numeral.

Vocabulary

y Tally marks - A system of counting where a vertical line is used to represent each count until reaching five, where the fifth count is a diagonal line across the previous four

Materials

y Whiteboard and markers

y Tally Marks Worksheet

y Objects for counting (e.g. blocks, beads, butterflies)

y Number tracing and tally mark tracing sheets

Pre-Lesson Warm-up Guiding Questions

Start the lesson by gathering the students and reviewing numbers 0 to 5. Have them count aloud together. Then introduce the concept of tally marks, explaining that it is another way of representing numbers. Provide them with tracing sheets to practice drawing these tally marks.

Guiding Questions

1. How many fingers do we have on one hand? [We have 5 fingers on one hand.]

2. Can we use lines to show how many fingers we have on one hand? [Yes, we can draw 5 lines, one for each finger.]

3. What would it look like if we represented 3 toys with lines? [We would draw 3 lines, one for each toy.]

Introduce the Lesson (Try it Together)

Today we’re going to learn a new and fun way to represent numbers. We’ve already learned numbers from 0 to 5, and we know how to count objects. But what if we could show these numbers using just lines? Yes, lines! This is what we call ‘Tally Marks.’ It’s just like playing a game of drawing lines. Are you ready to explore this fun game?

Step 1: “Let’s start with our fingers. How many fingers do you have on one hand? Let’s count together: 1, 2, 3, 4, 5. Great job! You have 5 fingers.”

Step 2: “Now, let’s pretend our fingers are lines that we can draw on the board. I’ll represent each of your fingers with a line on the board. Let’s count together as I draw the lines: 1 (draw a vertical line), 2 (draw another vertical line), 3 (draw a third vertical line), 4 (draw a fourth vertical line), and 5 (draw a diagonal line crossing the four vertical lines).”

Step 3: “See, we have represented 5 fingers with 5 lines, and the fifth line is a bit special as it crosses over the other four lines. This is how we draw tally marks for the number 5.”

Step 4: “Now, let’s try to represent other numbers. How many eyes do we have? Yes, 2! Let’s represent this with tally marks.”

1 = 1 = 0 = 2 = 2 = 3 = 3 = 4 = 4 = 5 = 5 =

Struggling Learners

Provide a variety of real-life objects such as blocks, buttons, or fruits. Have the students count these objects, then guide them in drawing the tally marks corresponding to the number of objects. Do this repeatedly with different sets of objects until they can accurately represent the numbers with tally marks.

Early Finishers

Ask students to extend their knowledge by drawing tally marks for numbers up to 10. Provide worksheets that require them to match numbers 6-10 with the correct tally marks. Example: Here’s a number 7; can you represent it with tally marks? First, we draw 5 lines and cross the fifth line. Then, we add 2 more lines to make 7.

Challenge and Explore

Introduce students to the concept of counting by 5s using tally marks. Explain that each group of 5 tally marks can be considered as ‘one’ when counting by 5s. Example: How many tally marks do we have here? Show them 10 tally marks as two groups of 5. Now, we can count by 5s: 5, 10. So, we have 10 tally marks!

Discussion Questions

1. If I have 5 candies, and I eat 1, how many candies do I have left? Can you show me that number with tally marks? [You have 4 candies left. The tally marks for 4 are ||||.]

2. I have drawn some tally marks here (draw 3 tally marks). Can you tell me what number this is, and can you show me that number using your fingers? [That’s the number 3. (Student shows three fingers)]

Assess

Provide a worksheet with a variety of objects ranging from 0 to 5. The students will count the objects and draw the corresponding tally marks. They will also write the numeral that represents the number of objects.

Common Errors

Students may struggle with the concept that the fifth tally mark crosses the other four rather than being another vertical line. Students may also get confused between the number of objects and the corresponding tally marks. Use real objects to demonstrate and reinforce the concept.

Objective and Learning Goals

y Identify ways to make 5.

y Combine two amounts to make 5.

y Count up to 5 objects.

Vocabulary

y Five frame - a rectangle split into 5 spaces; used to count up to 5

y In all - counting the total amount

Materials

y Tape or chalk

y Plates (5)

y Dry-erase boards

y Dry-erase markers

y Five frames (1 per student)

y Two-sided counters (5 per student)

y Dice (1 per student)

y Linking cubes

Pre-Lesson Warm-up Guiding Questions

Create a five frame with tape on the floor or with chalk outside. Have students sit in a circle around the five frame. Place an amount of plates (from 0 to 5) in the five frame. Students write the number of plates on their dry-erase boards. For example, place 3 plates in the five frame. Students write “3” on their dryerase boards.

Guiding Questions

1. How many plates are in the five frame in all? [answers vary] Is that more or less than 5?

2. How many empty spaces are in the five frame? [answers vary]

Introduce the Lesson (Try it Together)

Look at Let’s Learn. Explain that you can combine numbers, or put numbers together, to count how many in all. Have students count the separated green cube (1). Then have them count the separated red cubes (1, 2, 3, 4). Explain that you can combine the green and red cubes to make one long train. Then, count all of the cubes combined (1, 2, 3, 4, 5). Explain that there are different ways to make 5. Try the next example together. Count and write how many green. Count and write how many red. Count how many in all (trace the numbers 1, 2, 3, 4, and 5).

Activity

Pass a five frame, 5 two-sided counters, and a die to students. Students place 5 counters in their five frame, yellow side up. Students roll a number and flip over that many counters to be red in their five frame. Students count how many yellow counters they have and how many red counters they have to make 5.

For example, a student starts with 5 yellow counters in the five frame. A student rolls a 3. The student flips over 3 of the counters to be red, then counts 3 red and 2 yellow make 5.

Struggling Learners

1 4 2 3 3 2 4 1 5 0

0 1 2 3 4 5 5 4 3 2 1 0

Show students how to make different combinations of 5 using linking cubes. Direct students to find 1 blue linking cube. Then direct them to find and connect 4 yellow linking cubes. Show students how these two groups can combine to make 5. Tell students to combine the two colors and count them in all (1….2…3…4…5). Repeat with 2 blue cubes and 3 yellow linking cubes, 3 blue cubes and 2 yellow cubes, and so on.

Early Finishers

Students can work with a partner or race a timer. Students use their five frame, counters, and dice. Students roll a die and use their counters to fill in the five frame. For example, if the student rolls a 2, they put 2 counters in the five frame. Students keep rolling to add more counters to the five frame. If the student rolls a 6, they clear their board. The first student to make a 5 wins (or if the student gets a 5 before the timer is up, they win). Repeat.

Challenge and Explore

Read the challenge problem to students. Allow students to use a five frame and two-sided counters to act out each part of the problem.

Bob has 2 dogs and 3 cats. Tim has 3 dogs and 2 cats. Do they each have the same amount of pets?

Discuss the results by asking the following questions:

1. How many pets does Bob have? How do you know? [Bob has 5 pets because the counters fill the five frame]

2. How many pets does Tim have? [Tim has 5 pets because the counters fill the five frame.]

Assess

Gather students around the five frame on the ground. Put 2 plates and 2 pieces of paper in the five frame. Tell students to give a thumbs up if it makes a 5 and a thumbs down if it does not make a 5. Repeat with other combinations of numbers like 4 plates and 1 piece of paper.

Common Errors

Students may not count up to 5 in order (1, 2, 3, 4, 5). Students may not have 1 to 1 correspondence when counting the manipulatives or shapes. When counting how many in all, students may count each shape, color, or image by group instead of all together.

Chapter 5

In Chapter 5, we will solve addition problems through symbols, pictures, and story problems.

• Combine numbers to create 5 in all

• Identify and represent addends in addition problems

• Find the sum up to 5 in addition problems

• Recognize + as addition and = as total

• Understand and create number sentences and addition sentences

• Understand and solve story problems related to addition

2 + 1 = 3

Vocabulary Words

Level K Chapter 5-1

Objective and Learning Goals

y Combine two numbers using picture representation.

y Count and write how many in all.

y Create combinations of two numbers to get a total.

Vocabulary

y Combine - to put together or to count in all

y In all - counting the total amount

Materials

y 5 beans/counters for each student

y 5 linking cubes for each student

y Five- frame for struggling learners

Pre-Lesson Warm-up Guiding Questions

Pass out 5 linking cubes to each student. Say, “I have 5 cubes in all” Count them together. Then have students make two stacks of cubes, one stack of 3, and the other of 2. Hold up the stack of 3 cubes. Say, “I have 3 cubes.” [students repeat] Hold up the stack of 2 cubes. Say, “I put on 2 more.” [students repeat] Add the stack of 2 to the stack of 3. Say, “I have 5 in all.” Count out the 5 cubes. Ask students how else they can break apart the 5 cubes. [4 and 1, 2 and 3, 5, and 0] Do the same process with each example.

Guiding Questions

1. What are some different ways we can combine the two stacks of cubes to make 5? [4 and 1, 1 and 4, 3 and 2, 2 and 3, 5 and 0, 0 and 5]

2. When we put the two stacks together, does the total of cubes get bigger or smaller? Why? [the number gets bigger because we are combining or adding two amounts together]

Introduce the Lesson (Try it Together)

Tell students that you are combining, or adding, two numbers together. Look at the Let’s Learn section. Read through the instructions in the Teacher Notes on the student page and work through the examples together. Let’s continue on the next page. Work through Try it Together. In number 4, remind students that it is okay to add 0 to the original group. Ask what happens to the answer. Then look at number 5. Have students use their linking cubes or counters to help. Have them make the total (4 in all) and then separate the starting number of 2. How many to we need to put in to get 4 total? [2]

Activity

Have students partner up and give each student five linking cubes. One student puts some cubes in each hand and then says what they have in each hand. For example, “I have 3 cubes in one hand and 1 cube in my other hand. How many do I have in all?” The partner then says how many cubes in all. They can count the cubes, if needed. Then switch partners. Students may use some of all of the cubes.

Apply and Develop Skills (Practice)

Guide the students through the practice pages together. Remind them to count how many they start with and how many more they add on. Then help them with the star problem on the next page, reminding them that they know how many in all, and they must figure out how many more they need to get to that number.

3 1 4 2 4 1 5 2 1 1 0 4 5 2 5

Struggling Learners

Have students place counters for the Try it Together problems on a five frame. For number 1 (3 fish and 1 more fish), tell students to start with 3 counters in the five frame. Then put in 1 more counter. Ask students: Why did we put 3 counters in the five frame? [because it started with 3 fish] Why did we put in 1 more counter? [because 1 more fish was put in] How many counters are there in all? [4] So what is the total of 3 fish and 1 more fish? [4 fish] Repeat for the rest of Try it Together.

Early Finishers

Have students take out their linking cubes. Have them make a stack of 4. Say: You have 4 linking cubes in all. Take off 1 cube. How many more do you need to make 4? [3] Now make a stack of 4 again. If you have 4, what is another amount you could start with? [answers will vary: 0-4]. Have students remove the amount of cubes they are starting with and stack them together. Then ask: How many more do we need to add to make 4 now? [answers will vary: 0-4] Have students add that amount to their stack. Do you have 4 cubes? Have students try another combination of ways to make 4. Then have them try 3, 2, and 1.

Challenge and Explore

Have students take out their linking cubes and turn to their partner. Say, “I have 5 linking cubes, and my partner has 5 more cubes. How many in all? Let’s count together: 1, 2, 3…10! We have 10 cubes in all! Now, how many different ways can you make 10 in all?” As students work with their partner, have them share the different ways they can make 10. Examples are 10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, and the reverse. Record these ways on chart paper, using drawings and words.

Assess

Pass out a piece of paper to students and have them draw and write the answer to solve this problem: 3 blue flowers are in the pot. Put 1 more flower in the pot. There are ____ [4] flowers in all.

Common Errors

Students may not understand that “put more in” means to combine or get a bigger total. Make sure students know to count all of the items or pictures when it says there are more.

Level K Chapter 5-2

Objective and Learning Goals

y Combine two numbers using picture representation.

y Count and write how many in all.

y Create combinations of two numbers to get a total.

y Find the sums in addition problems with math symbols (plus and equal).

Vocabulary

y Plus sign - math symbol to show addition

y Add - to bring two or more numbers together to make a total; counting up to make more

y Addend - any number added to another number

y Equal sign - math symbol to show in all; total

Materials

y 2 paper cups and a small box

y Pom-poms

y Beach ball

y Linking cubes for struggling learners

y Playing cards 0-5

y Dry-erase boards and markers

Pre-Lesson Warm-up Guiding Questions

Cut out the bottoms of two paper cups. Attach the cups to the wall near the floor. Place the box with an equal sign drawn on the front under the cups. Place a plus sign between the two cups. Tell students you will add pom-poms with your magic adding machine. Count aloud while putting 2 pom-poms in the first cup. Ask students: “How many pom-poms did I start with?” [2] Next, point to the plus sign and say you will add more. Count out 3 pom-poms and put them in the second cup. Ask students: “How many more pom-poms did I put in?” [3] Pull out the box underneath to find out how many in all. Count the pom-poms with students. Ask: “I put in 2 and added 3 more. How many are there in all?” [5] Repeat with 4 pom-poms and 1 more; 2 pom-poms and 2 more.

Guiding Questions

3 + 2 = 5 2 + 2 = 4

1. How did the magic machine work? [put pom-poms in two cups and they combined in the box]

2. Point to the plus sign. Name it and say it is for adding. Based on what happened with our pom-poms, what do you think it means to add? [answers will vary: combining, putting more in, counting up]

3. Point the equal sign on the box. Name it. Based on what happened with our pom-poms, what do you think equal means? [answers will vary: the total, how many in all]

Introduce the Lesson (Try it Together)

Tell students that we are combining, or adding, two addends together. Addends are the numbers we put together. Look at the first group of numbers in Let’s Learn. Read through the Teacher Notes on the bottom of student page to guide students through the practice problems together. Then move on to the Try it Together section. Look closely at number 3. There are no lions for the second addend. Read the sentence “2 and no more is.” Ask students, “When we add ‘no more,’ what number do we use to show that nothing is added? [0] Great! Zero is the second addend!”

Activity

Grab a large beach ball and permanent marker. Write addition problems with sums up to 5 all over the ball, leaving the sums blank. Have students stand in a large circle to play “addition catch.” Students toss the ball to a classmate in the circle. The student who catches the ball solves the addition problem that their right thumb is closest to. Keep tossing the ball around the circle so each student has a turn.

4 + 1 = 5 2 + 3 = 5 2 + 0 = 2

Apply and Develop Skills (Practice)

Move on to the practice. Encourage students to count the objects carefully and write the addends (the numbers the objects represent) on either side of the plus sign. Then, write the total after the equal sign. On the second page, students will write the entire addition sentence on their own. Have them carefully write their numbers and symbols.

Struggling Learners

Provide students with linking cubes. Have students add the two amounts given in Try it Together by building stacks. For example, for 4 elephants and 1 more, students build a stack of 4 cubes and another stack with 1 cube. Tell students to add or combine the stacks. Then ask students: How many cubes in all? [5] Tell students that they found what 4 plus 1 equals by combining the two numbers or addends. Repeat for the rest of Try it Together. Allow students to use linking cubes for independent practice, if necessary.

Early Finishers

Pass out playing cards or number cards with only numbers 1 through 5. Students put cards face down. They pick up two cards and write the addition sentence and sum on their dry-erase board (like 2+1=3). Students may draw circles on their boards to help them solve as well. Repeat with two new cards.

Challenge and Explore

Show students the following incorrect problem: 1+3=5. Tell students to be the teacher and fix the problem to make it correct.

Ask students: Why is this problem wrong? [1+3 does not equal 5] What does 1+3 equal? [4] What two addends equal 5? [2 and 3; 4 and 1] What can you change to make this problem correct? [Answers may vary. Answers can include: change the 1 to a 2; change the 3 to a 4; or change the 5 to a 4]

Assess

Write the problems 2 + 2 = ____, 1 + 3 = ____, and 5 + 0 = ____ on the board. Have students draw pictures and solve for the sums on a piece of paper.

Common Errors

Students may confuse the plus sign and the equal sign. Practice by discussing what each symbol means. Have students touch and say the names of the signs as they read the number sentences. Students may also confuse the order of the numbers and symbols. Have them practice saying the sentence as they write it. “Two plus three equals five.”

Level K Chapter 5-3

Objective and Learning Goals

y Represent addends with pictures.

y Solve sums up to 5.

y Write number sentences to match pictures.

Vocabulary

y Addend - any number added to another number

y Sum - answer to an addition problem

y Number sentence - numbers and symbols used together to show a math problem

Materials

y 5 pieces of construction paper

y Dry-erase boards and markers

y Linker cubes or counters

y 10 note cards

y Paper for each student labeled A-J

y Paper for early finishers with 5 columns labeled 1-5

Pre-Lesson Warm-up Guiding Questions

Write the numbers 1 through 5 on separate pieces of construction paper. Hang the papers around the room. The teacher turns around and counts to ten. While counting, students move to one of the numbers to stand under. After counting to ten, call out an addition sentence (for example, 1+3). Students standing under the sum have to sit down. 1+3=4, so students under 4 need to sit. Keep playing until one student is left standing. This student becomes the new “teacher” that counts and calls out the addition sentences.

Guiding Questions

1. What strategies did you use to solve the problem? [answers will vary: counting up, using fingers, etc]

2. Did any sums get repeated? Why? [Yes. Different combinations of addends can result in the same sum]

Introduce the Lesson (Try it Together)

Tell students that we will use models and pictures to add and to check the sum. Look at the number sentences by Flash in Let’s Learn. Ask students, “What do you notice about these two number sentences? [they have the same sum] How did Flash solve for the sum? [he drew pictures of each addend] Count the crayons above each addend and check his work. Now look at Glow. She is asking us to draw models of number sentences.” Guide students in coloring the linking cube model by coloring the first four cubes one color and the last cube a different color. Show how it models the number sentence 4+1=5. Then guide students through drawing pictures/symbols for 3+2=5. “Let’s Try it Together. First practice writing plus and equal signs. Make your lines nice and straight. Put your pencil on number 2. Look at the model. Match each model to the number sentence it shows. Put your pencil on number 3. Read the number sentence. Draw circles to show the addends and the sum. Then write the sum.”

Activity

Write addition sentences on 10 separate note cards and tape them around the classroom. Sums should be left blank and addition sentences should be labeled A-J. See the example below:

Students walk around with a piece of paper labeled A-J. They will stop at a note card, draw circles for the addends, and write the sum. Make sure students write the sum next to the correct letter for each note card they find.

Apply and Develop Skills (Practice)

Guide students through the practice pages. On the first page, students will create their own model of sums of 5 and 4. Then have them write the number sentence. Be sure the model and the sentence match. On the second page, students will draw circles to represent the number sentence to help them solve. Have students count their circles to be sure they match correctly. In the last section, encourage different methods to solve. Students can draw pictures, use their fingers, or use counters to help them solve.

Struggling Learners

Give struggling students a dry-erase board and marker to solve the independent problems so they have plenty of room to draw circles for each number.

Early Finishers

Pass out a paper with 5 columns. Label each column with a number 1-5. Have students write down every number sentence that has the column label sum. Remind students they can write the addends in reverse order. For example, in the 4 column, students should write 0 + 4, 4 + 0, 1 + 3, 3 + 1, 2 + 2. Students can work with a partner to find all the combinations. Pass out 5 linking cubes or counters to help students. Remind them to make the sum first, then divide the counters into two addends.

Challenge and Explore

Let’s practice adding up to 10! Tell students to hold their hands in front of them. Their left hand is the first addend, their right hand is the second addend. Have them hold up 3 fingers on their left and 4 fingers on their right. Say and model, “I have 3 fingers and I add 4 more. How many do I have in all?” Model counting each finger to get the answer 7. Have students call out different addends to hold up on each hand, and count up to the sum together.

Assess

Pass out a paper with the number sentences 2 + 1 = ____, 1 + 3 = ____, and 4 + 1 = ___.

Tell students to draw circles and write the sum for each number sentence.

Common Errors

Students may draw too many circles, or their circles may not match the addends. Make sure they draw directly above or next to the addends to keep track.

Level K Chapter 5-4

Objective and Learning Goals

y Find and write the addends in a word problem.

y Solve for the sum in an addition number sentence.

y Draw and solve for sums up to 5 in word problems.

Vocabulary

y Number sentence - numbers and symbols used together to show a math problem

y Addition sentence - numbers, plus sign, and equal sign used together to show addition

y Addend - any number added to another number

y Story problems - word problems or problems that use stories to indicate mathematical application and thinking

y Sum - the answer, or result, when adding numbers

Materials

y Dry-erase boards and markers

y Handful of dominoes for each student–no more than 5 total dots

y 1 paper bag per student

y Linking cubes or counters for students

y Timers

Pre-Lesson Warm-up Guiding Questions

On chart paper, write out the story problem: Sam has 3 Rachel has 2 . How many do they have in all? Ask students, “What information is given?” [3 fish and 2 fish] Circle the addends as the students say them. Say, “To help us solve this problem, let’s draw a picture.” Draw 3 fish then + then 2 more fish. Say, “What is our story problem asking us to find? [how many in all] Let’s count together.” Count up the fish and draw the new total. Finally, write out the number sentence with student help.

Guiding Questions

1. What is a story problem? [a story that gives us a math problem to solve]

2. What information do we need to think about to help us solve? [what information are we given, and what do we need to find]

3. What are some strategies we can use to help us solve? [circle important information, draw a picture]

Introduce the Lesson (Try it Together)

Read through the Teacher Notes on the Let’s Learn student page to support students through understanding story problems. Focus on circling the important information (the addends) and drawing pictures to represent the problem. Students may use circles to represent the addends. They do not need to draw the exact picture. Move to the Try it Together section. Continue to read problems aloud. Circle addends and draw pictures to represent the number sentence before writing it.

Activity

Provide each student with a handful of dominoes (dots totaling no more than 5) in a paper bag. Students grab a domino out of the bag and write the matching addition sentence on a dry-erase board. Then have them count the dots to help find the sum. When they are done with one, have them take out another domino. Walk around the room to see that students’ number sentences and sums match the dominoes.

Apply and Develop Skills (Practice)

On the practice pages, encourage students to circle the addends in the story problem and then draw a picture before they write the number sentence. When they move to the second page, tell students they can draw a picture on a dry-erase board if they need help to solve. They can also use their fingers to count up as they add.

Struggling Learners

Act out story problems. For example, in Try it Together, grab 3 linking cubes to be the cars. Act out 2 “cars” driving on the road. Then have the student drive 1 “car” with the other 2. Ask the students: What is happening with the cars? [another car is joining the first 2] How many cars started on the road? [2] How many cars joined? [1] How many cars are there in all? [3] My number sentence is 2 + 1 = 3. Repeat for as many problems as necessary.

Early Finishers

Students continue to play the domino activity with a timer. They race to see how many number sentences they can write before their timer runs out. Have them switch bags with a neighbor.

Challenge and Explore

Write the following story problem on the board and read it aloud: Joe has 2 fish. He goes to the store and buys some more. Now he has 4 fish in all.

Guiding Questions:

1. What parts of number sentence do we know? [we know the start, and we know how many fish he has in the end] 2. What part do we need to know? [how many fish he bought]

3. How can we solve this? [answers will vary: start at 2 and count up to 4, draw a picture to see what is missing, etc.]

4. How many fish did Joe buy? [2]

Assess

Write the following word problem on the board and read it aloud:

Andy has 2 apples. He buys 2 more apples. How many apples does he have in all?

Have students draw a picture, write the number sentence, and solve for the sum on a piece of paper.

Common Errors

Students may write the addends in the wrong spots in the number sentence. Go step by step with students to make sure the words match up with the numbers.

Chapter 6

In Chapter 6, we will develop fluency in addition by utilizing tools like five frames, number lines, and counting on to solve up to 5.

• Understand and identify the terms addend and sum in addition problems

• Use the five frame to find sums

• Learn about the number line as a tool to put numbers in order and help in counting

• Practice the strategy of counting on to find sums

• Solve story problems that describe a real-life scenario where addition needs to be applied

• Recognize and learn vertical notation for addition

+ 3 2 5

Level K Chapter 6-1

Objective and Learning Goals

y Students will use a five frame to find sums.

y Students will find sums through 5.

Vocabulary

y Addend - the numbers that are added together in an addition sentence

y Sum - the answer to an addition problem.

Materials

y Blank five frame

y Beans, pennies, or cubes for Struggling Learners

y Blank ten frame for Challenge and Explore

Pre-Lesson Warm-up Guiding Questions

The teacher should hand out a blank five frame to each student as well as 5 pennies, beans, or cubes. Make sure the object you use fits inside each square on the five frame. Review how to use the five frame. Write the number “2” on the board and tell students to put that many pennies in their frame. Count with students the number of pennies in their frame. Remind students to put their finger on each penny as it’s counted. Have students take the 2 pennies out. Now write the number “5” on the board. Walk around to make sure students are putting 5 pennies correctly in their five frames. Depending on your class, you could continue this work by having students place 0, 1, 3, or 4 pennies in their frame.

Guiding Questions

1. How many pennies are placed in each square of the five frame? [one]

2. How does the five frame make it easier to count objects? [Answers will vary but could include it’s easier because all the pennies are in a line. Students might also say that the five frame separates the objects.]

Introduce the Lesson (Try it Together)

Look at Let’s Learn with students. First, have students look at the addition sentence. Explain that the first addend or number being added is 3. Have students look at the five frame and count the 3 pennies that are there. Now, look at the second addend, or number being added a one. Tell students to trace the circle in the five frame. The circle is the same as a penny. To find the sum, or answer, all we have to do is count how many are in the five frame. Tell students to point to each penny or circle and count each together as a class. Now, trace the total from the five frame after the equal sign to complete the addition sentence.

Activities

Repeat the same process with the problems in Try it Together. On the next Try it Together problems, remind students that the first addend, or first number in the addition problem, is shown in pennies. The second number is shown in dotted circles.

Struggling Learners

Give struggling learners a blank five frame and beans, pennies, or cubes. Students can use them to fill the five frame for each addition sentence.

Early Finishers

Students who finish early can work with a partner to practice using a five frame. One partner can say or write a problem on a white board. The other partner should show and solve the problem using pennies, beans, cubes, or counters in the five frame. Then partners can switch roles.

Challenge and Explore

Give students an addition sentence, such as 4 + 3. Have students try to use a five frame to solve the sentence. When students find that there aren’t enough spaces, ask them how they think they could solve the problem. Students may suggest adding spaces to the five frame or not using the five frame and counting on a number line. Students may also suggest collecting 4 of an object and 3 of an object, and then counting how many there are altogether. The teacher can show students a ten frame and explain how it can be used to solve the problem. Give students a few problems to solve using the ten frame.

Assess

Write each of the addition problems shown below on the board one at a time. Ask students to show the problems in their five frame. You could either have students show the problems using a manipulative or have students draw circles in the five frame. Have students write the sums to the addition problems next to the five frame.

3 + 2= [5]

4 + 0 = [4]

1 + 2 = [3]

2 + 2 = [4]

Common Errors

Students may forget to count the circles they drew with the pennies that were there. Remind students to count everything in the five frame. Some students may miscount. Remind students to point to each penny/circle in the five frame when counting.

Level K Chapter 6-2

Objective and Learning Goals

y Identify parts of a number line.

y Use number lines to add.

Vocabulary

y Number line - helps put numbers in order; a tool to help in counting

Materials

y Stacking cubes in 2 colors/5 per student (Pre-Lesson)

y Image of number line path (Pre-Lesson)

y Plastic counters/15 per student (Try It Together)

y Sticky notes (Struggling Learners)

y Anchor chart (Struggling Learners)

y Cup of beans (Early Finishers)

y Image of number line 0-10 (Early Finishers)

y Paper (Early Finishers)

Pre-Lesson Warm-up Guiding Questions

Day 1 of 2: Provide each student with 5 stacking cubes, 2 red and 3 blue. Place them in one pile. Tell students to build 2 towers, one red and one blue. Compare the 2 towers. Which is taller and which is shorter? Connect the 2 towers in a horizontal fashion. Students can now see the colors are still separate units or cubes but still see how the colors are grouped and which is longer or shorter. Count the cubes up and reinforce that there are 5. How could you write this using addition? [2+3=5] Draw the model on the whiteboard, showing 2 red plus 3 blue equals 5 cubes in all. Next, provide each student with a number path like the image below. What do they notice about the number path? Make sure the number path is large enough that the cubes can match up to the boxes on it to show one to one correspondence. Using the same cubes, break up the horizontal tower and have students place one cube on 1. Place another cube on 2. How many cubes are on the path now? [2] Place one cube on 3. How many cubes are on the path? [3] Say, “Now that we have 3 cubes on the path, let’s add 1 more cube. How many cubes are on the path now?” [4] “Yes, 3+1=4.” Add a 5th cube to the number path. Ask students to create a new number sentence. [4+1=5] Show students that each number on the path is placed directly and equally spaced from the next number. Remove all cubes from the number path.

Guiding Questions

1. What number is first on the number path? [0] 2. What number comes after 2? [3]

3. What number is before 5? [4]

Make a blank number path on the whiteboard with empty boxes. Ask students to come up and fill in what number should be in each box.

0 1 2 3 4 5

Number Path

Introduce the Lesson (Try it Together)

Day 2 of 2: In the Let’s Learn section, discuss how number paths look similar to number lines. A number line helps us count. Look at the number line, discuss what is seen (tick marks, even spacing, arrows, numbers in order, etc.), and then count the numbers while tracing. In the next section, count aloud the numbers and fill in the box of what number is missing. Note that 0 starts the number line, and 5 ends the number line. In the Try it Together, match the missing number on the number line to the numbers in the right margin. Fill in the empty number line with numbers and follow the microphone cues. Once completed, provide students with counters. Model 0 counters under 0, 1 counter under 1, 2 counters under 2, etc, to show the numbers on line represent amounts.

Struggling Learners

Make a large number line on an anchor chart or white board showing tick marks but missing the numbers. Provide struggling learners with sticky notes with missing numbers (0-5). Have students place sticky notes in order on the number line. Print out a large picture of a frog to use with students. Ask students: What number does our number line start with? [0] Place the frog on 0. If I made one “hop” from 0, what number would I land on? [1] Model a hop with the frog. If I made 2 hops from 0, what number would I land on? [2] Model 2 hops from 0. If I started at 1 and made 3 hops, what number would I land on? [4]

Early Finishers

Provide students with a pre-made number line starting at 0 and going up to 10. Affix the number line to white paper. Give each student a cup of beans and glue. Have students glue the beans underneath each of the numbers on the number line. So, under 0, there will be no beans. Under 1, there will be 1 bean. Under 2, there will be 2 beans glued one underneath each other. Go all the way up to 10.

Challenge and Explore

Read the story problem. Jim has 2 apples. He buys 2 more apples. How many apples does Jim have in all? Draw a number line and show how to solve the story problem. Circle the number of apples Jim has in the beginning. Show the number of hops to add more apples. Put a box around the number you land on.

Ask Students

1. What number did you start on? [2]

2. How many hops did you make? [2]

3. What number did you land on? [4]

4. So, what addition sentence can you write from looking at this number line? [2+2=4]

Assess

Pass out a piece of paper with a number line drawn, leaving out the tick marks and the numbers 0 - 5. Ask students to draw in the tick marks and missing numbers. Use this number line to answer the following questions.

1. If you start on 1 and make 1 hop, what number will you land on? [2]

2. If you start at 0 and add 3 hops, what number will you land on? [3]

Common Errors

Students may want to always start at 0 on the number line. Students may also not understand that numbers on a number line represent a concrete amount.

Level K Chapter 6-3

Objective and Learning Goals

y Use the counting on strategy to solve for sums up to 5.

Vocabulary

y Addend - any number added to another number

y Sum - the answer, or result, when adding numbers

Materials

y Chalk or tape

y Die

y Dry-erase boards

y Dry-erase markers

y 5x5 bingo grid/student

y Handful of counters/student

y Paper

y Pencils

Pre-Lesson Warm-up Guiding Questions

Make a hopscotch board on the floor with 6 spaces (labeled 0 to 5), either outside with chalk or inside with tape. Roll the die two times (or roll 2 dice; reroll if dice land on a 6). Students write the addition sentence on their dry-erase boards. Choose a student to jump the sum on the hopscotch board. Repeat so all students get a chance to jump on the hopscotch board.

Guiding Questions

1. How did you solve for the sum?

[Answers may vary. Answers may include: counting on, drawing circles; counting fingers; etc.]

2. Is there a way to check if your sum is correct?

[Yes]

3. If so, how?

[Answers may vary. Answers may include: Drawing again; subtracting from the sum to get the other addend; counting back; etc.]

Introduce the Lesson (Try it Together)

Introduce the counting on strategy for solving addition problems. Use an octopus picture to illustrate. Initially, there are 3 octopuses. Ask students to keep “3” in mind while counting the rest, leading to a total of 5. Emphasize that fingers can also be used to count on, exemplified by 4+1. Keep “4” in mind, count up “1” on the fingers, resulting in 5.

Activity

Practice counting on with more examples. For an activity, distribute 5x5 bingo grids and counters. Students randomly fill grids with numbers 0-5. Play Addition Bingo by writing addition problems on the board. Students solve and mark the answer on their grid. The game continues until a student gets 5 sums in a row.

4 5 5

Apply and Develop Skills (Practice)

Continue working through the rest of the Try it Together and independent practice. Remind students to count up in order to add quickly. If necessary, students can draw pictures to help.

Struggling Learners

For struggling learners, allow students to have a dry-erase board and marker to draw out their problems for the Addition Bingo activity, Try it Together, and independent practice. Tell students to draw circles for each addend and then count on to find the sum.

Early Finishers

Students can play bingo by themselves by using a die for their addition problems. Tell students to roll the die two times. Write these two numbers on a dry-erase board and find the sum. Then put the counter on the sum on the bingo grid.

Challenge and Explore

Write the problem on the board and have students tell you the addends.

Ask students: Are there only two addends that equal 5? [No] How did you find the addends? [Answers may vary. Answers may include: counted on; used my fingers; etc.]

Assess

Write the following problems on a piece of paper for each student, and have students solve for the

Common Errors

Students may count from zero each time instead of counting up from the first addend. Students may lose track of their counting. Make sure students keep track of the second addend either with a picture or fingers.

Level K Chapter 6-4

Objective and Learning Goals

y Solve addition story problems with sums up to 5 using vertical addition and the counting up method.

y Draw pictures to solve addition story problems.

y Write the correlating addition sentence for story problems.

Vocabulary

y Story problems - word problems or problems that use stories to indicate mathematical application and thinking

Materials

y Pretend apples or pictures of apples (Pre-Lesson)

y Pretend apples, bananas, milk jugs (Activities)

y Dry-erase boards

y Dry-erase markers

y Shopping bags (Pre-Lesson and Activities)

y Counters, beans, or linking cubes (Struggling Learners)

y Linking cubes (Struggling Learners)

y Note cards (Early Finishers)

Pre-Lesson Warm-up Guiding Questions

Gather 5 apples or cut out 5 paper apples. Write the following story problem on the whiteboard or anchor chart: Jim has 2 apples. He buys 3 more. How many apples does he have in all? Pretend to be at the grocery store. One student can be Jim. Have a student take a shopping bag and pretend to be shopping for apples. Ask all of the students: How many apples does Jim need to put in his bag first? [2] The student should take 2 apples and place them in his bag. Ask all students: How many apples does Jim need to buy? [3] The student then takes 3 more apples. Ask all the students: How many apples does the student have in his bag? [5] Have another student be the cashier and have Jim take the apples out of the bag. Count as a class as the apples are removed. (1…2…3...4…5)

Guiding Questions

1. To find out how many apples Jim bought, did you add or subtract? How do you know? [Add, because Jim got more.]

2. What would the addition sentence be? [2+3=5]

Remind students that when we write a number sentence like this, we call it a horizontal math problem. Horizontal means going side to side. Today we are going to learn about solving vertical math problems. Vertical means going up and down. Write the problem above in vertical format to show the difference.

Introduce the Lesson (Try it Together)

Read the word problem in the Let’s Learn. Tell students to circle the two amounts of ice cream. What are the 2 addends in the story problem? [2 and 1] Show students that 2 addends can be written vertically and mean the same as horizontal addition. Show students that the equal sign line means the same as the = symbol. Trace the addends. Introduce the counting up strategy. Find the larger number first. Circle it. Then start counting up from that number only counting the number of times noted in the second addend. Use your fingers to help or use a number line. In Try it Together, have students circle the addends, draw circles, and solve by counting up from the higher number.

Activities

Students will act out story problems as you read. Place out in front of the classroom five of each: apples, bananas, milk jugs. This is a pretend grocery store. Supply students with shopping bags. You read the story problem. One student will act out the story problem while the remainder of the class will write addition sentence on their dry-erase boards. Example: Tim gets 3 apples. He gets 1 more. How many does he have?

Draw a line to match. Write how many.

Joe has 5 He gets 0 more . How many does he have in all?

1 is running. 1 more starts running, too. How many are running?

2 sprouted yesterday. 3 more grew today. How many are there altogether?

Draw a picture. Write how many.

Jim gets 3 Sam gives him 2 more How many does Jim have now?

There are 2 at the zoo. 2 more come to the zoo. How many are there?

1. Jim gets 3 Sam

Struggling Learners

2. Sammy had 1 and he gets 2 more

How many does Sammy have now?

3. Jack has 1 and he gets 3 more How many does he have altogether?

4. Dan buys 1 and his friend gives him

James read 1 book.

He read 2 more.

How many books did James read?

4 birds were in the nest.

1 more bird flew in the nest.

How many birds were in the nest?

Matt had no pencils.

How

Use beans or counters to act out each of the story problems as the students read. For example, in number 1 for Try it Together, students will get 3 counters and then 2 more. Then have students count them in all. After using the counters, have students draw their counters and write the vertical addition sentence. The teacher can model the counting up strategy using linking cubes by starting with the larger addend of 3 cubes and then adding 2 more cubes to make 5.

Early Finishers

Students can act as the teacher and write their own addition story problems with sums up to 5 on note cards. The front side is the story problem, and the back side is room for the vertical addition sentence. Then, trade the story problems with other early finishers, solve, and return back to the original writer of the story problems to check the answers.

Challenge and Explore

Write the story problem on the whiteboard and solve with students. Jerry has no food. He went to the store and did not buy any food because he had no money. How much food does Jerry have? Have students solve on their own dry-erase boards.

Ask Students

1. How much food does Jerry have? [none]

2. What would the addition sentence look like for this story problem? [0+0=0]

3. Why are the addends both 0?

[ Jerry had nothing and bought nothing. Nothing is the same as 0.]

Assess

Have students write their own addition story problem with sums up to 5. Provide a drawing and show the vertical addition sentence with the solution.

Common Errors

Students may want to subtract instead of add. Make sure students record the sum in the correct place. When teaching the counting up strategy, students may want to start at 0 even if the addend is not a 0. Start at the higher addend first and then add the next addend.

Chapter 7

In Chapter 7, we will learn to subtract using pictures, five frames, and number lines.

• Understand that subtraction means to count down or take away

• Understand that the answer to a subtraction problem is called a difference

• Cross out pictures to find the difference

• Use a five frame to find differences

• Count down on a number line to find the difference

• Solve story problems using subtraction

Vocabulary Words

Level K Chapter 7-1

Objective and Learning Goals

y Subtract by counting down from a given number, specifically focusing on the numbers 0-5.

Vocabulary

y Subtract - to take an amount away from a starting amount

y Count down - a method of subtraction where you start with a number and count down to find the difference

y Difference - the result of subtracting one number from another

Materials

y Sticky notes

y Chart paper

y Marker

y Beach ball

y Dry-erase board

y Dry-erase marker

y Bears or beans

Pre-Lesson Warm-up Guiding Questions

Put 3 sticky notes on an anchor chart. Ask students: How many sticky notes did I start with? [3] Now, take off 1 sticky note. Write the number 3 on the chart paper. Ask students: What did I do? [took away a sticky note] Write a minus sign next to the 3. Ask students: How many did I take away? [1] Write a 1 next to the minus sign (3-1). Ask students: How many sticky notes are left on the chart paper? [2] Write an equal sign and a 2 next to the subtraction sentence (3-1). Show students that they just solved the subtraction sentence 3-1=2 (point to the problem while solving it). Repeat by starting with 4 sticky notes and taking away 3.

Guiding Questions

1. What does it mean to subtract? [to take away]

2. How do we know how many to start with? [the first number, or the whole number, tells us how many to start with]

3. How do we know how many sticky notes to take away? [the second number tells us how many to take away]

Introduce the Lesson (Try it Together)

We’ll use pictures for subtraction. In an example with cookies, Flash starts with 5 and crosses off 3. Students physically cross off the 3 cookies, signifying subtraction, leaving 2 cookies.

Students then trace the number 2 for the difference and continue this with more examples. Remind them to use circles to represent numbers and cross off circles for subtraction.

Activity

In the activity, a beach ball with subtraction problems is used. Students stand in a circle and toss the ball. The catcher solves the problem closest to their right thumb, continuing until all students have a turn.

1 1 1 2 0

Struggling Learners

Give struggling students bear counters or beans to physically take away for each subtraction sentence. Tell the students to put out bears or beans for the starting number. Then, tell students to take away bears or beans for the second number in the subtraction sentence. Finally, tell students to count how many bears or beans are left over.

Early Finishers

Pass out a 5 grid (like below) to students with numbers 1 to 5 written at the bottom of each column. Students roll a die two times, subtract the two numbers, find the difference on their grid and color above the difference. For example, if the student rolls a 4 and a 3, they subtract 4-3 and color in directly above the 1. Students keep rolling and subtracting. The first student to get all the spaces colored in to the top of the column wins.

Challenge and Explore

Read the word problem to students and tell them to solve for the difference.

Tim has 4 bananas. He eats 1 banana. How many bananas does he have left?

Ask Students

1. What does it mean to subtract something? [To ‘subtract’ something means to take it away from a group or a total]

2. How can we subtract numbers by counting down from a given number? [starting from the larger number and then counting backward as many times as the smaller number]

Assess

Pass out a paper with the subtraction sentences 5-1=__ [4], 4-2=___ [2], and 3-3=___ [0]. Tell students to draw circles and write the difference for each subtraction sentence.

Common Errors

Students may draw circles for both numbers instead of crossing off circles for the second number in the subtraction sentence.

Level K Chapter 7-2

Objective and Learning Goals

y Use a five frame to subtract.

Vocabulary

y Difference - the answer to a subtraction problem

Materials

y Manipulatives (pennies, counters, cubes) for Struggling Learners

y For Early Finishers, prepare sets of subtraction problems on index cards. Prepare index cards with one subtraction problem on each card. Put the subtraction problem on the front of the card and the difference on the back.

y Sheet of 10 frames and a crayon for Challenge and Explore

y Sheet of blank five frames for Assess

Pre-Lesson Warm-up Guiding Questions

Hold up 5 crayons. Walk around and give a student 2 crayons. Ask, “How many crayons do I have left? [3] Now, have the student give the crayons back. Repeat the same process as before but this time give a student 4 crayons. Now, how many crayons do I have left? [1]

Guiding Questions

1. What happened to the number of crayons I had when I gave them away? [Answers will vary but should include that I had fewer crayons or I didn’t have as many crayons.]

2. How many crayons would I have if I gave 5 crayons away? [I’d have 0 crayons because I gave them all away.]

Introduce the Lesson (Try it Together)

Tell students that today we are going to practice our subtraction using a five frame. Show a blank five frame and ask if students remember using a five frame for addition. Ask a student to explain how a five frame was used for addition. [Students should say something like we drew circles in the five frame to show the addends. Then we counted the circles we drew to find the sum or answer.]

Look at the Let’s Learn. Have students point to each penny in the five frame as you count aloud as a class. Now ask, “How many pennies are there?” [4] Now, let’s take away 3 pennies. Have students take their pencils and trace the dotted lines to cross out 3 of the pennies. Ask, “How many pennies are left?” [1] Now, connect the total number of pennies in the five frame to the 4 in the subtraction sentence and the number of pennies crossed out to the 3 in the subtraction sentence. Students should then trace the 1 to show how many pennies are left.

Repeat the same process for at least the first two problems in Try it Together. It’s important for students to recognize that the first number in a subtraction sentence represents the total amount you have. The second number tells what you’re taking away or what is being subtracted.

Activity

As you move through the practice activities, students will be asked to draw circles in the five frame to represent the total. The teacher may need to model a problem or two before students can fill in the five frame independently.

2 2 1 0 1 1 0 4

Struggling Learners

Struggling learners may need a manipulative (pennies, counters, cubes) to show each subtraction sentence. Struggling learners may need to be reminded that the first number in the subtraction sentence represents the total, what you’re starting with.

Early FInishers

Prepare index cards with one subtraction problem on each card. Put the subtraction problem on the front of the card and the difference on the back. Have students work with partners. Give each partner 5 pennies and the group one set of index cards. One student chooses a problem and puts it so both partners can see. Each partner uses the manipulatives to show the problem and find the difference. Once both students have found the difference, students can check the back of the card to see if they were correct.

Challenge and Explore

Give each student a ten frame and a crayon. Show students the problem 8 - 2. Ask students to try and show that problem in the ten frame. After giving students a minute or two to try, show students how to solve the problem. In your modeling, be sure to fill the top 5 frame with circles before filling in any circles on the bottom 5 frame. Show students how to cross out 2 circles. Count together the circles that are left. [6]

Now, give students additional problems to try: 10 - 6 = [4] 9 - 4 = [5]

Assess

Give students some blank five frames and a crayon. Put the following problems on the board one at a time. Ask students to show the problem in their five frame and solve. Walk around while students are working to assess understanding.

5 - 2 = [3]

4 - 1 = [3] 3 - 3 = [0]

Common Errors

Students may count what is crossed out as their answer, or difference. These students may need to be reminded that what they are crossing off they no longer have. Students may add in what is being subtracted instead of crossing off. Remind students that the first number is our total, and then we take away, or cross off, the second number.

Level K Chapter 7-3

Objective and Learning Goals

y Represent subtraction problems using a number line.

y Demonstrate how to correctly count backwards on a number line.

Vocabulary

y Subtract - to take an amount away from a starting amount

y Number line - helps put numbers in order; a tool to help in counting

Materials

y Chalk, dry-erase markers, or masking tape

y Large whiteboard for display

y Number flashcards

y Printed frog image

y Small whiteboards for students

y Pencil

y Colors

Pre-Lesson Warm-up Guiding Questions

Start with a number line drawn with chalk outside or tape/ dry-erase markers in the classroom. Ask for a volunteer to follow your instructions. Ask the student to start on the 4 and to move two steps backwards. Ask the volunteer and the class what number the student is on now. While the activity is taking place, write the subtraction problem on the whiteboard. Repeat with at least 2 or 3 more volunteers.

Guiding Questions

1. How is this similar to what we did in our last lesson? [both include taking something away; ending with a lower number; etc.]

2. When you’re hopping back, how do you know it’s subtraction? [you’re ending at a lower number]

3. Why do we hop to each number instead of skipping? [to track the numbers we’ve counted]

Introduce the Lesson (Try it Together)

Tell students to look at the number line on the Let’s Learn page. Tell them we will learn to subtract using a number line. The number line is the same one used in addition, but we will hop backward instead of forward. Tell students to circle the first number in the subtraction problem. Tell students to trace the “hop” lines, and ask them what number they finish on. Tell them that number is their final answer.

Activity

Distribute individual number lines for students to use, or tape them to their tables or desks. Also distribute a small printed frog. Allow students to name or decorate their frogs. Tell them that their frog will help them hop to each number to subtract. Using a modified deck of cards (A-5) or number flashcards, have students flip over two cards. Start with the larger number, and ask students to write it down on their whiteboard. Complete the subtraction sentence with the other number. Have students use their frogs to count back on the number line and complete the subtraction sentence.

Struggling Learners

Have students solve the problems from the Let’s Learn page on their own number line and ask them to compare their answers. If they get it incorrect, ask them why their answer is different than Flash’s. For continued support, have them use their frog and number line for the independent practice pages.

Early FInishers

Allow students to continue playing the deck of cards and frog activity game on their number line. Students can also use a timer to see how quickly they can finish solving 10 problems with their frog and number line.

Challenge and Explore

Have students roll a die until it lands on 6. Then roll the die one more time. Use the 6 and the next number they roll to write a subtraction sentence. Ask students if they can still use their number lines to help them solve this problem.

1. How would they have to change the number line to do this? [add a six after five]

2. Can you still solve this problem like we did with the others? [yes!]

Proceed to solve the problem by hopping to random numbers at various intervals (e.g, 6-3 looks like 6 to 4 to 3 to 1).

1. I took 3 hops. Is the answer correct? Why or why not? [no, you must hop to the number right next to the one you started on]

Assess

As a class or in groups, show the students a subtraction problem, such as 5 - 3. Demonstrate an incorrect way to solve and write the incorrect answer on the board. Ask students to give a thumbs up or thumbs down if they agree or disagree with the answer. Ask them to explain why it was wrong and write the correct answer on their whiteboards.

Common Errors

Students may go the wrong direction on the number line. Remind them to move toward the smaller numbers (left, toward 1, away from 5). Students may skip numbers instead of counting each one.

Level K Chapter 7-4

Objective and Learning Goals

y Solve subtraction story problems with differences up to 5.

y Draw pictures to solve subtraction story problems.

y Write the correlating subtraction sentence for a story problem.

Vocabulary

y Story problems - word problems or problems that use stories to indicate mathematical application and thinking

y Subtraction sentence - numbers, minus sign, and equal sign used together to show subtraction

Materials

y Pretend cookies or pictures of cookies

y Mixing bowl

y Baking tray

y Counters or beans

Pre-Lesson Warm-up Guiding Questions

Use a mixing bowl, baking sheet, spoon, and 5 pretend cookies or cut out 5 cookies from construction paper. Write the word problem on the board or an anchor chart: Bill bakes 5 cookies. He gives away 2 cookies to his friend Jim. How many cookies does Bill have left?

Tell students you will call up a student to act out the word problem and pretend to give away cookies. Call on one student to be Bill. Have the student come up and pretend to bake the cookies by stirring the bowl. Ask all students: How many cookies does Bill bake? [5] Tell the student (Bill) to put 5 cookies on a baking sheet. Ask students: How many cookies does Bill give to his friend? [2] Tell the student to give you (Jim) 2 cookies. Count, as a class, how many cookies are left on the tray (1…2…3) Ask students: How many does Bill have left? [3]

Guiding Questions

1. To find out how many cookies Bill had left, did you add or subtract? How did you know? [subtract because he gave them away and had less left over]

2. What would the subtraction sentence be for this word problem?

[5-2=3]

Introduce the Lesson (Try it Together)

Read through the Teacher Notes on the Let’s Learn student page to support students through understanding story problems. Focus on circling the important information and drawing pictures to represent the problem. Students may use circles to represent the numbers. They do not need to draw the exact picture.

Move to the Try it Together section. Continue to read the problems aloud. Circle the important information and draw pictures to represent the number sentence before writing it. On the last page, prepare students for a dictation sentence to solve using subtraction.

Apply and Develop Skills (Practice)

Guide students through the practice pages. In the first part, students will match the story problem to the vertical sentence. Encourage students to circle the important information to help them solve. In the bottom problem, students will draw a picture to model the problem. On the last page, read and solve the subtraction sentence. Then students will listen, draw, write a story problem, and solve it.

Struggling Learners

Allow struggling learners to use counters or beans to act out each word problem. For example, in the first practice problem, have students set out 2 beans for the flowers. Then take 1 way. Count how many are left. Draw a line to the subtraction sentence that shows 2 - 1 = 1. Continue with the next problem.

Early Finishers

Students can make up and solve their own story problems with a partner. Give partners counters or beans to use as props for their story problems. Encourage students to act out the problems as they say them.

Challenge and Explore

Write the following story problem on the board and solve it with students.

Jerry has 5 coins. He loses some. Now he has 3 coins. How many coins did Jerry lose?

Ask students: How many coins did Jerry start with? [5] How many did he have at the end? [3] What do we need to find out? [How many he lost]

Write the subtraction sentence showing all the parts as students solve.

Assess

Have students write or say their own story problem with differences up to 5. Write the subtraction sentence and solve.

Common Errors

Students may add instead of subtract. Be mindful that students are crossing out on their pictures and counting what is left.

Chapter 8

In Chapter 8, we will learn to recognize and write ordinal numbers, identify parts of a calendar, and tell time to the hour and half hour.

• Describe the position of an object using ordinal numbers

• Write ordinal numbers using words and numbers

• Use a calendar to identify days of the week, dates, and months

• Order the days of the week

• Tell time to the hour on an analog clock

• Write the time on a clock using numbers and o’clock

• Write the time on a clock using numbers and the : symbol

Vocabulary Words

Level K Chapter 8-1

Objective and Learning Goals

y Describe the position of an object using ordinal numbers.

y Write ordinal numbers up to fifths using words.

y Write ordinal numbers up to fifths using numbers.

y Recognize ordinal numbers up to tenths.

Vocabulary

y Ordinal numbers - numbers used to show order - first, second, third, etc.

Materials

y Popsicle sticks for student pairs labeled up to 10th/tenth

y 10 note cards: 5 with ordinal numbers, 1-5 in number form, and 5 in word form

y Note cards for early finishers to make a memory game

Pre-Lesson Warm-up Guiding Questions

Bring five students up to the front of the class and stand them in a line. Count the students together: 1, 2, 3, 4, 5. Point to the first person. Say, “We don’t say they are ONE in line. What do we say? [first] Good! Give this student the card that says FIRST. How about the next person? Are they TWO in line?” [second] Give the second person the SECOND card. Keep going until you get to the fifth person. Once done, have students hold up their cards and say the order together as a class. Say: “We put the students in order from first to fifth place. These are called ordinal numbers. We can use numbers, too.” Pass out the cards 1st-5th. Have students hold up the number cards and the word cards. What do you notice? [number cards show the number but have letters after the number, word cards have the same ending as number cards] Circle the endings on the number cards and word cards and repeat saying the ordinal numbers. Then have students mix up their order. Still holding their cards, ask another student to put them back in order. Do this a few times with just numbers and just words.

Guiding Questions

1. How are ordinal numbers the same as numbers we count with? [they use the same digit, they go in order]

2. How are ordinal numbers different? [they have different words or different endings]

3. Where else have you heard or used ordinal numbers? [I got third place, she is first in line, Fourth of July, etc.]

Introduce the Lesson (Try it Together)

Have students point to Glow. Read what Glow is saying. Say “When you are in the front, you are the FIRST PERSON.” Point to the words under Glow and read them together. Then have students point to Flash. Read what Flash says. Say, “Let’s count together from Glow to Flash-1, 2, 3, 4. He is person 4, so he is the 4th person.” Circle the 4th/fourth under Flash. You may also ask students to point the SECOND person or the FIFTH person. Then move to the caps. Which cap is THIRD? Circle the 3rd cap. What color is the third cap? Move to the Try it Together section and read the microphone instructions.

Activity

Make the popsicle sticks in advance. With the stick horizontal, write 1st on the left side and FIRST on the right side. Continue through 10th/TENTH. Make enough for one set per pair or group of three. Pass out the sticks to student groups and have them put the sticks in order. Have them practice saying the ordinal numbers out loud.

2nd 4th 1st 3rd

Apply and Develop Skills (Practice)

Have students trace the ordinal numbers, then color in the corresponding shape in that place. Read the instructions to students. On the second page, have students trace the ordinal words. Then draw lines from the hippos to the correct word based on each hippo’s place. Remind students to look at the number on the hippo to give them clues.

Struggling Learners

Give students the popsicle sticks 1st-5th. Have them put the sticks in order and then practice saying the order. Line up different objects next to the sticks. Ask students to tell you what place they are in. Use the sticks to help reference. Students can also place the sticks on their math pages to help them find the order.

Early Finishers

Students can practice writing the ordinal numbers and words on separate note cards. With a partner, they can play memory. Mix up the cards and place them face down. One student turns over 2 cards, trying to match up the ordinal number with the ordinal word. If they match, the student can go again. If not, turn the cards back over, and the next student has a turn.

Challenge and Explore

As a class, practice putting different things in order. Start with the alphabet. Have students write the first 5-10 letters. Ask them, “What is the SECOND letter of the alphabet? [B] What is the NINTH letter of the alphabet?” [I] Then move to the days of the week. You can do just school days (Mon-Fri) or all days (Sun-Sat). Ask students which day is the THIRD day [Wed/Tues] Continue having students look around the classroom for objects they can put in order. For an extra challenge, you can try the months of the year.

Assess

Put out 5 different objects on a table. Ask students to tell you what the 4th object is. Then have them tell you where a specific object is. Be sure they say the ordinal number.

Common Errors

Students may mispronounce ordinal numbers. They may say twoth, threeth, fiveth. Be sure to practice saying ordinal numbers. When writing in number form, most will have the “th” ending. Be mindful that FIRST, SECOND, and THIRD are 1st, 2nd, 3rd, not 1th, 2th, 3th.

Level K Chapter 8-2

Objective and Learning Goals

y Identify day, date, and month on a calendar.

y Order the days of the week.

y Identify the date of specific activities.

Vocabulary

y Day - 24 hours; there are 7 days in a week

y Date - a specific day on the calendar; month/day/year to represent that point in time

y Week - a group of 7 days; there are 52 weeks in a year

y Month - a group of 28-31 days; there a 12 months in a year

y Calendar - tells time by giving month, day, and year; a chart or system that organizes days, weeks, months, and year

Materials

y Variety of calendar pages for students to look at

y Print out of a calendar page for each student’s birthday month and lists of students’ birthdays

y Print out a calendar page of the current month for early finishers

y Page of days of the week for students to cut out

y Columns labeled 1st-7th

y Scissors, glue

Pre-Lesson Warm-up Guiding Questions

Take out a calendar and read through the months of the year together, starting with January. Say, “January is the first month of the year; it has 31 days.” Then read through the full year. Students may be familiar with all of the months of the year. Practice together the months of the year throughout the school year. Make groups of 3 students. Give each group 2-3 calendar pages. Have them look at the pages for a few minutes and tell each other what they see. Gather ideas from the class. It is okay if they can’t read the words. Encourage them to notice that something is written at the top. There are numbers to look at, the numbers on the calendars aren’t in the same places, etc. Once they have had time to look at the pages and discuss, tell them that they are looking at calendar pages. Point out the classroom calendar. What does a calendar tell us? It tells us the day, the month, and maybe the year. A calendar helps us keep track of time.

Guiding Questions

1. What do you notice about the calendar pages you looked at? [answers will vary]

2. How does a calendar help us keep track of time? [it tells us the month, day of the week, and date]

Introduce the Lesson (Try it Together)

In the Let’s Learn section, guide students through the parts of the calendar using the Teacher Notes at the bottom of the student page. Allow students to ask questions about the calendar. Discuss the difference between the day (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday) and the date (Tuesday, May 1). Give examples of the written date on the board, and have students repeat saying the date. In the Try it Together section, guide students through the instructions. They will trace and say the month, fill in the missing dates, circle specific dates, and say the date in which a specific activity happens. Have students practice saying the dates and seeing them written. For example: The last day of April is Monday, April thirtieth.

Activity

Pass out a list of the days of the week for students to cut out and a column page with columns listed 1st-7th. With a partner, have students say the names of the days and then order them from Sunday to Saturday. Glue the days in the correct column.

Apply and Develop Skills (Practice)

Guide students in filling out the missing information and ask them prompted questions. On the second page, remind them to look back at the calendar and look for clues to help them answer the questions.

Struggling Learners

Give students time to explore a real calendar. Have them point to the month and days of the week. Guide them to find the first and last days of each month. Practice pointing to the days of the week at the top. Count out the numbers on the calendar and point to them. Cover up one of the numbers and guide students to count up to it to find the correct number.

Early Finishers

Pass out a printable of the current month. Students will create a calendar with a schedule about their life. They can draw pictures on the days they have activities at school and/or personal activities. Have them share their calendar with a classmate.

Challenge and Explore

Group students by birthday month. Give each group a calendar page of that month and a list of the birthdays in their group. Students will find their birthday and write their name. If a student can’t remember it, refer them to the birthday list. Once groups are complete, call up each group one month at a time starting, with January. Say, “January is the 1st month of the year.” Tape up the January calendar. Each student will say their birthdate. Write out the sentence starter: My birthday is on (day), (month), (date). If no students have a birthday in a certain month, still hang up the calendar page and say, “No one has a birthday in (month).”

Ask Students

1. Which month of the year is 1st? 3rd? Last? [January, March, December]

2. Whose birthday is the 2nd in the month of (month)? [answer will vary–show how to find the second birthday of said month]

Assess

Students look at a calendar of the current month. Ask them to point to the name of the month and say the month if they can read. Ask them to point to the 4th day of the month. What day of the week is the 4th day on? Students may point to the correct day if they cannot read the word.

Common Errors

Students may mix up days of the week and days of the month. Remind students that days of the week go from Sunday to Saturday. Sunday is the 1st day, and Saturday is the 7th day. Days of the month vary from month to month. Look at the different calendar examples. Point out that the 1st day of each month is on a different day of the week.

Level K Chapter 8-3

Objective and Learning Goals

y Tell time to the hour on an analog clock.

y Write the hour with o’clock and :00.

y Recognize the hour on a number line.

Vocabulary

y O’clock - what we say after the numbers when telling time to the hour

y Hour hand - the short hand on the clock that points to the hour

y Minute hand - the long hand on the clock that points to the minute

Materials

y Chart paper with analog clock and 1-12 number line on it

y Demonstration clocks for student pairs

y Number lines to 12

y Large number cards 1-12

Pre-Lesson Warm-up Guiding Questions

On a piece of chart paper, draw an analog clock and below it a number line from 1-12. Have it ready to show students after the warm up. Bring 3 students to the front and have them stand next to each other. Give them the number cards 1, 2, and 3. Ask students: What comes next? [4] And then? [5] Continue to have students come up to join the line and take a number card until you get to 12. Ask: What does this look like? [a number line] “We could keep going with this line, right? But look what happens if we make this line into a circle.” Keeping in order, have students form a circle, so number 12 ends up next to number 1. “Let’s all say our numbers–1, 2, 3…12. What happens when we get to 12?” [we start over at 1] Go around the circle a few times saying the numbers out loud. Say: We can use a number line to help us tell time. A clock is a number line that is in a circle. Point out the chart paper with the number line and clock on in. Point to number 3 on the number line. Have a student come up and point to the 3 on the clock.

Guiding Questions

1. How are a clock and a number line the same? [they count numbers in order starting at 1]

2. How are clocks and number lines different? [a clock is a circle, it goes from 1-12. A number line can keep going.]

Introduce the Lesson (Try it Together)

Introduce the clock to students. Guide students through the parts of the clock using the Teacher Notes in the Let’s Learn section. Then move to Try it Together. “Look at the first clock. Which number is the hour hand pointing to? [4] Read with me: It is 4 o’clock.” Circle the number 4 on the number line. Move to the second clock. What number is the hour hand pointing to? [8] Trace the 8 and say, It is 8 o’clock. Circle the 8 on the number line. Now look at the last problem. What number is circled on the number line? [2] Trace the hour hand to point to 2. Then trace the 2 on the time. We can also write time in this form: 2, two dots, then two zeroes. It still says 2 o’clock.

Activity

Pass out demonstration clocks to student pairs. After they locate the hour hand, have students practice moving the hour hand to different numbers and saying the time. Have a sentence starter written on the board for students to practice with: It is _____ o’clock.

Apply and Develop Skills (Practice)

Guide students through the practice problems. On the first page, they look at the clock, then circle the number that the hour hand is pointing to on the number line. Then they will write the hour. On the second page, students will look first at the number line to see the circled number and draw the hour hand on the clock face. Then they will write the hour.

Struggling Learners

Give students a demonstration clock and a number line. Move the hour hand to a number on the clock. The student will point to the number on the number line. Have the student say the time. Then the teacher points to a number on the number line. The student will move the hour hand to the number on the clock. Then say the time. Use the sentence starter: It is ____ o’clock.

Early Finishers

With a partner, practice saying the time out loud and then moving the hour hand on the clock. For example, one partner will say: 6 o’clock. The other partner will move the hour hand to the correct time on the clock.

Challenge and Explore

Go on a clock scavenger hunt. Go to different rooms and places around the school and look for analog or digital clocks. On analog clocks, have students point out the hour and minute hands. Challenge them to read the hour. If they find a digital clock, have them read the hour. Look for similarities and differences of the clocks they find.

1. Is it easy or hard to read the hour on some clocks? Why? [answers will vary depending on the clocks they find]

2. How can we tell the difference between the hour and minute hands? [hour hand is short, minute hand is long]

Assess

Circle a number on a number line from 1-12. Have students move the hour hand on a demonstration clock to that same number. Then have them say the time using the sentence starter: It is _____ o’clock.

Common Errors

Students will get the hour hand and minute hand mixed up. On our pages, they are red and blue. Remind students that the shorter, red hand points to the hour. Have them look at other examples of clocks and find the hour hand.

Level K Chapter 8-4

Objective and Learning Goals

y Read the minute hand at the 12 and 6.

y Write the time to the hour and the half hour.

Vocabulary

y Hour hand - the short hand on the clock that points to the hour

y Minute hand - the long hand on the clock that points to the minute

Materials

y Demonstration clocks

y Chart paper with clock and number line from lesson 8-3

y Red hour hand and blue minute hand

y A printout of a clock face and minute/hours hands for students to cut out and make their own clock

y Round fasteners for movable clock hands

Pre-Lesson Warm-up Guiding Questions

Review the chart made yesterday with the clock and telling time with the hour hand. Using a cutout of a red hour hand, point to different times and have students tell the time. Write the time on the board, changing between “o’clock” and “:00.” After a few rounds, introduce the minute hand. Say, “The minute hand is the long hand. When the minute hand is pointing to the 12, we say o’clock. For 3 o’clock, the hour hand is at the 3 and the minute hand is at the 12.” Demonstrate on the chart, using the cutout of the blue minute hand as well. Have students try to place the hands correctly when you call out a time.

Guiding Questions

1. Which hand is the longer hand? [minute hand]

2. The time is 6 o’clock. Where does the hour hand point to? [6]

3. Where does the minute hand point to?[12]

Introduce the Lesson (Try it Together)

Guide students through the Let’s Learn section by reading the Teacher Notes at the bottom of the student page. Remind students that a clock is a circular number line, so it starts over at 12. Move to the Try it Together section. Remind students that the hour can be written using o’clock or :00. Guide students through each time. When you get to number 3, ask students what is different about the minute hand. It is at the 6, not the 12. It is halfway around the clock. The minutes are now at :30 instead of :00. The hour hand is pointing to the 1, and the minute hand is at the 6. The time is one-thirty. Trace the time and say it together.

Activity

Partner up students and give each pair a demonstration clock. Have one student set the time to the hour. Be sure the minute hand is on the 12. Write the sentence frames on the board: The minute hand is on the ____ .

The hour hand is on the _____. What time is it?

The partner will then say the time.

Apply and Develop Skills (Practice)

Guide students through the practice pages. Remind them that the minute hand will either be at the 12 or the 6. When it is at the 12, we write :00 and say “o’clock.” When it is at the 6, we write :30 and say “thirty.”

Struggling Learners

Use demonstration clocks for students to explore time with. Have them make the times shown in their workbook pages and practice saying the time out loud. If the time is written out, practice pointing out the clues that help tell the time. For example, if the time is 4:00, label the hour part and the minute part. Tell students to point to the hour part. Move the hour hand to that number. Now look at the minute part. Where does the minute hand point to if is says: 00? [to the 12] Move the minute hand to the 12. If the minute part says :30? [to the 6] Label the minute hand with an “M” and the hour hand with an “H” for more clarity.

Early Finishers

Do the same activity with a partner, saying where the hands are pointing, but this time, the minute hand can be at the 12 or the 6. Make sure the partner listens closely to know if the minutes are :00 or :30. They can practice writing the digital time.

Challenge and Explore

Pass out the worksheet of the clock face and hands. Have students color and cut out the clock. Fasten the hands with a round fastener so they move. Take students through their day like Glow took them through her day. Say, “What time does school start?” Write the time on the board, and have students move their own clock to the correct time. Do this with different activities throughout the day, using time to the hour or half-hour only.

1. How can we be sure which is the minute hand, and which is the hour hand? [minute hand is long, hour hand is short]

Assess

Write and say the time 10:00. Have students move the hands of the clock to the correct time and say the time. Then write and say 4:30. Have students move the hands of the clock to the correct time and say the time.

Common Errors

Students may get the hour and minute hands mixed up. Remind students that the hour hand is short, and the minute hand is long.

Counting from 0 to 10 with pennies

Counting from 0 to 10 with pennies

In

Chapter 9, we will practice understanding and writing numbers 6 to 10.

• Recognize numbers 6 to 10 in picture, word and number form

• Write numbers 6 to 10

• Count numbers 6 to 10

• Represent a number of objects with numbers 6 to 10

• Assign number values to objects while counting

6 7 8 9 10

Objective and Learning Goals

y Count and write numbers from 0 to 7.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects

Materials

y Anchor charts

y Crayons or markers

y Modeling clay

y Ten frame

y Note cards

Pre-Lesson Warm-up Guiding Questions

Draw a 6 on an anchor chart. Ask students: What are different ways to represent the number 6? [Answers may vary. Answers may include six fingers, six circles, 4+2=6, etc.] Write student responses around the 6 on the anchor chart. Draw a 7 on an anchor chart. Ask students: What are different ways to represent the number 7? [Answers may vary. Answers may include seven fingers, seven circles, 5+2=7, etc.] Write student responses around the 7 on the anchor chart.

On an anchor chart or board draw groups of objects (3 stars, 5 circles, 7 squares, 6 rectangles, 2 triangles). Play “I spy” with number clues. For example, tell students: I spy 7 of something. Students raise their hands to answer (7 squares). Keep playing.

Guiding Questions

1. How do you keep track of your counting? [Answers may vary. Answers may include drawing, pointing, crossing off, etc.]

2. Which is more, 6 or 7? How do you know? [7 because there are more objects when counting]

Introduce the Lesson (Try it Together)

Look at the apples in the Let’s Learn. Show students how to cross out the apples as you count. Count out loud together while counting (1…2…3…4..5..6). How many apples are there? [6] Repeat for the 7 apples.

Now tell students to count the number of apples below and practice writing 6. Notice where to start writing 6 at the top where there is tiny one. Say: “Curve around until it sticks, that is the way to make a 6.” Repeat the rhyme as students write. Next move onto number 7 and say: “Across the sky and slant the line, make a 7 every time.” Now tell students to count and circle the number of birds in number 1 of Try it Together. Tell students to cross out each bird while counting. How many birds are there?[6] Which number is 6? [students point to the 6] Have students circle the 6 and continue counting and circling or writing the numbers 6 and 7.

Activities

Pass out modeling clay. Provide number cards from 1-7. Students pick a card, and make clay balls for each number. Students can play a game with a partner. Pick one card and see who can make the number of clay balls the fastest. Use stickers if clay is not available.

6 7 6 7 6 7

how

7 6 6 7 6 7 4 5 7 6

Apply and Develop Skills (Practice)

Continue working through the rest of the Try it Together and independent practice. Remind students to cross out while counting to keep track.

Struggling Learners

When making clay balls, allow struggling learners to use a ten frame. This will help students to keep track of their counting.

Early Finishers

Pass out 14 note cards. On 7 of the note cards, students write numbers from 1-7. On the other 7 note cards, students draw circles to match each number. Then, students flip over all cards face down. Students flip over 2 cards at a time to find a match.

Challenge and Explore

Go outside and challenge students to find 6 or 7 items in nature. Students put their items in a paper bag and share with the class what they found. Another option is to go on an indoor scavenger hunt. Search the classroom for 6 things yellow. Search the classroom for 7 blue items. Come up with more color groupings as needed.

Have students draw circles for the numbers 6 and 7 on a sticky note. Add their drawings to the anchor charts. Assess

Common Errors

Students may lose track of counting. Students may also draw numbers backwards. This typically occurs with numbers 2, 6 and 7.

Objective and Learning Goals

y Count and write numbers from 0 to 9.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of items

Materials

y Anchor charts

y Dry-erase board

y Dry-erase marker

y 5x5 Bingo grid / student

y Counters or beads

y Number cards (1-9)

Pre-Lesson Warm-up Guiding Questions

Draw an 8 on an anchor chart. Ask students: What are different ways to represent the number 8? [Answers may vary. Answers may include eight fingers, eight circles, 4+4=8, etc.] Write student responses around the 8 on the anchor chart. Ask students: What are different ways to represent the number 9? [Answers may vary. Answers may include nine fingers, nine circles, 5+4=9, etc.] Write student responses around the 9 on the anchor chart.

Call out a number and have students draw that many circles on a dry-erase board. Students switch boards with a partner, or hold up their board to show a partner. Partners count and check that the number of circles matches the number you called out.

Guiding Questions

1. Which number was the easiest to draw? [Answers will vary.]

2. Why are some numbers easier to draw or write than others? [The smaller the number, the easier to draw because there are not as many items to draw.]

Introduce the Lesson (Try it Together)

Look at the apples in Let’s Learn. Show students how to cross out the apples as you count. Count out loud together while counting (1..2..3..4..5..6..7..8). How many apples are there?[8] Practice writing the 8. Tell students the rhyme to help us remember how to make an 8. “Make an “S” but do not wait, race back up to make an eight.” Repeat for the 9 apples. Tell students the rhyme for writing a 9. Say: “Make a circle and then slant the line, that is the way to make a 9.”

Now tell students to count and circle the number of stars in number 1 of Try it Together. Tell students to cross out each star while counting. How many stars are there? [9] Which number is the 9? [students point to the 9] Tell students to circle the 9 and continue on with the rest of Try it Together

Activities

Pass out blank 5x5 bingo grids. Students draw different amounts of circles in each box (no more than 9 circles per box). Tell them that amounts may repeat in more than one box, but they should draw at least one group of each amount 1-9. After students have filled in their grids, write a number on the board. Students find the number of circles for the number called out and cover it with a counter or bead. Keep calling out numbers until a student gets 5 in a row.

Struggling Learners

Struggling learners can use a number line to help when selecting the correct number for Try it Together and independent practice. The number line shows students the numbers in order so they can select the correct number for the amount they count.

Early Finishers

Students can use their bingo boards to play bingo independently. Pass out number cards from 1 to 9. Students pick cards, put a counter or bead on the number of circles, and then continue until they get 5 in a row.

Challenge and Explore

Students collect a number of objects from their desk (from 1 to 9). Students lay these objects on their desk. Then, students stand up and walk around to music. When the music stops, they freeze at another student’s desk. Students count the objects and raise their hand to share how many they counted. Play music again and students find another desk. Keep repeating.

Tell students to draw 8 of one shape and 9 of a different shape on a sticky notes. Add their drawings to the correct anchor charts.

Common Errors

Students may lose track of counting. Students may also write numbers backwards. This typically occurs with numbers 2, 6 and 7. Students may draw a 6 and 9 upside down.

Objective and Learning Goals

y Count, draw and write the number 10.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects

Materials

y Anchor charts

y Dry-erase board

y Dry-erase marker

y Cup

y Counters or beads

y Note cards

y Paper

y Pencil

y Number line

y Dice

y Sticky Notes

Pre-Lesson Warm-up Guiding Questions

Draw a 10 on an anchor chart. Ask students: What are different ways to represent the number 10? [Answers may vary. Answers may include ten fingers, ten circles, 6+4=10; etc.] Write student responses around the 10 on the anchor chart. Collect some beads or counters and a cup. Tell students that you are going to show them a number of beads or counters and they are going to race to call out the number, without counting. Put a number of beads in the cup (from 1-10) and shake it. Do not tell the students how many are in the cup. Show the beads, either by dumping them out into your hand or on a table. Call on students to say the number they see. As they get better at recognizing the amount without counting, you can even dump them and then cover them - so the students have to recall how many without physically counting each one. For example: Take 3 counters and shake them in the cup. Dump them onto the table. Wait 2 seconds, and then cover them with the cup. Repeat with various amounts of beads and counters (from 1 to 10).

Guiding Questions

1. Why did we race to count the numbers? [Answers may vary. A sample answer is: To recognize numbers quickly so we can do other math problems]

2. What is an easier way to organize the counters to count quickly? [Answers may vary. Sample answers include: In groups; in a ten frame; etc.]

Introduce the Lesson (Try it Together)

Look at Let’s Learn with students. Have students count the circles in the ten frame, the fingers on the hands, and the dots on the domino aloud with you. Then students trace the number 10. Walk around and make sure students trace the 1 first and then the 0. Have students listen to directions when coloring 10 of each shape with different colors. For number 1, tell students to use their blue crayon and color 10 circles. Count aloud as you color ten. Repeat with the rest of the shapes. In Try it Together, practice counting 10 stars and writing the number ten. Continue to color 10 and circle 10 items. Cross off if needed while counting. In the practice pages to follow, color only 10 stars in number 1 even though there are 12 stars. In numbers 2 - 5, cross off while counting. Make sure students count carefully.

Activities

On ten different note cards draw different amounts of shapes (from 1 -10). Label the note cards with letters from A through J (one letter per card). Hide the note cards around the room. Students walk around with a paper (labeled A - J) and write the number of shapes on each card.

Struggling Learners

Struggling learners should practice recognizing numbers on a ten frame to help students get faster at recognizing numbers. Show students an amount of counters on a ten frame and have them call out the number. Repeat for different numbers from 0 to 10.

Early Finishers

Students use a number line (from 1 to 10) and set of dice. Students use their dice to roll numbers on the number line. When the student rolls a number, they cover the number up with a counter or bead. Students keep rolling until all numbers are covered. Students can play with a partner and race to see who can cover up the numbers on the number line first.

Challenge and Explore

Students work in partners. They take turns drawing circles on their board (up to 10) and flashing the board to their partner. Their partner has to quickly say the number of circles on the board.

Assess

Have students draw a picture of 10 objects on a sticky note. Have students write the number 10 next to their pictures. Add their pictures to the anchor chart.

Common Errors

Students may write the number 10 with the 0 first (01). Students may also miscount objects. Have students cross out the objects as they count.

Objective and Learning Goals

y Count, draw and write numbers from 0 to 10.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects

Materials

y Blank ten frames

y Counters (or beans)

y Dry-erase boards

y Dry-erase markers

y Handwriting paper

y Number cards (0 to 10)

y Painter’s tape (or chalk)

y Paper

y Pencils

y Timers

Pre-Lesson Warm-up Guiding Questions

Make a life size ten frame on the floor with painter’s tape (or outside with chalk). Have students stand in the ten frame one at a time. As each student stands in the frame, count the number of students in the ten frame. Tell students to write the number of students in the ten frame on their dry-erase boards. When the ten frame is filled with students ask students: “How many students are in the ten frame?” [10]. Repeat this activity with different numbers of students in the ten frame.

Guiding Questions

1. How does the ten frame help to count? [It organizes all of the objects to keep track while counting] 2. Why is it important to write numbers clearly and have the same amount drawn as everyone else?

[So everyone knows what number we are writing or showing.]

Introduce the Lesson (Try it Together)

Look at the first pond in Let’s Learn with students. Ask students: “How many ducks are in the first pond? [0]. How many ducks are in the second pond? [10]. Which was easier to count? Why?” [The first pond was easier because there were no ducks to count.] Show students how to cross out while counting the frogs. Then, carefully trace the number that matches the amount of frogs. Ask students, “How many frogs did you count?” [5]. When starting the matching section, ask students what are they expected to do in this section. Discuss what is presented. Pictures are on one side and numbers are on the other. Read through the numbers first as students point to each number. Next, count the number of shells in the first box aloud as students cross off each item. Draw a line to find the matching number. Continue this process by carefully counting the pictures while crossing out and then looking for the correct number match.

Activities

Put students in partners. Provide students with a ten frame each and counters or beans for the ten frame. Pass out number cards from 1 to 10. Students flip over one card and put that many counters in their frame. The student who makes the number quickest in their ten frame keeps the card. Keep playing until all of the cards are gone. The student with the most cards wins.

Apply and Develop Skills (Practice)

Continue working through the Try it Together and independent practice problems. Depending on the level of your group, you could have students work in partners or independently or work through the problems together as a class. Remind students to write their numbers clearly and to cross out objects to help keep track of their counting.

Struggling Learners

Struggling learners may need additional practice writing numbers. On handwriting paper, model how to write each number. Have students trace a few numbers and then have students practice writing numbers independently.

Early Finishers

Students will play the ten frame activity independently. Provide students with a timer, blank ten frame, counters (or beans) and number cards from 0 to 10. Students will see how many numbers they can build with counters in the ten frame before the timer runs out.

Challenge and Explore

Play mystery number with students. Give clues to students and have students write the mystery number on their dryerase boards.

My mystery number is more than 0. My number fills up a ten frame. My number is all of my fingers. What is my number? [10]

My mystery number is less than 3. My number is more than 1. What is my number? [2]

Assess

Give each student a piece of paper with the numbers 3, 6 and 10. Have students draw circles for each number. Then tell students to write the number 8 on their own. Finally, ask students to draw 4 triangles.

Common Errors

Some students may need to be reminded to cross off objects while counting to help them from miscounting objects. Students may write their numbers quickly but illegibly or backwards.

Chapter 10

In Chapter 10, we will explore di erent ways to represent the numbers 0-10.

• Recognize numbers in a ten frame

• Recognize numbers on a number line

• Use a number line to count

• Count pictures and shapes

• Quickly recognize the number of dots on dice or dominoes

Vocabulary Words

Objective and Learning Goals

y Recognize and identify numbers in a ten frame.

Vocabulary

y Ten frame - a grid with 2 rows of 5 to make 10 boxes; aids in counting to 10.

y Count - to say or write numbers in order; to determine a total number of objects.

Materials

y Dry-erase boards

y Dry-erase markers

y Flashcards with numbers 1-10

y Flashcards with a varied arrangement of dots

y Pencils

y Pennies or other counters

y Ten frame

Pre-Lesson Warm-up Guiding Questions

Review numbers 1-10 with the students. Ask questions like “Can you count from 1 to 10?” or “Can you show me the number 5 on your fingers?” Begin by asking students to sit in a circle or at their desks. Show a flashcard with a simple arrangement of dots (ex: 3 dots). Encourage students to count the dots and call out the number. Show a few more flashcards with different dot arrangements, allowing students to practice counting.

Guiding Questions

1. What do you notice about ten frames? [there are 10 boxes, 5 are on top, 5 are on bottom...]

2. How can a ten frame be helpful? [A ten frame is a math tool that helps us organize and count numbers]

3. Why do you think it’s important to be able to recognize numbers in a ten frame? [It’s a valuable skill for addition and subtraction]

Introduce the Lesson (Try it Together)

Look at the pennies in Let’s Learn. Model how to count each penny in the ten frame. Count out loud together while counting (1…2…3..etc). How many pennies are there? [7] Then demonstrate how to trace the numbers. Repeat for the next two problems.

Now tell students to count and match the number of pennies in the ten frame by drawing a line to the correct number in number 1 of Try it Together. How many pennies are there? [3] Ask students to draw a line from each ten frame to the matching number that represents the amount of pennies in that frame. Encourage them to count and compare.

Activities

Distribute blank ten frame templates and a set of counters to each student. Call out a number (ex: 8), and have students use the counters to fill in the ten frame to represent that number. Discuss and compare the different ways students filled their ten frames.

Struggling Learners

Play a game of “Guess the Number” where students have to guess the number of pennies in a ten frame by looking at the arrangement. Provide real pennies or manipulatives for hands-on counting and matching.

Early Finishers

Divide the class into pairs and have students take turns showing a ten frame with pennies while their partner identifies the number. Conduct a whole-class activity where students hold up a card with a number and others have to show the corresponding number on their own ten frame.

Challenge and Explore

Introduce double ten frames for more advanced learners. Explore larger numbers and addition/subtraction concepts using ten frames. Have students use their own dry-erase boards and draw ten frames and dots for their partner. Their partner then counts and writes the number on their own dry-erase board. The process repeats as the partners switch roles.

Ask Students

1. How can using two ten frames help us count larger numbers? [one full frame is 10, so you can start counting from there]

2. How many dots fill two ten frames? [20]

Assess

Show students a ten frame with 8 pennies. Ask how many there are. [8]

Fill in the ten frame with the number 4. [Four pennies should be placed in the ten frame.]

Bonus:

I have 7 apples and I eat one. How many do I have left? Draw a ten frame and fill in the ten frame accordingly. [7 dots should be placed in the ten frame, then they cross out one leaving 6]

Common Errors

Counting Errors: Some students may count the dots in a ten frame inaccurately. Encourage them to double-check their counts. Incomplete Ten Frames: Ensure that students understand that a full ten frame should have ten dots, and incomplete ten frames should reflect the correct quantity.

Objective and Learning Goals

y Understand how to use a number line as a tool to identify, sequence, and count numbers from 0 to 10.

y Recognize and locate numbers on a number line and count forward using the number line.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects.

y Number line - helps put numbers in order; a tool to help in counting.

y Sequence - the arrangement of numbers in a particular order.

Materials

y Blank and filled number line charts from 0 to 10

y Colored markers or pencils for circling numbers

y Dry-erase board

y Markers

Pre-Lesson Warm-up Guiding Questions

Pass out filled out number lines to each student. Say, “Let’s play a game of ‘Jump on the Number Line.’ I’m going to call out a number, and I want you to imagine that you’re a grasshopper jumping to that number. When you land, circle it with your colored marker.” For example, “Hop to the number 4 and circle it orange.” Continue this process a few times using different numbers from 0 to 10.

Guiding Questions

1. What is a number line? How does it look? [is has numbers in order, it is like a road for numbers]

2. How is number line helpful? [it helps us see the order of the numbers, it helps with counting]

Introduce the Lesson (Try it Together)

Look at the Let’s Learn section. Flash says “I can hop up the number line and count.” Instruct students to trace the hops from 0 to 10. Then, instruct students to start at 0 and hop to the number 4 and circle it. Then, look at the Try it Together section. Tell students to trace the numbers in the number line. Then tell them to use the number line to find the missing number in the sequence. Ask, “what number comes after 4 and before 6?” [5]. Continue this process for all the examples.

Activities

Instructions: Place 2 large number lines (0-10) on the board or wall. Divide the class into 2 teams and have each team line up next to one number line. Provide each team with a colored marker. Tell students that they will race to circle all the numbers on the number line.

Make sure the 2 students in the front of the lines are holding the markers. Tell the class that when I say “go” the student holding the marker will come up to the board, circle a number from the number line, and say the number out loud. Then they will give the marker to the next student in line and who will come up to board. When your turn is over go to the back of the line. Whichever team circles all the numbers first wins!

Struggling Learners

Provide struggling learners with a pre-drawn number line where all numbers are already filled in. This simplifies the task and helps them focus on identifying and completing the missing numbers.

Early Finishers

Challenge early finishers to create their own number line but extend it beyond 10, for example, up to 20. Ask them to fill in the numbers and provide colored markers to make their number line more engaging. Example: students create a number line from 0 to 20, color each number, and use creative decorations to make it visually appealing.

Challenge and Explore

Have students design a number line game where their peers need to identify missing numbers or perform addition/subtraction on the number line they created. For example, create a game where players roll a dice, move their game piece along the number line, and answer questions related to numbers and sequences. Such as, “you landed before 6, and after 4. What number did you land on?” [5]

Ask Students

1. What would happen if we tried to count on the number line but skipped a number?

[If we skip a number on the number line, our counting wouldn’t be in order, and we might miss some numbers]

2. Can you think of a real-life scenario where a number line might be helpful for counting?

[Answers may vary. A number line can help us count the days on a calendar or the steps on a staircase]

Assess

Display a blank number line chart from 0 to 10 on the board. Call out numbers randomly (ex: 3, 6, 2) and have students locate and circle them on their own number line using the corresponding colored markers. Example: “Circle the number 6 in orange.”

Common Errors

Students may count numbers instead of spaces or hops. When moving 3 spaces, they may count the number they are already on as 1 space, instead of moving to the next number first. Students may skip numbers on the number line when counting. Students may place numbers in the wrong sequence on the number line.

Objective and Learning Goals

y Identify and count the number of shapes within a set.

y Sort objects by shape and accurately count the number of each shape within a set.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects

y Shapes - geometric figures such as triangles, squares, and circles

y Sort - to arrange objects into groups based on their similarities or differences

Materials

y Crayons (blue, red, green)

y Dry-erase board

y Pictures of shapes (triangles, squares, circles)

Pre-Lesson Warm-up Guiding Questions

Begin by engaging students in a warm-up activity to prepare them for the lesson. Display a few pictures of various shapes (ex: triangles, squares, circles) on the board. Ask students to name each shape as you point to them. Then, ask students to count how many of each shape they see in the pictures.

Guiding Questions

1. Can you name some shapes you see in the pictures? [I see triangles, squares, and circles in the pictures]

2. How many circles can you count in this picture? [I can count 3 circles in the picture.]

Introduce the Lesson (Try it Together)

In the Try it Together section, there is a page of 4 triangles, 2 squares, and 5 circles. Direct students to cross off the triangles with a blue crayon and count them. Have them write the number of triangles down. Next, instruct students to cross off the squares with a red crayon and count them. Have them write the number of squares down. Finally, guide students to cross off the circles with a green crayon and count them. Have them write the number of circles down.

Activity

Students will find and count shapes within a time limit. Divide students into teams or pairs. Ask students to designate one team member as the recorder (they can take turns). Instruct teams to choose a team name and remember it. Start the timer (ex: 5 minutes) and say, “Go!” Teams search for shapes in the classroom or outdoor area. When the time is up, call a stop. Gather the class and ask each team to share the shapes they found and the numbers they counted. Discuss strategies that teams used for quick identification and counting.

Struggling Learners

Provide visual cues or labels for each shape in the Try it Together section. Offer one-on-one assistance or smaller group instruction during activities. Use manipulatives, such as shape blocks or stickers, to reinforce sorting and counting skills.

Early Finishers

Encourage early finishers to create their own shape sets and challenge their peers to count them. Provide additional shape sets for them to sort and count independently.

Challenge and Explore

Use more complex shapes or irregular shapes for advanced learners. Introduce shapes in different orientations to enhance observation skills. Have students draw, count, and write the number of shapes they see.

Ask Students

1. How do you know when you have counted all the shapes in a set? [When there are no shapes left to count or cross off.]

2. Can you think of any real-life objects that are shaped like triangles, squares, or circles? [Examples may include pizza slices (triangles), building blocks (squares), and wheels (circles).]

Assess

After completing the sorting and counting activities, assess students’ understanding by asking them to independently draw a picture with shapes and write the corresponding numbers to represent the quantities of each shape.

Common Errors

Common errors may include misidentifying shapes, skipping shapes when counting, or not accurately recording the counts. Encourage students to double-check their work and count each shape carefully.

Objective and Learning Goals

y Count and write numbers from 0 to 5.

y Recognize and count dots on a dice and domino.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects.

Materials

y Plastic bears

y Dice

y Dry-erase board

y Dry-erase marker

y Dominoes

Pre-Lesson Warm-up Guiding Questions

Pass out 5 plastic bears to all students. Roll a die for all students to see. Ask students what number is on the die. [answers will vary depending on what the die lands on] Tell students to count out that many bears on their desk. Walk around to check student work. Roll again and repeat.

Then, show students a domino. (Make sure the domino shows a number 5 or lower). Tell students to count out that many bears on their desk. Walk around to check student work. Choose another domino and repeat.

Guiding Questions

1. Do all dots on a die or domino look alike? [Yes, so it’s easy to count]

2. Why are the dots always in the same spot on a die or a domino? [So we can count them quickly and easily]

Introduce the Lesson (Try it Together)

Look at the dice in Let’s Learn. Go through each die pictured and count the dots. Write the number. Look at number one in Try it Together. Model pointing to each dot to count them. Ask students, “How many dots are on the die?” [5] Find the number to match. Draw a line. Next look at the domino and model how to count the dots on the domino. Find the match. Repeat throughout the rest of this page. On the next page, take time to model how we count the dots on dominoes in the same way. Ask, “How many dots are on the domino?”[1] Write the number. Review number rhymes to practice correct number formation.

Activity

Students work with a partner. One partner gets a die (0-5). The other partner gets a handful of dominoes. The partner with the die rolls it. At the same time the partner with the dominoes randomly pulls one from the pile. The student with the die counts the dots on the die. The student with the domino counts the dots on the domino. Students call out the number they counted. Then the student with the domino puts the domino back in the pile. Students play again- roll the die, pull a domino from the pile, count the dots. Depending on the level of the class students can also determine which number is bigger or smaller. Students could also add the two numbers together.

Apply and Develop Skills (Practice)

Continue working through the rest of the Try it Together and independent practice problems. Remind students to point to each object or cross off each dot as they count in order to keep track.

Struggling Learners

Provide each student with a die and some dominoes, a dryerase board and marker. Together look at each side of the die or domino and count the dots one by one. Then, have students practice rolling the die or looking at the domino and writing the number on the dry-erase board. Play until they have increased speed with number recognition.

Early Finishers

Pass out a die, a number line with numbers 1 through 5, counters and a timer to each student. Students will roll the die and place a counter over that number on their number line. Students can set a timer to see how fast they can cover all numbers. Students can also play with a partner to see who can cover all of the numbers first.

Challenge and Explore

Have students roll a set of dice or choose 2 dominoes and add the total number of dots.

Ask students:

Which do they prefer using: the dice or the dominoes? Why? [Students answer may vary.]

Assess

Roll a die and have students write the number of dots on a piece of paper. Repeat 3 times.

Then show students 3 different dominoes. Have students write the number shown on a piece of paper.

Common Errors

Make sure students are counting and keeping track. Some students may need to cross out the dots as they are counted. Some students may need to be reminded to point to each dot as it’s counted.

Chapter 11

In Chapter 11, we will compare numbers 0-10.

• Count and compare groups of objects

• Determine groups that are more, less or equal

• Draw pictures to show more or less

• Create equal groups

5 7

Objective and Learning Goals

y Compare two groups of numbers (from 0 to 10) to find which is more.

y Compare groups to find which are the same amount.

Vocabulary

y More - a bigger number or greater amount; a term used to compare number values

y Same - the amounts are equal

Materials

y Balls (or any other similar objects)

y Dice

y Dry-erase boards

y Dry-erase markers

y Linking Cubes

y Hula hoops

Pre-Lesson Warm-up Guiding Questions

Put 2 hula hoops on the floor (or tape two circles on the floor). Put 3 balls (or any object available) in the first hula hoop circle. Place 9 more balls (or any other object) in the second hula hoop. Have students look at the balls in each group. Ask students: Which group has more? [the one with 9] Now, put 4 balls in both hoops. Ask students: Now which has more? [neither] This means they are the same.

Guiding Questions

1. How do you know which one has more? [Answers may vary. A sample answer may be: The group with 9 has extra balls in it compared to the group with 3 balls] 2. What does it mean to have more?

[Answers may vary. A sample answer may be: bigger number or greater amount]

Introduce the Lesson (Try it Together)

Look at the cupcakes in Let’s Learn. Ask students: How many cupcakes are in the first group? [6.] How many cupcakes are in the second group? [2.] Why did Flash say the first group has more? [Because 6 is a bigger number than 2]

Review number formation using rhymes. Discuss how the number of ice cream cones is equal or the same. Show students what an = sign looks like when used in math; 4 = 4.

Repeat for Try it Together. Have students look at each group, count how many in each group and decide which group has more.

Activities

Pass out linking cubes to all students. Tell students to make a stack of 8 linking cubes. Next, tell students to make a stack of 4 linking cubes. Ask students: Which stack has more? [The stack with 8.] How can you tell that the stack of 8 has more without counting? [Place the stacks next to each other and see that it’s taller.] Repeat with the numbers 2 and 7, 5 and 10, and 3 and 3.

Struggling Learners

Struggling learners should use linking cubes for Try it Together. Students count each group and make corresponding stacks. Then, they compare their stacks to find which has more. For example, in number 1 of Try it Together, students should make a stack of 7 for the first group of candies and then a stack of 9 for the second group of candies. Students then put the two stacks next to each other to determine which number is more. Ask students: Which stack is taller? [The stack with 9.] So, which group is more? [9]

Early Finishers

Students roll a dice and write the number of dots down on a piece of paper. Then, students write a number that is more than the one they rolled. Students can also play with a partner. One student rolls a dice. They both call out a number that is more than the dice number (only numbers from 0 to 10). Students cannot repeat the same number they said the last turn. Whichever student is faster to say a number that is more than the number on the dice gets a point. Students can keep track of points on a dry-erase board. Keep rolling to see who gets the most points.

Challenge and Explore

Play mystery number with students. Tell these clues to students and have them write the mystery number on their dry-erase boards.

My number is more than 5. It is more than 7. 9 is more than my number. What is my number?

Students write the number 8 on their dry-erase boards.

Assess

On dry-erase boards (or paper), tell students to draw 4 circles. Then, tell students to draw another group with more than 4 circles. Repeat for 5 circles and 8 circles. (You could also do triangles or rectangles to practice drawing shapes).

Common Errors

Students may think that objects drawn bigger mean there are more of them. They may assume bigger is the same as more.

Objective and Learning Goals

y Compare two groups of numbers (from 0 to 10) to find which one is less.

Vocabulary

y Less - not as many; smaller number or amount; term used to compare number values

Materials

y Balls (or similar objects)

y Dice

y Dry-erase boards

y Dry-erase markers

y Linking cubes

y Hula hoops

Pre-Lesson Warm-up Guiding Questions

Put 2 hula hoops on the floor (or tape two circles on the floor). Put 9 balls (or any object available) and put them in the first hula hoop circle. Put 2 balls (or any other object) and place them in the second hula hoop. Have students look at the balls in each group. Ask students: Which group has more? [the one with 9.] Which group has less? [the one with 2]

Guiding Questions

1. How do you know which one has less?

[Answers may vary. A sample answer may be: The group with 2 has not as many balls in its group compared to the group with 9 balls.]

2. What does it mean to have less?

[Answers may vary. A sample answer may be: not as many; a smaller amount.]

Introduce the Lesson (Try it Together)

Look at the squares in the Let’s Learn. Ask students: How many squares are in the first group? [10] How many squares are in the second group? [7] Why did Glow say the second group has less? [Because 7 is a smaller number of has not as many squares.] Have students write in the numbers. Continue counting group one, write number, count group two, write number, compare and circle which group is less. In Try it Together, count each group and circle which is less.

Activities

Pass out two ten frames and counters to each student. Tell student to put 6 counters in one ten frame. Put 2 counters in the other ten frame.

Ask students

1. Which ten frame has less? [The frame with 2]

2. How do you know it has less without counting?

[Answers may vary. A sample answer may be: There were more empty spaces.]

Repeat with numbers 10 and 3, 4 and 5, and 6 and 7.

Struggling Learners

Struggling learners should use the ten frames and counters for Try it Together. Students count each group and fill in each ten frame with counters. Then, students compare their ten frames to find which has less. For example, in number 1 of Try it Together, students should fill in a ten frame with 9 counters and the other ten frame with 5 counters for the groups of squares. Ask students: Which frame is not filled as much? [The frame with 5.] So, which group is less? [5]

Early Finishers

Students receive a number line, counters, beads and a set of dice. Students roll the dice and pick a number that is less than the number rolled on the dice. Then, they place a counter on that number on the number line. For example, students roll a 5 and can cover the 3 on the number line. Students keep playing until all numbers are covered on the number line.

Challenge and Explore

Play mystery number with students. Tell these clues to students and have them write the mystery number on their dry-erase boards.

My number is less than 5. It is less than 3. My number is not less than 1. My number is not 1. What is my number?

Students write the number 2 on their dry-erase boards.

Assess

On a piece of paper draw three different comparisons and tell students to circle which is less for each grouping.

y 4 stars and 3 stars

y 2 squares and 9 squares

y 3 circles and 1 circle

Common Errors

Students may think that objects drawn smaller mean there are less of them. They may assume smaller is the same as less.

Objective and Learning Goals

y Compare numbers (from 0 to 10) to find which is more.

Vocabulary

y More - a bigger number or greater amount; a term used to compare number values

Materials

y Balance (or stick with string and two cups ties to the ends)

y Dry-erase boards

y Linking cubes or plastic bears

y Sticky notes

Pre-Lesson Warm-up Guiding Questions

Gather sticky notes, a balance, and linking cubes or plastic bears. Write the numbers 3 and 6 on sticky notes. Place the sticky notes on each side of the balance. Tell students you are going to see which number is more: 3 or 6. Place 3 cubes or bears on one side of the balance (matching the sticky note) while counting out loud with students. Repeat for 6 cubes/ bears on the other side. Ask students: Now that we have counted out each number, which number is more? [6] How do you know? [the balance is heavier on the side with 6]

Guiding Questions

1. How can you tell a number is more without counting bears or using a balance? [Answers may vary. A sample answer may be: drawing, using a number line, counting, etc.]

2. Give an example of when you would need to know if a number is more in your life. [Answers may vary. A sample answer may be: When deciding how many snacks I want when given a choice between two numbers.]

Introduce the Lesson (Try it Together)

Look at the flower seeds and watering cans in Let’s Learn. Ask students: How did Flash decide that 7 is more than 5? [He drew a picture.] Why is 7 more than 5? [Because there are 2 extra watering cans than flower seeds.] Tell students to trace the circle around 7 to show that it is more than 5. Count aloud the next problem of sprouts and sunflowers. Ask which one is more and circle 4. For the last problem, have students count clovers. First, write the number, then count flowers and write the number. Compare the two numbers. Which one has more? [flowers] Ask students, which number should they circle. [8] Remind students to cross off as they count to help keep track of the amount in each group. In Try it Together, students will need to draw images to help decide which number is worth more. Students should count the circles out loud 1…2…3…4. Repeat for the squares. Ask student which is more. [5] In number 3 students will need to draw independently. Count items after drawing, cross off as students count, and circle which number is higher.

Activities

Split students into even groups (4 groups). Write 2 numbers on the board between 0 and 10. All students are to draw circles and write which is more. One student is the team speaker from each group and tells which number is more by raising their hand. The first student that raises their hand and says the correct number, gets a point for their team. Continue playing and rotating team speakers.

Struggling Learners

Struggling learners should draw circles in ten frames to help visually see which is more. Pass out 2 ten frames (laminated) for the activity for students to draw circles in for each number comparison. They could also use counters or coins to help reuse the ten frame.

Early Finishers

Students write their own mystery number clues on a note card. Suggest that students use “My number is more than ___” clues. Students can then exchange their mystery number clues with another early finisher and solve for the mystery number. Example: My number is more than 1. My number is not more than 3. What is my number? [2]

Challenge and Explore

Read the story problem to students.

Jim has 4 toys. John has more toys than Jim. John does not have more than 10 toys. How many toys could John have?

Ask students

1. How do you know how many toys John has? [He has between 5 and 9 toys because those numbers are more than 4. Also, it’s a number between 5 and 9 because 10 is still larger than those numbers.]

2. Can the answers be different? Why? [Yes, because there are multiple numbers that are more than 4.]

Assess

Call out two numbers and have students draw and write the number that is more on their dry-erase boards. Call out the following numbers: 1 and 9; 3 and 4; 8 and 4.

Common Errors

Students may think that objects drawn bigger are worth more.

Level

Objective and Learning Goals

y Compare two numbers (from 0 to 10) to which is less.

y Compare two numbers (from 0 to 10) to which are equal.

Vocabulary

y Less - not as many; a smaller number or amount; a term used to compare number values

y Equal - exactly the same value or amount

Materials

y Balance (or a stick with a string and 2 cups tied to the ends)

y Dry-erase boards

y Linking cubes or plastic bears

y Sticky notes

Pre-Lesson Warm-up Guiding Questions

Collect sticky notes, a balance, and linking cubes or plastic bears. Write the numbers 10 and 4 on the sticky notes. Place the sticky notes on each side of the balance. Tell students you are going to see which number is less, 10 or 4. Place 10 cubes or bears on one side of the balance that matches the sticky note. Count out loud with students. Repeat with the 4 cubes on the other side. Ask students: Now that we counted out each number, which number is less? [4] How do you know? [the balance is lighter on the side with 4] Next clear off the balance and count out 2 cubes or bears on each side. Ask students: Look at the balance. What is happening with both sides now? [it is even or lined up] When the balance is even, it means that it is the same on both sides.

Guiding Questions

1. How can you tell a number is less without counting bears or using a balance? [Answers may vary. Sample answers may be: drawing, using a number line, counting, etc.]

2. What is another word for the same in math? [equal - when there is the same value or amount]

Introduce the Lesson (Try it Together)

Look at the strawberries and pumpkins in Let’s Learn. Ask students: Are the strawberry groups equal or are the pumpkin groups equal? [Strawberry groups are equal.] How do you know? [There are 3 in each group and they are the same.] Have students point to the groups below of melon slices and green apples. Ask students to count how many are in each group. Does the number below the group match how many are in each group? [yes] Decide which group has less and circle it. [The apple group has less than the melon group.] So how can you compare 5 with 6? [5 is less than 6] In the next groupings, find which 2 are equal. Count them all first. Note number under each group represents amount in each group. Circle the groups with the same or equal. Remind students what an equal sign looks like in math; 3 = 3. In the Try it Together, tell students that you will draw images to help decide which number is worth less. Together trace the circles in number 1 and count out loud. Repeat for the 6 squares. Which number is worth less? [3] How do you know? [There are not as many shapes drawn.] Continue to count and circle less. Draw the same number of images shown or less based on directions. When drawing less, any amount less than the original amount is correct.

Activities

Write 2 numbers (from 0-10) on 10 different note cards and hide them around the room. Examples: 4 and 10, 3 and 7, 2 and 2, etc. Students get a piece of paper and walk around the room to find the note cards. When the students find a note card, they write both numbers down and circle the number that is less. If 2 numbers are equal, draw an equal sign between the 2 numbers.

Struggling Learners

During the group activity, struggling learners should be encouraged to draw circles to represent the numbers they found on their note cards. Then use the drawings to determine which number is less based on the two numbers.

Early Finishers

Students write their own mystery number clues on a note card or paper. Suggest that students use: “My number is less than____” clues. Students can then exchange their mystery number clues with another early finisher and solve for the mystery number. Example: My number is less than 8. My number is not less than 6. What is my number?

Challenge and Explore

Read the word problem to students:

Mark has 4 pets. Dan has less pets than Mark. How many pets could Dan have?

Ask students

1. How do you know how many pets Dan has? [He has between 0 and 3 pets, because those numbers are less than 4. ]

2. Can the answers be different? Why? [Yes, because there are multiple numbers less than 4.]

Assess

On a small piece of paper or note card, write the 3 sets of numbers below. Tell students to circle the number that is less or write the equal sign if they are equal. Review what the equal sign looks like prior to assessment.

Numbers for note cards: 3 and 5 9 and 6 7 and 7

Common Errors

Students may think that objects drawn smaller are worth less.

Chapter 12

In Chapter 12 we will use di erent models to practice addition from 0-10.

• Use a ten frame to add from 0-10

• Use a number line to add from 0-10

• Use pictures to solve vertical addition problems

• Solve addition story problems using pictures

3 1 + 4

Vocabulary Words

Objective and Learning Goals

y Use a ten frame to add numbers from 0 to 10 accurately.

y Develop students’ understanding of addition within the range of 0 to 10.

Vocabulary

y Add - to bring two or more numbers together to make a total; counting up to make more.

y Sum - the answer, or result, when adding numbers

y Ten frame - a grid with 2 rows of 5 to make 10 boxes; aids in counting to 10

Materials

y Colored circles (red and yellow)

y Pencils or crayons

y Ten frame (one per student)

Pre-Lesson Warm-up Guiding Questions

Display a ten frame on the board or use a visual aid. Ask students, “What is a ten frame used for?” Guide them to understand that a ten frame helps us count and add numbers quickly. Then ask, “What do you notice about the ten frame? How is it organized?” Allow students to share their observations and discuss the arrangement of the ten frame. In the Let’s Learn section, look at the ten frame example with 7 red circles and 2 yellow circles, along with the problem 7 + 2 = 9. Flash says, “I can add in a ten frame!” Beneath the example, look at the problem 5 + 3 = __ and a ten frame with 5 red circles and 3 yellow circles. Instruct students to trace the answer, 8, in the addition sentence.

Guiding Questions

1. How can we use a ten frame to add numbers? [We can place the circles on the ten frame to represent the numbers being added and count the total number of circles.]

2. What does the plus sign (+) mean in an addition problem? [The plus sign (+) means we are combining two or more numbers together to find the total.]

Introduce the Lesson (Try it Together)

In the Try it Together section, look at the ten frame with two different colored circles corresponding to addition problems. Say, “we have 1 red circle and 5 yellow circles. How many are there in all?” [6] Ask students to write the sum for each ten frame provided. Repeat this process. On the independent practice page, tell students to look at the equation 3 +2 = __ in number one. Then, tell students to look at the equation. Say, “we have 3 red circles and need to add two more. Can you trace two more circles?” Instruct students to trace the missing circles to complete the math sentence. Then ask, “How many do we have in all?” [5] Ask students to write the sum. When completing the rest of the problems, remind students that they must draw in the circles by looking at the second addend in the addition sentence.

Activities

Divide the class into two teams. You can have a “Team A” and a “Team B.” Explain to the students that they will have a “Ten Frame Race.” Prepare two ten frame templates on the board or a large sheet of paper. Each ten frame should have some empty boxes. Call out a simple addition problem (ex: 4 + 3) to the students. The race begins when you say, “Go!” Each team needs to quickly fill in the ten frame with counters or drawings to represent the numbers in the addition problem. In this example, Team A needs to place 4 counters in one ten frame and 3 counters in the other. The first team to fill in the ten frame correctly and shout out the sum (in this case, “7”) wins that round. Continue with different addition problems, giving each team a chance to fill in the ten frame and shout out the sum.

Struggling Learners

Provide additional guidance and support during the Try it Together section. Offer blank ten frames and counters or beans for students to physically represent the numbers and practice counting. Use number lines to show the progression from one number to another when adding on a ten frame.

Early Finishers

Encourage early finishers to create their own addition problems using the ten frame and solve them independently. They can also draw pictures to represent the addition problems and write the corresponding sums.

Challenge and Explore

Challenge students to solve addition problems beyond 10 using the ten frame. They can also explore different ways to represent the same sum using the circles on the ten frame. You may also increase the numbers in the addition problems or add missing addends (ex: 8 + __ = 10).

Ask Students

1. Why is using a ten frame helpful for addition? [A ten frame helps us visualize numbers, making it easier to add them together. It’s a great tool for understanding addition.]

2. Can you think of other ways we use visual aids in math? [Yes, we use things like number lines, counters, and diagrams to help us with different math concepts.]

Assess

1. Display a ten frame with 3 blue circles and 2 red circles. Ask the students to write the addition problem and find the sum. [3 + 2 = 5]

2. Display 6 yellow circles and 4 green circles. Instruct the students to write the addition problem and find the sum. [6 + 4 = 10]

3. Display 1 orange circle and 8 purple circles. Have the students write the addition problem and find the sum. [1 + 8 = 9]

Common Errors

Common errors to watch out for may include: Miscounting the circles in the ten frame. Forgetting to write the sum in the addition sentence. Misinterpreting the addition problem and the ten frame representation.

Objective and Learning Goals

y Use a number line to add between 0 and 10.

Vocabulary

y Number line - helps to put numbers in order; a tool used to help in counting

Materials

y Dry-erase boards

y Dry-erase markers

y Number line

y Red/Yellow counters - ten per student

y Linking cubes - two different colors

y Chalk or tape to make a number line

y Paper bags

y Number cards 0-9

Pre-Lesson Warm-up Guiding Questions

Draw a big number line on the floor or ground with chalk or tape. Have it numbered from 0-10. Ask a student to stand on the number 2. Then ask the student to take two hops forward. What number is the student on now? [4].

Guiding Questions

1. What number did we start on? [2]

2. How many hops did we take? [2]

3. What number did we end on? [4]

4. How can I write this problem as an addition sentence? [2 + 2 = 4]

Continuing asking different students to start at a number and take a certain number of hops to another number. Have student say or write the addition sentence.

Introduce the Lesson (Try it Together)

Tell students that today we will focus on solving horizontal addition sentences using a number line. Take a look at the Let’s Learn number one and ask what are the 2 addends in the first example. [3 and 5]. How do we know where to find 3 on the number line? [look for the third mark and the number 3]. When we add on a number line, what direction do we go? [from left to right] Continue working in this section, by counting on the number line using “hops.” Start with the first addend and stop at that point. Then, use the second addend to guide you to find the overall sum. Use your pencil to mark from one number to the next with hops as students count out loud. Trace or write the answer. Remind students that they should count all hops to find the sum, or count up, using the addends. Move on to the Try it Together section. Encourage students to trace the circle which is the first addend on the number line. The number of hops they make is the number of the second addend. Have them circle the number they end up on, and count their hops to double check. Practice pages only have the first addend circled on the number line. Students must look at the second addend in the addition sentence to determine how many hops to make.

Activity

Prepare number lines and use number cards from 0 - 9 and place them in a paper bag. Pass out number lines or dry-erase boards and markers to each student. Have one student come up to the front of the class and pull two numbers of the hat. Have student show the class the two numbers. Ask students to start at 0 and draw hops on their number line to count to the first number. Then, have students start at that number and add the number of hops that the number is requiring (ex: If the numbers 2 and 3 were drawn, start at 0, draw 2 hops and stop at 2. Then, start at 2 and hop 3 times to the right. What number are you at? This is the sum. For a movement activity, use tape to create a number line on the floor and have students hop the addition problem on the number line.

Draw hops the number line. Write the sum.

the first addend on the number line. Draw the hops. Write the sum.

Struggling Learners

Provide students with a number line and 2 different colored sets of linking cubes. Use the addition sentences in the Let’s Learn section. Use one color for the first addend and the other color for the second addend. Link them together to find sum. Match the sum on the number line to the sum of the linking cubes. Turning the linking cubes horizontally will help visualize the number line.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Each group pulls out one domino at time and turns it horizontally. Look at the dots on the domino. The left set of dots is the first addend. The right set of dots is the second addend. Note that if there are no dots in one section, the addend is zero. Write their addition sentence on their dry-erase boards. Find the sum. Compare the two sums. Students can say: “My sum of ___ is bigger/smaller than _____’s sum.”

Challenge and Explore

Provide students with a number line and two number cubes that are 0-5 (not 1-6). Have students roll the set of dice and use the numbers as the two addends. Have students start at 0 and draw hops to find the sum. Have students write the addition sentence horizontally and solve.

Assess

Provide student with a number line and three addition sentences:

4 + 2 = [6]

5 + 2 = [7]

3 + 3 = [6]

Tell student to use their number lines as a guide, but to use their dry-erase boards to write this sentence horizontally and solve. Repeat this for each problem.

Common Errors

Students may write the answer next to the second addend or prior to the first addend. Make sure students write the sum to the right of the equal sign on the blank horizontal line. Reinforce that when trying to solve an addition sentence using a number line, the first addend in the addition sentence is the number to start at on the number line. The second addend tells the number of hops to make on the number line.

Objective and Learning Goals

y Solve addition problems using pictures

y Recognize the elements of a vertical addition sentence Vocabulary

y Vertical addition - a number sentence with numbers stacked going up and down Materials

y Dominoes

y Dry-erase boards

y Dry-erase markers

y Plastic cup - one per student

y Red/Yellow counters - ten per student

Pre-Lesson Warm-up Guiding Questions

Show students that we can write addition sentences in 2 ways. Write the addition sentence: 2 + 1 = ? horizontally. Ask students to find the sum. [3] Now, re-write the addition sentence vertically and draw circles next to each addend. Find the sum. Ask students: What is different? [The problem is written up and down.There is a line underneath the 2 addends.] What is the same? [The addends are the same and the sum is the same.] Reinforce that no matter which way the addition sentence is written, the sum is still the same. Show a model of 2 dominoes each having 2 dots on one side and 1 dot on the other side. Show one horizontally and ask how many dots are there in all? [3] Show another of the same domino vertically and ask how many dots are there in all? [still 3]

Guiding Questions

1. How do we know 3 and 1 are the addends? What clues or pictures tell us what the addends are? [the balloons]

2. Where is the equal sign in the addition sentence? [It is the vertical line underneath the second addend.]

Introduce the Lesson (Try it Together)

Tell students that today we will focus on solving addition sentences vertically. Take a look at the Let’s Learn and ask what are the 2 addends in the first example. [3 and 1] Continue working in this section, by counting the first row of pictures and recognizing this is the first addend. Cross off as students count out loud. Trace or write the first addend. The second row is the second addend. Trace or write the second addend after counting the second row. Count all of the pictures to find the sum, or count up, using the bigger addend first and add to that number. Continue practicing counting the pictures first before writing the addends in the Try it Together section.

Activity

Prepare number cards from 0 - 9 and place them in a hat or paper bag. Pass out dry-erase boards and markers to each student. Have one student come up to the front of the class and pull two numbers of the hat. Have student show the class the two numbers. Ask students to write a vertical addition sentence using these 2 addends and draw pictures to show each addend. Compare how students answered the addition sentence and that the addends can be in different spots and still give the same sum.

Struggling Learners

Provide students with 2 different colors of linking cubes when completing simple addition sentences. Use one color for the first addend and the other color for the second addend. Link them together to find sum.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Students each pull out one domino and turn it vertically. Look at the dots on the domino. The top set of dots is the first addend. The bottom set of dots is the second addend. Note that if there are no dots in one section, the addend is zero. Write their addition sentence on their dry-erase boards. Find the sum. Compare the two sums. Students can say: “My sum of ___ is bigger/smaller than _____’s sum.”

Challenge and Explore

Provide students with a cup of 10 counters in red and yellow. Have students shake the cup and pour an amount of counters on to their dry-erase boards. Separate the two color counters into 2 addends. Write an addition sentence vertically on dry-erase board and solve. Show using counters.

Assess

Provide student with the horizontal addition sentence: 3 + 2 = ? Tell student to use their dryerase boards and write this sentence vertically with pictures and solve. Give a second horizontal addition sentence to solve: 5 + 4 = ? Solve the same way.

Common Errors

Students may write the answer next to the second addend. Make sure students write the sum underneath the equal sign which is a horizontal line.

Objective and Learning Goals

y Solve story problems using drawings.

y Write and solve addition sentences.

Vocabulary

y Addition sentence - numbers, plus sign and equal sign used together to show addition

y Story problem - word problems or problems that use stories to indicate mathematical application and thinking

Materials

y Beans or red/yellow counters

y Dry-erase boards and markers

y Number cards for students 0-10

y Plus signs and equal signs for partners

y 3 separate images of the same flower (3 roses)

Pre-Lesson Warm-up Guiding Questions

Write the following story problem on the board: Abe picked 1 flower. Alan picked 2 flowers.

While reading the first sentence aloud, hold up one image of a flower. Read the second sentence and hold up 2 more images of the same flowers.

Guiding Questions

1. How many flowers did they pick in all? [3]

2. Can anyone draw a picture to show this addition sentence?

3. What are the parts of an addition sentence? [numbers you add/addends, a plus sign, and equal sign, the total/sum]

4. What does the addition sentence for this story problem look like? [1 + 2 = 3]

Introduce the Lesson (Try it Together)

In Let’s Learn read aloud the story problem to the class. Have students trace the circled addends in story problem. Note how the first addend in the problem is drawn with 2 apples next to Flash. Trace the 2 in the number sentence. Note how 4 apples are underneath the 2 apples. Count the number of apples. Trace the 4 in the number sentence. Count all of the apples and trace the sum of 6. Tell students they can solve story problems by drawing pictures. Have students follow the same steps for the second story problem, but trace circles for cookies instead. Continue working on the two problems in Try it Together. Read them together. Have students continue to circle the addends in the story problem, and draw a picture in the space below. They can use a circle or square to represent the addends.

Activity

Divide the class into partners. Give each pair a set of number card 0-10 and cards with plus sign (+) and equal sign (=). Challenge students to write their own number sentence using the cards. After they create a number sentence, have them build it using beans/counters/blocks. Does their sentence match their objects? Students will check their work and make any corrections. Keep making sentences until time is up.

5 6 3 0 8 6

Struggling Learners

Provide students with a handful of yellow and red counters. Break them into 2 groups based on colors. Write an addition sentence with the 2 groups. The yellow group is one addend and red group in the second addend. Write the sentence on the dry-erase boards. Next, teacher comes up with a story problem related to 2 students in the group. Example: Dan has 3 red counters. Mark has 4 yellow counters. How many counters are there in all?

Early Finishers

Pass out the 0-10 number cards and the plus signs and equal signs to early finishers. They will create addition sentences, then make up their own story problem to go with the sentence. Have students pair up to share their story problems and solve together. This can be done orally. The number cards will help students keep track of the addends in their story.

Challenge and Explore

Write the following problem on the board and read it out loud:

Abe picked 2 flowers. Alan also picked flowers. They have 5 flowers in all.

1. What is different about this story problem? [we know the total. We don’t know how many flowers Alan picked.]

2. What does this addition sentence look like? [ 2 + ? = 5]

3. What strategies can we use to solve this problem? [answers will vary: count up from 2 to 5, count out the total with beans/counters then find the missing addend, etc.]

4. How many flowers did Alan pick? [3]

Assess

On the last page of independent work, check problems 1 and 2. Look at #1 to see that the drawing matches up with the problem. Look at #2 to see the numbers written match the numbers in the problem and that the sum is correct.

Common Errors

Students may not draw the correct number of addends or sum that the story problem is giving. Check that student work is accurate.

Chapter 13

In

Chapter 13, we will use di erent strategies to practice subtraction 0-10.

• Use a ten frame to subtract from 0-10

• Use a number line to subtract from 0-10

• Use pictures to solve vertical subtraction problems

• Solve subtraction story problems using pictures

− 9 3 6

Vocabulary Words

Objective and Learning Goals

y Use ten frames as a tool to solve for the difference with numbers 0 to 10.

Vocabulary

y Difference - the result of subtracting one number from another

y Minuend - the number being subtracted from in a subtraction sentence

y Subtract - to take an amount away from a starting amount

y Subtrahend - the amount being subtracted in a subtraction sentence

y Ten frame - a grid with 2 rows of 5 to make 10 boxes; aids in counting

Materials

y Counters (10 per student)

y Dice (2 per student)

y Dry-erase boards

y Dry-erase markers

y Objects such as stuffed animals (10)

y Painter’s tape

y Teacher prepared ten frame worksheet

Pre-Lesson Warm-up Guiding Questions

Make a ten frame on the floor with Painter’s tape. Place an object / bear in each box. Students should sit in a large circle around the ten frame. Remind students that this grid is a ten frame and we use it to help in counting up or taking away. Have 3 students remove 1 object each. Ask students: “How many did we start with?” [10] “How many do we have left?” [7] Repeat this as many times as you like with other amounts of objects.

Guiding Questions

1. What does it mean to subtract?

[Take some amount from the total]

2. When we use a ten frame for subtraction, what do we do to the numbers that we are taking away? [take them away, cross them out]

Introduce the Lesson (Try it Together)

Tell students that today we will focus on subtraction from 0-10 using a ten frame. Take a look at the Let’s Learn and show students what the Minuend is and the Subtrahend are. In 7 - 4, the 7 is the minuend and the 4 is the subtrahend. To subtract means that we are taking some number from another. In this case, we are taking 4 from 7 when we have 7 - 4. Have the students count the dots in the first ten frame. Then have them mark out 4 of the dots. This leaves 3. Trace 3 as the answer.

Continue working in this section by using a ten frame to subtract. Have students mark out the subtrahend in the Try it Together section to find the amount left.

Activity

Use the dry-erase boards and dry-erase markers to have students quickly write how many are left from a series of subtraction problems. The focus on speed will help them build fluency. 7 - 3 = [4]; 8 - 2 = [6]; 5 - 4 = [1]. Repeat process to include other numbers less than 10.

Struggling Learners

Provide students with 10 linking cubes with 5 of one color stacked on top of a different color. Start with 10 and take away. For example, you have 10 cubes, now take 4 away, how many are left? [6] Once accurate, take three cubes away and use 7 as your total to take away from. Have students do 7 - 5, then 7 - 4, and continue through this process to build fluency with subtraction.

Early Finishers

Provide students with a bag of 10 pennies and have them use the ten frame to subtract from 10 in a series: 10 - 1; 10 - 2; 10 - 3, 10 - 4, 10 - 5, 10 - 6, 10 - 7, 10 - 8, 10 - 10. The students can write their answers on their dry-erase board to keep track. Once they have done this with 10s, they can do 9s, then 8s, all the way to 1.

Challenge and Explore

Provide students with a ten frame and set of dice. Have students roll the dice and use the largest number as the minuend and the smallest number as the subtrahend. The students should model the subtraction problem using the ten frame.

Assess

Provide students with a ten frame for reference. Have them solve the following problems using the ten frame as a tool. The answers can be written on their dry-erase board.

8 - 4 = [4] 10 - 2 = [8] 5 - 3 = [2]

Common Errors

Students may mix up the subtrahend and the minuend. Also, students may add instead of subtract. Guide students by asking: “What is the total amount you started with?” and “How much are you taking away?”

Level K Chapter 13-2

Objective and Learning Goals

y Use a number line as a tool to solve for the difference with numbers 0 to 10.

Vocabulary

y Difference - the result from subtracting one number from another

y Minuend - the number being subtracted from in a subtraction sentence

y Subtract - to take an amount away from a starting amount

y Subtrahend - the amount being subtracted in a subtraction sentence

Materials

y Counters (10 per student)

y Dice (2 per student)

y Dry-erase boards

y Dry-erase markers

y Painter’s tape

y Paper bags

y Teacher prepared number line worksheets

Pre-Lesson Warm-up Guiding Questions

Write the subtraction sentence 7 - 4 = ? Tape a number line to the floor using Painter’s tape. Have one student start at 0 and hop to 7. Tell students that since we have a (-) we are going to hop towards 0 instead of 10. Have the student hop backwards 4 times. Ask students: “We started at 7, now where are we?” [3]. You can repeat this process to include more students.

Guiding Questions

1. Where do we start on the number line? [0]

2. When we subtract on a number line, what direction do we go? [from right to left, left is negative.]

Introduce the Lesson (Try it Together)

Tell students that today we will focus on solving subtraction sentences using a number line. Take a look at the Let’s Learn and ask what are the minuend and the subtrahend in the example. [Minuend is 8, Subtrahend is 3] Continue working in this section by counting on the number line using “hops.” Start with the first minuend [8] and then hop back left 3 times to arrive at 5. It is also helpful if you start at 0, hop right 8 times, then back left 3 times to arrive at your answer. Use your pencil to mark from one number to the next with hops as students count out loud. Trace or write the answer. Continue practicing using the number line to solve subtraction problems in the Try it Together section. On the second practice page, look at the number line to determine if the answer is right or wrong. Circle the check mark if the answer is right. Circle the x if the answer is wrong. Draw hops on the new number line to solve. Write the correct answer near the star.

Activity

Place number cards 0-9 in a paper bag. Pass out number lines or dry-erase boards and markers to each student. Have one student come up to the front of the class and pull two numbers of the hat. Have student show the class the two numbers. Identify the bigger number. Then, ask students to start at 0 and count on the number line to the bigger number. Then, have students subtract the smaller number by hopping left on the number line. (ex: If the numbers 2 and 5 were drawn, identify 5 as the bigger number and start there. Then, to subtract, take 2 hops to the left. Ask students, where do you land? [3] This is the difference.) For a movement activity, use tape to create a number line on the floor and have students hop the subtraction problems on the number line.

Struggling Learners

Use counters to count out the minuend. Place one counter under each number on the number line. Count back by removing one counter at a time. Use the number line to see how many counters are left. (Example: 8 - 3 = 5 Place 8 counters underneath the number 1-8 on the number line. Remove 3 counters one at a time. See that you are left with 5 counters (and the last counter is under the number 5). Repeat this process for other subtraction problems.

Early Finishers

Students gather a number line, a counter and a die. Students roll the die, find the number on the number line and place a counter on it. Next, students roll the die again. If the number is smaller than the first roll, students will hop the counter that many times backwards on the number line. If the number is larger, move the counter to the larger number and hop back the number from the first roll. Students then write their subtraction problem down on a dry-erase boards.

Challenge and Explore

Partners can play a number line subtraction game. Students get two dice, one number line and two-color counters. Students take turns rolling the dice, solving the subtraction problem shown, and covering the difference on the number line with a counter. If there is already a counter on the difference, students lose their turn. Students play until all numbers have a counter. The player with the most counters on the number line wins.

Assess

Provide students with a number line and a counter. Give students a subtraction sentence to solve using their number line such as: 8 - 3 = [5] or 74 = [3]. Students can place their counter on the answer/difference. Repeat for at least 3 subtraction sentences.

Common Errors

Students may hop to the right instead of the left when doing subtraction problems. Students may miscount the number of hops. Make sure students write the difference to the right of the equal sign on the blank horizontal line.

Objective and Learning Goals

y Solve vertical subtraction sentences using pictures.

Vocabulary

y Difference - the result from subtracting one number from another

y Minuend - the number being subtracted from in a subtraction sentence

y Subtract - to take an amount away from a starting amount

y Subtrahend - the amount being subtracted in a subtraction sentence

y Vertical subtraction - a vertical number sentence with numbers stacked going up and down

Materials

y Dominoes , Dry-erase boards, Dry-erase markers

y Linking cubes, Number line

y Plastic cup - (1 per student)

y Red/Yellow counters (10 per student)

Pre-Lesson Warm-up Guiding Questions

Show students that number sentences can be written both vertically and horizontally. Write 7 - 5 = ? horizontally. Find the difference. [2] Write the subtraction sentence vertically. Find the difference. Either way that the subtraction sentence is written, the difference is still the same number.

Guiding Questions

1. How do we know which number is the total, the minuend? [we look at the amount we started with]

2. How do we know how many to take away, the subtrahend? [we look at how many are leaving]

Introduce the Lesson (Try it Together)

Show students how to write a vertical subtraction sentence. In Let’s Learn ask students to draw 9 circles or balls like Flash has on their dry-erase board. Tell students to cross out or erase the amount of the balls Flash lost. Ask students: “How many balls does Flash have left?” [5] Show students how to write the vertical subtraction sentence. Point to the minuend, subtrahend and difference. Work in this section by coloring the balloons first and recognizing the first number in the number sentence is the total, or minuend. Next trace the X’s on the 3 balloons. The second number is the amount to take away, or the number of balloons crossed out. This is called the subtrahend. We subtract to find the total amount left. Count how many balloons are left over that are not crossed out. This is the difference. In the Try it Together section, use pictures to solve the subtraction problems. Practice writing horizontal and vertical subtraction problems. On the independent practice pages, find the picture that will solve each subtraction problem.

Activity

Provide students with a dry-erase board and dry-erase markers. Have them draw the problem out. Tell them that, Isaac has 8 dogs. [draw 8 dogs or triangles] He gave 2 dogs to his cousins. [cross out 2] How many dogs does he have left? [6] Now, have students write this problem in a vertical subtraction sentence. Repeat with similar problems.

Struggling Learners

Provide students with a set of red/yellow counters. Have them place all counters yellow side up. Tell students to write the number of counters they have on their dry-erase board. Then, tell students 3 are given away. Have students place this number underneath the minuend on their dryerase boards. Have students either flip over the counters to the red side or remove them from the pile. Ask students: “How many yellow counters are left?” and have students write their answer on the dry-erase board.

Early Finishers

Provide students with a number line, linking cubes and dice. Students roll their set of dice, subtract the two numbers making sure the larger number is the minuend and the smaller number is the subtrahend. Then, find the difference on their number line and cover it with a linking cube. If they solve for a difference that already has a linking cube, then they add a linking cube on top to make a stack. Students continue playing to see which number can get the tallest stack.

Challenge and Explore

Read the following problem to students and have them write the vertical subtraction sentence on their dry-erase boards. Then, have students solve the problem. Change the numbers in the story problem and solve for a second time.

Jacob received 8 stickers. He lost 2 stickers. How many stickers does he have left?

Assess

Rewrite the following horizontal subtraction problems vertically and solve. Draw pictures if needed.

Common Errors

Students may add instead of subtract. Students may also write the difference for the subtraction problem next to the numbers instead of below the equal line. Students may think they have to solve both the vertical and horizontal subtraction problems even though they are the same. Remind them that if the two numbers being subtracted are the same, then the difference is the same.

Level K Chapter 13-4

Objective and Learning Goals

y Solve story problems using drawings.

y Write and solve vertical subtraction sentences.

Vocabulary

y Difference - the result from subtracting one number from another

y Minuend - the number being subtracted from in a subtraction sentence

y Subtract - to take an amount away from a starting amount

y Subtrahend - the amount being subtracted in a subtraction sentence

y Story problem - word problems or problems that use stories to indicate mathematical application and thinking

y Subtraction sentence - numbers, minus sign and equal sign used together to show subtraction

y Vertical subtraction - a vertical number sentence with numbers stacked going up and down

Materials

y Counters

y Dry-erase boards

y Dry-erase markers

y Plastic Bears

y Bracelets or Rings (Struggling Learners)

Pre-Lesson Warm-up Guiding Questions

Hold up 5 plastic bears. Demonstrate subtraction by “giving away” 4 plastic bears to students. Write the subtraction sentence: 5 - 4 = ? horizontally and vertically on the board. Ask students: “What does this - sign mean?” [to subtract, or to take away]. I had 5 bears and I gave away 4. How many are left? [1] You can create short story problems based on the students in the classroom.

___ has 8 ____.

___ gave 4 ____ away. How many _____ does ____ have left?

Introduce the Lesson (Try it Together)

Tell students that today we will focus on solving subtraction number sentences from story problems. Take a look at the Let’s Learn and ask what are the minuend and subtrahend in the Flash's example. [8 and 3]

Guiding Questions

1. What number represents our total number that we start with? [the minuend, answers may vary, but the total amount or first amount may be common answers]

2. When we take away from the total, what operation are we performing? [subtraction.]

Continue working in this section by leading students through the process of writing the subtraction number sentence from the story problem. Continue practicing this process in the Try it Together section.

Activity

Have students use their dry-erase board to fill in the blanks for problems such as the one below. Allow students to be creative.

___ has 7 ____.

___ gave 2 ____ away. How many _____ does ____ have left?

John has 9 He gave 4 to his brother. How many does he have left? There are 6 3 fly away. How many are left?

There are 4 3 swim away. How many are left? 9 6 4 4 3 3 5 3 1

He let 3 go. How many are left? 5 3 2

2. Abe caught 5 in the

Rose had 8 slices of She gave 4 slices of to her friends. How many slices of does she have left? 8 4 4

Struggling Learners

Provide students with bracelets or rings to demonstrate each problem. By removing the bracelets or rings from their hands, they will be able to feel what it means to “take away”. If students are struggling with one-to-one correspondence, encourage them to count one bracelet or ring at a time.

Early Finishers

Partition students into pairs to write their own story problems on dry-erase boards. Have them switch and solve. Then, have students check each other’s work. The students can then erase and repeat.

Challenge and Explore

Provide students with a more challenging word problem that is multi-step such as:

Jacob had 10 pieces of candy. He gave 3 pieces to Isaac and 2 pieces to Amy. He ate 1 piece. How many pieces does he have left. [4]

5 are on the table. Mike bumped into the table and 2 fell o . How many are left?

3. Jack had 8 He gave 3 to Kevin. How many does Jack have left?

Ellie has 3 . She gave 2 to her sister. How many does Ellie have left? 8 5 3 3 2 2 5 3 1

Assess

Provide students with a story problem to solve on their dry-erase boards. A sample problem could be:

John has 9 apples. He gave 2 to his friend. How many apples does John have left? [7]

Common Errors

Students may not correctly identify if the problem is addition or subtraction. Students may not cross out the right amount when subtracting.

Chapter 14

In Chapter 14, we will count and write the numbers 11-20.

• Identify numbers 11-20

• Count numbers 11-20

• Write numbers 11-20

• Use a ten frame to count numbers 11-20

Vocabulary Words

Objective and Learning Goals

y Write numbers from 11-14.

y Count and identify quantities of 11-14.

Vocabulary

y Count - to say or write numbers in order; to determine a total number of objects

y Amount - a total, or quantity, of something

y Pattern - items that repeat in a specific order

Materials

y Beans or counters (14 per student)

y Dominoes

y Dry-erase boards

y Dry-erase markers

y Handwriting paper

y Number cards (0-14)

Pre-Lesson Warm-up Guiding Questions

Have students gather their dry-erase board and dry-erase markers. Have students write 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Now, let’s count. Say: “Right now, we have 0 students standing up. Now, if we have 1 student standing up (___ please stand up), how many do we have standing? [1] Continue to do this until 10 students are standing. Then, ask students: “What comes after 10?” [they may or may not answer] Write the number 11 say it. Then have students write 11 and say the number. Continue this process until 14.

Guiding Questions

1. What patterns do you notice in the numbers as we write them? [they start to repeat, 11 is two ones, then 12 is a one and two]

2. What number comes after 10? [11]

Introduce the Lesson (Try it Together)

Read aloud what Flash is saying: I can count past 10. Have students touch the triangles as you all count together. Stop when you get to 10. Then ask: “What comes next?” [11]. Keep counting the triangles to 14. Students will trace the number 14 and say: there are 14 triangles. Count the objects above each number together and trace the number. Encourage students to mark objects as they count. Then count the objects, and circle the correct amount. On the Try it Together page, first say and trace the numbers. Then count one group of objects. Draw a line to the numbers that matches.

Activity

Provide student pairs with number cards from 0-14. Have them mix up the cards. One at a time, they draw a card, say the number and count up to it. Then put the number in a line in order until all cards are face up. They can also build each number as they say it with beans or counters.

Struggling Learners

Provide students with handwriting paper with the numbers 11, 12, 13 and 14 available to be traced. Have them write the numbers until they have successfully developed the skill. Then, have students draw dots or use beans/counters to represent the quantity of each number accurately.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Students each pull out one domino and turn it horizontally and count the dots. Then, students will take their beans or counters to “add to” the amount on the domino to make 14. Then have them write this as an addition number sentence (ex: a domino that is 1:2 will need 11 more added to it, 3 + 11 = 14) on their dry-erase board.

Challenge and Explore

Prepare bags of 14 objects (beans, counters, pennies, etc.) and provide a bag to each student or to each pairs of students. Have students pull 12, 13, or 14 objects out of the bag and write that number on their dry-erase board. Have students find as many different ways to make 2 groups that equal the number of objects, 12, 13 or 14. They can separate the total into two piles, then write the amount in each pile. This leads to finding addends to equal the number.

Questions

1. Is there more than one way to make 2 groups? [yes] Have students share some answers.

2. Can you make 2 equal groups or any of the numbers? [yes, 12 and 14]

3. Do you think we can make three groups? Try it! Have student share their answers.

[Example: For 3 groups if the amount was 14: group of 3, group of 9 and group of 2. Students could write on their dry-erase boards: 3 + 9 + 2 = 14.]

Assess

Have students separate their beans or counters into 12, 13, or 14 pieces and have them write the correct number on their dry-erase board.

Common Errors

Students may write the numbers in backwards order such as 41 for 14. When students are writing numbers in a line, look for accurate spacing between digits and between separate numbers.

Objective and Learning Goals

y Write numbers from 15-17.

y Count and identify quantities of 15-17.

Vocabulary

y Count - list or name one by one in order to find a total

y Amount - a total, or quantity, of something

y Pattern - items that repeat in a specific order

Materials

y Beans (17 per student)

y Counters

y Dry-erase boards

y Dry-erase markers

y Handwriting paper

y Number cards (15-17)

y Ten-frames (2 per student)

Pre-Lesson Warm-up Guiding Questions

Pass out two ten frames to each student and 17 beans/ counters. Together fill in the first ten frame and count to ten. Remind students that when the ten frame is filled, it means they have 10. Have them put 1 counter in the next ten frame. How many do we have now? [11] We have one 10 and 1 more for 11. Yesterday we counted to 14. How many beans do we need to get to 14? [10 and 4 more]. Have student make that on their ten frames. Ask students what number comes next? [15. Some students many not know]. Add another counter to make 15. Continue this process to 17.

Guiding Questions

1. What number comes after 14? [15] 15? [16] 17? [17]

2. How does the ten frame help us count? [we know its 10, we don’t need to count each piece again]

3. What patterns to you notice? [the second number goes up by one, numbers are repeating, etc.]

Introduce the Lesson (Try it Together)

Read aloud what Flash is saying: I can count past 15. Have students touch the circles as you all count together. Stop when you get to 14. Ask “What comes after 14? [15] Continue counting to 17. Students will trace the number 17 and say: there are 17 circles. Count the objects above each number together and trace the number. Encourage students to mark objects as they count. Then count the objects, and circle the correct amount. On the Try it Together page, first say and trace the numbers. Then count one group of objects. Draw a line to the numbers that matches. Students can then practice writing the numbers 15-17 without line guides.

Activities

Provide students with number cards from 15-17 in random order and provide the students with a handwriting sheet. Have them draw a card and write the number. Repeat until they have written all numbers multiple times.

Prepare bags of 17 objects (beans, counters, pennies, etc.) and provide a bag to each student or to each pairs of students. Have students pull 14, 15, 16, or 17 objects out of the bag and write that number on their dry-erase board.

Struggling Learners

Provide students with handwriting paper with the numbers 15, 16, and 17 available to be traced. Have them write the numbers until they have successfully developed the skill. Then, have students draw dots or build the numbers with blocks or counters to represent the quantity of each number accurately.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Students each pull out one domino and turn it horizontally and count the dots. Then, students will take their beans or counters to “add to” the amount on the domino to make 17. Then have them write this as an addition number sentence (ex: a domino that is 1:2 will need 14 more added to it, 3 + 14 = 17) on their dry-erase board.

Challenge and Explore

Prepare bags of 17 objects (beans, counters, pennies, etc.) and provide a bag to each student or to each pairs of students. Have students pull 15, 16, or 17 objects out of the bag and write that number on their dry-erase board. Have students find as many different ways to make 2 groups that equal the number of objects, 15, 16 or 17. They can separate the total into two piles, then write the amount in each pile. This leads to finding addends to equal the number.

Questions

1. Is there more than one way to make 2 groups? [yes] Have students share some answers.

2. Can you make 2 equal groups for any of the numbers? [yes, 16]

3. Do you think we can make three groups? Try it! Have student share their answers.

[Example: For 3 groups if the amount was 16: group of 3, group of 8 and group of 5. Students could write on their dry-erase boards: 3 + 8 + 5 = 16.]

Assess

Have students separate their beans or counters into 15, 16, or 17 pieces and have them write the correct number on their dry-erase board.

Common Errors

Students may write the numbers in backwards order such as 51 for 15. When students are writing numbers in a line, look for accurate spacing between digits and between separate numbers.

Objective and Learning Goals

y Write numbers from 18-20.

y Count and identify quantities of 18-20.

Vocabulary

y Count - list or name one by one in order to find a total

y Amount - a total, or quantity, of something

y Pattern - items that repeat in a specific order

Materials

y Beans or counters (20 per student)

y Dominoes

y Dry-erase boards

y Dry-erase markers

y Handwriting paper

y Number cards (0-20)

y Ten Frames (2 per student)

Pre-Lesson Warm-up Guiding Questions

Pass out two ten frames to each student and 20 beans/ counters. Together fill in the first first ten frame and count to ten. Remind students that when the ten frame is filled, it means they have 10. Have them fill in the second ten frame. Say to students now we have another ten. When we have one ten frame and another ten frame how many do we have in all? (20). Next, have students remove 5 counters from the second 10 frame. Ask, how many do we have with a 10 and 5? [15] Let’s count up together as we fill in the empty spaces. [16, 17, 18, 19, 20]

Guiding Questions

1. What number is two ten frames?[20]

2. When we have 15, how many more do we need to get to 20?[5]

3. How does the ten frame help us count? [we know it’s 10, we don’t need to count each piece again]

4. What patterns to you notice? [the second number goes up by one, numbers are repeating, etc.]

Introduce the Lesson (Try it Together)

Read aloud what Flash is saying: I can count to 20. Have students touch the squares as you all count together. Stop when you get to 17. Ask “What comes after 17?” [18] Continue counting to 20. Students will trace the number 20 and say: there are 20 squares. Count the objects above each number together and trace the number. Encourage students to mark objects as they count. Then count the objects and circle the correct amount. On the Try it Together page, first say and trace the numbers. Then count one group of objects. Draw a line to the numbers that matches. Student can then practice writing the numbers 18-20 without line guides.

Activity

Provide student pairs with number cards from 0-20. Have them mix up the cards. One at a time, they draw a card, say the number and count up to it. Then put the number in a line in order until all cards are face up. They can also build each number as they say it with beans or counters.

Struggling Learners

Provide students with handwriting paper with the numbers 18, 19, and 20 available to be traced. Have them write the numbers until they have successfully developed the skill. Then, have students draw dots or build the numbers with blocks or counters to represent the quantity of each number accurately.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Students each pull out one domino and turn it horizontally and count the dots. Then, students will take their beans or counters to “add to” the amount on the domino to make 20. Then have them write this as an addition number sentence (ex: a domino that is 1:2 will need 17 more added to it, 3 + 17 = 20) on their dry-erase board.

Challenge and Explore

Prepare bags of 20 objects (beans, counters, pennies, etc) and provide a bag to each student or to each pairs of students. Have students pull 18, 19, or 20 objects out of the bag and write that number on their dry-erase board. Have students find as many different ways to make 2 groups that equal 18, then 19, then 20. They can separate the total into two piles, then write the amount in each pile. This leads to finding addends to equal the number.

Questions

1. Is there more than one way to make 2 groups? [yes] Have students share some answers.

2. Can you make 2 equal groups or any of the numbers? [yes, 18 and 20]

3. Do you think we can make three groups? Try it! Have student share their answers.

[Example: For 3 groups if the amount was 20: group of 3, group of 11 and group of 6. Students could write on their dry-erase boards: 3 + 11 + 6 = 20.]

Assess

Say a number 18-20 to a student. Have them write the number and count out that many objects.

Common Errors

Students may write the numbers in backwards order such as 81 for 18. Students may write 10 as 20 or 0 as 20. When students are writing numbers in a line, look for accurate spacing between digits and between separate numbers.

Objective and Learning Goals

y Use ten frames as a tool to compose numbers 10 to 20.

Vocabulary

y Add - to bring two or more numbers together to make a total; counting up to make more

y Addend - any number added to another number

y Penny- a coin that has the value of 1 cent in the U.S.

y Sum - the answer, or result, when adding numbers

y Ten frame - a grid with 2 rows of 5 to make 10 boxes; aids in counting

Materials

y Beans or counters (20 per student)

y Dice (2 per student)

y Dry-erase boards

y Dry-erase markers

y Pencils or crayons

y Pennies (20 per student)

y Ten frames (2 per student)

Pre-Lesson Warm-up Guiding Questions

Hand out two ten frames to each student or partners and 20 counters/beans. Write the addition sentence: 10 + 0 = ? horizontally. Tell students the first ten frame shows the first number, or addend. Fill in your ten frame to show this number. Now, ask students: “What do we do if we have more than 10?” [add another ten frame] Full ten frames always equal 10. So, if 10 + 0 = 10 we have 1 ten frame. Now, if we have 10 + 1, we have 1 ten frame plus one more part of a ten frame. Continue practicing with different numbers in the second addend.

Guiding Questions

1. How do we find the sum of 2 numbers? [combine the amounts of each to find the total]

2. When we are adding 2 numbers and 1 number is a complete ten frame, what is the amount of the first addend? [10]

3. What patterns to you notice when we add to a 10? [answers will vary: the second addend is the second part of the answer]

Introduce the Lesson (Try it Together)

Let’s look at Flash’s ten frames. He has a complete ten frame which is 10. He has a part of another ten frame that has 6 in it. We can add together the 10 and 6 to find his total sum. Ask students: “How many pennies does Flash have?” [10 + 6 = 16].

Remind students if they have a full ten frame, they can count up from 10 starting the next ten frame. Work the practice problems together. Move to the Try it Together section. Have student first count the 10, then trace and count the circles the next ten frame. Point out that the first addend is the first ten frame, 10. The second addend is the number of circles in the second ten frame. Ask students what is different about problem 3. The second addend is missing! Help them to count up to the answer and write the missing addend.

Activity

Make a human ten frame by placing two lines of 5 students facing each other. Ask students: “How many students are in this group? [10] We have 2 groups of 5 or 5 groups of 2. This is the ten frame. Now, if we were to add 3 more students over here, we have 10 + 3 = 13. Repeat by moving a number of students in and out to add to the ten frame to equal sums between 10-20.

Struggling Learners

Provide students with 20 pennies, beans, or counters. Provide 2 ten frames for the students to work with. Have them place 10 pennies, beans, or counters on 1 of the ten frame to complete the ten frame. Clarify that this equals 10. Use the second ten frame as an “add to” the first ten frame. Have students add various pennies, beans, or counters to the second ten frame to equal a total between 10-20.

Early Finishers

Provide students with 20 counters/beans. Have them count out a total of 10-20. Once they have their total, have them make a group of 10 and count how many are in the other group. Practice writing addition sentences saying, for example, “ 14 = 10 + 4.” Or they can say “14 is a 10 and a 4.”

Challenge and Explore

Provide students with 1 die, 2 ten frames, and 20 pennies. Have the students start with the ten frames full of 20 pennies. Students roll the die and remove that amount of pennies, counters, or beans from one of the ten frames and write on their dry-erase board how many are left. This will challenge the students to work backwards with addition as an introduction to subtraction.

Questions

1. If I start with 20 and remove 4, how many do I have left? [16]

2. Is it easier to take away number or add numbers? [answers will vary]

Assess

Provide students with the following numbers: 13, 15, 18. Have students use pennies, counters, or beans to create a group of ten and a group of 3 for 13, 5 for 15, and 8 for 18 to show the addends of the addition sentence that would lead to the sum using a ten frame.

Common Errors

Students may write just the ones value and skip the tens place value because they are disregarding the first ten frame and only counting the second frame.

Chapter 15

In Chapter 15, we will count by 1s, 10s and 2s.

• Count to 100

• Count by 1s starting at any number

• Use ten frames to skip count by 10s

• Use number lines and pictures to skip count by 2s

Vocabulary Words

Objective and Learning Goals

y Count by 1s to 50.

y Count forward from any number within the sequence.

Vocabulary

y Number line - helps put numbers in order; a tool to help in counting

y Sequence - when things are put in a certain order: first, next, last

Materials

y Blank sheets of paper

y Sticky notes with numbers from 1 to 50

Pre-Lesson Warm-up Guiding Questions

Make a giant number line to 50 together as a class. Place students into 5 groups and give each group one sheet of paper and a set of sticky notes (ex: 1-10, 11-20…). Each group should make one section of the number line by sticking their sticky notes in the correct order on their paper. (It is ok if students need some help.) Arrange the numbers in order to make one big number line.

Guiding Questions

1. What is a number line? [A number line is a line with numbers written in order. It helps us see how numbers increase or decrease in value.]

2. What number comes next: 18, 19, 20? [21]

Introduce the Lesson (Try it Together)

In Let’s Learn use the caterpillar to count to 50. Tell students to point to each number as they count. Point out that we are counting one number at a time. Pick numbers to ask students to start counting from. Tell them to use the caterpillar to help them. On the Try it Together page, practice counting together to 50 again. Tell students to point to the 3 with their crayon. Find it on the “track” by starting at 1 and counting up. Color in the 3 on the “track” and then cross it off at the top. Continue finding the rest of the numbers. Practice writing the number that comes next. On the practice pages, read the numbers out loud to students and have them use the number lines to write the number that comes next. Point out that number lines can start or stop at any number (the arrows show that we can continue counting).

Activity

Partner up students. Tell one partner to count 50 but to make some mistakes on purpose. The job of the other partner is to catch the mistakes. When they hear a mistake they should put their hand up like a “stop” sign and say the next correct number in the sequence. After some time switch roles. Students can use the Let’s Learn caterpillar to assist in counting and making intentional errors.

Struggling Learners

Use a song or chant to help students learn the number sequence. Keep practicing counting to 50. Help students start to notice patterns in the number sequence. (ex: it goes from “teens” to “twenties” to “thirties”..., each group has a 1, 2, 3…9 and then you go to the next group (ex: 21, 22, 23…29, 30, 31…).

Early Finishers

Give students paper and ask them to create a number line that goes as high as they can. Allow them to look at the giant number line as a reference.

Challenge and Explore

Challenge students and ask them to start at 50 and count backwards to 1. Pair students with a partner if they need help.

Ask Students

1. What are some patterns you notice about the names of the numbers? [it goes from “teens” to “twenties” to “thirties”..., each group has a 1, 2, 3…9 and then you go to the next group (ex: 21, 22, 23…29, 30, 31…)]

2. What are the next 3 numbers after 50? [51, 52, 53]

Assess

Ask students what comes next: 9, 10, 11, ? 17, 18, 19, ? 21, 22, 23, ? 45, 46, 47, ?

Common Errors

Students may skip numbers because they are counting too fast. Students may get confused with tens (29, 30, 31). Students may have trouble with the “teen” numbers.

Level K Chapter 15-2

Objective and Learning Goals

y Count by 1s to 100.

y Count forward from any number within the sequence. Vocabulary

y Number line - helps put numbers in order; a tool to help in counting

y Sequence - when things are put in a certain order: first, next, last Materials

y 100 Objects

y Highlighter

y 10 Small baskets or bins

Pre-Lesson Warm-up Guiding Questions

Show students a collection of 100 objects. Ask them to guess how many there are. Tell them that there are 100 and write 100 on the board. Discuss the number 100 by giving examples of things we can have 100 of. Ask students which number 100 comes after when we count [99]. Practice counting from 1-100 as a class.

Guiding Questions

1. What number comes next: 23, 24, 25? [26]

2. What numbers do you say when you start counting at 11 and stop at 20? [12, 13, 14, 15, 16, 17, 18, 19, 20]

3. What number comes after 99? [100]

Introduce the Lesson (Try it Together)

Use the racetrack to count out loud to 100. Tell students to use their fingers to point to the numbers as they “drive” along the racetrack. Remind students that in order to win this race we need to drive very slowly and carefully so that we don’t miss any numbers. Point out that we are counting one number at a time. Pick numbers to ask students to start counting from. Tell them to use the racetrack to help them. On the Try it Together page, practice counting together to 100 again. Tell students to point to the 4 with their crayon. Find it on the “racetrack” by starting at 1 and counting up. Color in the 4 and then cross it off at the top. Continue finding the rest of the numbers. On the practice pages, read numbers out loud to students and have them find the missing numbers or the numbers that come next. Point out that number lines can start or stop at any number (the arrows on the number line show that we can continue counting).

Activity

Partner up students. Tell one partner to start counting from 50-100 but to make some mistakes on purpose. The job of the other partner is to catch the mistakes. When they hear a mistake they should put their hand up like a “stop” sign and say the next correct number in the sequence. After some time switch roles. Students can use the Let’s Learn racetrack to assist in counting and making intentional errors.

Struggling Learners

Pair up students and have them practice counting to 100 together. Partners can count in unison or take turns saying the next number. Students can use the Let’s Learn racetrack for a visual. In addition, as you count out loud as a class, stress the tens. Clap or stomp your foot when reaching a 10s. Example: 28, 29, 30.

Early Finishers

Provide a small group students with 10 small bins or baskets. Students need to hunt around the classroom searching for a group of 10 of the same object and place it in the basket. Place 10 blocks in one basket. Place 10 pencils in another basket. After all baskets are filled with the 10 items, practice counting out the items up to 100 as a small group.

Challenge and Explore

Give students a number from 1-100 and ask them to say the next 3 numbers. For an additional challenge, ask what 3 numbers come after 100.

Ask Students

1. What are the next 3 numbers after 58? [59, 60, 61] 2. What number comes before 40? [39]

Assess

Ask students to count starting at 9. Stop them when they get to 26.

Ask students to count starting at 42. Stop them when they get to 49.

Ask students to count starting at 93. Stop them when they get to 100.

Common Errors

Students may skip numbers because they are counting too fast. Students may get confused with tens (29, 30, 31). Students may have trouble with the “teen” numbers.

Level K Chapter 15-3

Objective and Learning Goals

y Counting by tens.

y Use a ten frame.

Vocabulary

y Ten frame - a grid with 2 rows of 5 to make 10 boxes; aids in counting to 10

Materials

y Objects for counting (at least 50)

y Pencils or crayons

y Pennies or plastic colored counters

y Ten frame

y Teacher prepared ten frame worksheet (10 ten frames)

y Teacher prepared tens cards (10, 20,…100)

y 10 stickers for each student

Pre-Lesson Warm-up Guiding Questions

Give students 50 objects to count. Ask, did it take a long time to count to 50? [yes] Can anyone think of an idea to help us count faster? [skip counting] Tell students that when we want to count faster we can count a few objects at a time. This is called skip counting because we are skipping some numbers. First, we make our objects into groups. (Demonstrate how to group objects into groups of 10.) Now, we count our groups. Since we have 10 in each group, we can skip 10 numbers when we count. Point to the first group and ask: Without counting, how many are here? [10] The first number we will count is 10. What are some examples of numbers I skipped? [1,2,3…] Show students that 2 groups together are 20. Point out that you didn’t have to count 11-19 because you knew that there were 10 in the group. Continue until 50.

Guiding Questions

1. What is it called when we count 10 objects at time instead of one at a time? [skip counting by 10s]

2. What is an example of time you might want to count by 10s? [when you have a lot to count or want to count faster]

3. How is counting by 10s different than regular counting? [it is faster because we skip some numbers, we use bigger numbers etc]

Introduce the Lesson (Try it Together)

Tell students that we are going to learn how to count by 10s to help the farmer find his lost animals which are hiding by the 10s. Start at 1 and count to 100. As you move along the game board, whisper each number together. When you reach a 10, say the number out loud and cover that space with a counter. Once all 10s are covered, clear the counters and color in the 10s with a highlighter or crayon. Count by 10s out loud as a class.

Tell students that it is easy to count by 10s with ten frames because we know that there are 10 inside each ten frame. In the Try it Together section, have students color in the the ten frames. Allow students to count by ones but encourage them to start noticing patterns (ex: 1 ten frame is 10, 2 ten frames are 20, 3 ten frames are 30…). Encourage students to guess how many will be in 4 or 5 ten frames. When students are finished coloring, have them point to each ten frame as they count out loud by tens. In the practice pages, tell students to count when they fill out the ten frames. Encourage students to notice how many ten frames are completed when drawing out each number. Remind students that each ten frame is a group of ten. If a number fills 4 ten frames then it can be made into 4 groups of ten. Continue practicing counting by tens by filling in the missing numbers. Circle ten of each object and skip count to find how many there are.

Activity

Give each student a ten frame and ten stickers. Have them put a sticker in each box. Ask students to find a partner. Count by 1s and then by 10s to see how many stickers they have altogether. Rearrange students in different size groups to practice counting by 10s to find how many they have in all.

Struggling Learners

Struggling learners may confuse counting by 1s with counting by 10s. Help students realize that when we count by tens we are skipping 10 numbers because we are counting 10 objects at a time.

Continue to practice counting to 100 with a visual like the game board on the Let’s Learn page. Have students whisper all the numbers but mark the 10s by saying them out loud, clapping as they say them, and/or circling them.

Early Finishers

Tell students to draw a lot of pictures for friend to count. When students are finished have them trade papers and circle groups of 10. They should count by 10s to see how many there are. Ask students if there were any left over.

Challenge and Explore

Give students an empty ten frame worksheet (with 10 ten frames). Tell students to pick a 10s card (10-100). Tell students to guess how many ten frames their number will fill and to write their guess on a sticky note. Then use counters to make that number using ten frames and see if their guess is correct.

Ask Students

1. If we have 2 ten frames that are full with stickers, how many stickers do we have? [20]

2. If we have 7 ten frames that are full with stickers, how many stickers do we have? [70]

3. If we have 30 stickers, how many 10 frames will they fill? [3]

Assess

Ask students to count by 10s out loud.

Provide students 40 objects to count. Ask students to place them into groups of 10 and to count by 10s.

Common Errors

Students may confuse counting by 1s and by 10s. Students may not realize skip counting by 10s involves skipping 10 numbers.

Students may not realize that skip counting is only for counting groups.

Students may confuse the 10s with the “teen” numbers because they sound similar.

Level K Chapter 15-4

Objective and Learning Goals

y Use a number line as a tool to skip count by 2s.

Vocabulary

y Add - to bring two or more numbers together to make a total; counting up to make more

y Number line - helps put numbers in order; a tool to help in counting

y Sum - the answer, or result, when adding numbers

y Sequence - the arrangement of numbers in a particular order

Materials

y Beans or colored counters

y Number line

y Pencils or crayons

Pre-Lesson Warm-up Guiding Questions

Have students stand up with their chair behind them. Tell them we are going to count from 0-20 as we sit and stand up. BUT, we are not going to say the number out loud when we sit. All students are standing and say ZERO. Then they sit down and mouth the word ONE. Then stand and say TWO. Then sit and mouth THREE. Keep doing this until they get to 20. Continue doing a counting pattern where you only say the even numbers. You can march, handclap/knee slap, etc.

Guiding Questions

1. Which numbers did we say out loud? [0, 2, 4, 6…]

2. Ask for volunteers to count only saying the numbers we said out loud.

3. This is skip counting by 2s. When might we want to count by 2s? [counting many objects, when you have two of something]

Introduce the Lesson (Try it Together)

Tell students that today we will focus on counting by 2s using a number line. Take a look at the Let’s Learn and ask students if we start at 0 and hop to 2 in 1 hop and hopped again to 4, what number would be next? [6]. If we are skip counting by 2s and we start at 0, where would we be at ___ hops? [3 hops would be 6, 4 hops would be 8]. Why is it helpful to add or hop by 2s instead of 1s? [we are able to get there faster]

Continue working in this section by counting on the number line using “hops.” Start where the frog is and count by 2s. Trace or write the answer. Remind students that they should count all hops to find the answer. Be sure they are skipping only one number between hops. In the Try it Together have students point to the pair of pictures and count up by 2s. They can write the number below it. On the last practice page, look for the blank box on the number line. This is the number that needs to be filled in. Count by 2s making sure to hop over 1 number or 2 spaces. If 2 boxes are blank, 2 separate numbers need to be identified on number line.

Activity

Prepare number lines and use counters or beans (approximately 20 per student or pairs of students) and place them in a paper bag. Pass out number lines or dry-erase boards and markers to each student. Ask students to divide their counters or beans into pairs and place in a line. Then, have students start at 0 and draw hops on their number line to count to 2, then to 4… all the way to 20. Then, have students start at that number and add the number of hops that the number is requiring (should be 10 hops). Then have students put 6 beans or counters together as the “start.” Then say, add three 2s, where will we end up at? [12] Repeat as needed.

Struggling Learners

Provide students with a number line and have them complete the problem first with beans or counters. Students should place beans or counters into pairs. Have students do this to 10 first, then 20 counting by twos. How many pairs or hops equal 10? [5] and repeat for 20 [10]

Early Finishers

Provide students with a set of number cards that have dots or images on them that are even numbers. Remove all odd values from the number cards. (For example, you can use a deck of cards that uses 2, 4, 6, 8, and 10; or you can use a deck of number cards 0-20 with only the even numbered cards). Have students draw from the deck and use that number as a starting point. They should write the number that they pulled on the dry-erase board and then make three hops of 2 to see where they end up at. For example, if they draw the number 14, three hops would be to 20.

Challenge and Explore

Provide students with a story problem such as:

A rabbit was hopping on a long number line by 2s. If the rabbit started at 14 and made 8 hops, where would the rabbit end up at? [30] What if the rabbit hopped back by 2 one space, what number would the rabbit land on from 30? [28]

Assess

Provide student with the following to solve:

Common Errors

Students may start at 2 instead of 0 when initially counting. The students may write 2, 2, 2, 2, when counting objects instead of 2, 4, 6, 8. When drawing hops, they may forget to skip a number in the middle.

Chapter 16

In Chapter 16, we will sort and count with Tally Marks, Graphs and Coins.

• Tally numbers 0-10

• Use tally marks

• Use bar graphs and picture graphs

• Make bar graphs

• Identify pennies

• Count pennies

• Identify dimes

• Count dimes

Vocabulary Words

Objective and Learning Goals

y Represent numbers 0-10 using tally marks.

y Understand how to interpret and create simple tally graphs.

Vocabulary

y Tally marks - tally marks are a way to count numbers by drawing vertical lines.

Materials

y Markers

y Number cards with tally marks

y Sticky notes for class activity

y Dry-erase board

Pre-Lesson Warm-up Guiding Questions

Begin by gathering the students in a circle on the floor or at their desks. Show them a stack of cards with numbers from 0 to 10. These cards can have both the numerical representation and tally marks for the numbers. Select one card without revealing it and hold it up without showing the students. Ask the students to guess which number is on the card by observing your tally marks. Encourage them to think about the tally marks and make their best guess. After allowing a few seconds for students to think, reveal the number on the card, showing both the numerical representation and tally marks. Discuss the tally marks on the card, emphasizing how they represent the number. Repeat this activity with several different cards, gradually increasing the complexity of the tally marks as students become more comfortable with the concept.

Guiding Questions

1. How many tally marks represent the number 1?

[One tally mark represents the number 1.]

2. Can you show me tally marks for the number 3?

[Tally marks for 3 look like this: |||]

0 1 6 2 7 3 8 4 9 5 10

Introduce the Lesson (Try it Together)

Flash says, “I can show numbers with tally marks!” Look at the Let’s Learn section and encourage students to trace the tally marks to become familiar with them. In the Try it Together section the tally marks for numbers are drawn. Students write the corresponding numbers next to the tally marks. Tell students to count the tally marks. Ask, how many do you count? Write the number of tally marks you count. On the independent practice pages, student will write tallies for the given number. Students will count shapes and create tally marks. Last, students will count images and write tallies and the corresponding number. Students may need to cross off shapes/images while counting and making tallies. This step will remove the chance of repeat counting.

Activities

Distribute sticky notes with different numbers to each student. Ask students to come to the front and add tally marks on the board based on the number they have. After all students have contributed, count and discuss the data as a class.

Struggling Learners

Provide struggling learners with a reference sheet that includes pre-drawn tally marks alongside corresponding numbers. For example, provide a reference sheet with tally marks from 0 to 5, along with their corresponding numerical values. Students can look at this sheet when writing numbers in tally marks.

Early Finishers

Challenge early finishers by asking them to create their own sets of tally marks for numbers beyond 10. This encourages creativity and a deeper understanding of tally marks. For example, students can create tally marks for numbers like 12, 15, or 18 and exchange them with their peers to solve and discuss.

Challenge and Explore

Encourage advanced learners to create more complex tally graphs with data collection. They can collect data from their peers or from real-life situations and represent it using tally marks. Have students create two questions about a tally graph showing favorite fruits. For example: How many students like apples? What is the most preferred fruit among students?

Ask Students

1. Can you think of another way to represent numbers, apart from tally marks? [Possible answers - using digits, using objects, using number words, etc.]

2. How can tally graphs help us understand information? [Tally graphs help us visualize and compare data easily.]

Assess

Write the tally marks for the number 9. [Represented by nine marks]

Count the tally marks and write the corresponding number: |||| [4]

Show students the following graph on the board: Red: III Blue: II White: I

How many students prefer each color?

Common Errors

Confusing the order of tally marks (vertical lines) and diagonal lines. Miscounting the number of tally marks for a given number. Misinterpreting the data presented in a tally graph. Forgetting to group tally marks in sets of five.

Objective and Learning Goals

y Input data into graphs.

y Interpret data in graphs to determine how many.

y Compare data in graphs to determine more and less.

Vocabulary

y Bar graph - a graph using rectangular bars that can compare amounts

y Data - a collection of information

y Interpret data - to review data and use it to inform

Materials

y Crayons

y Pattern blocks (Red, blue, green, and yellow)

Pre-Lesson Warm-up Guiding Questions

Begin with providing students with a set of pattern blocks (3 red, 4 yellow, 2 blue, and 1 green). Ask students: “How many blocks to we have?” [10]. Now, let’s sort the blocks into colors. Ask students: “ How many of each color do we have?” On a dry-erase board or chart paper, draw the shapes on the left side (y-axis) and write the numbers 0-5 across the bottom (x-axis). Draw the grid and then re-ask students how many of each color. When asking, shade in the number of sections on your bar graph to make the graph. Ask students questions such as the following: “Which color is shown the most?” [yellow]. “Which color is shown the least?” [green]

Guiding Questions

1. How do we make a bar graph? [draw bars for the number of objects we have]

2. How can we use a bar graph to compare different numbers and objects? [see which bars are taller or shorter]

Introduce the Lesson (Try it Together)

Tell students that today we will focus on sorting and counting data to put into a bar graph. Take a look at the Let’s Learn and ask students: “How many of each color does Flash have?” Then, ask students: “Why is it good to have a bar graph?”

Continue working in this section by tracing the correct answers. Continue practicing making the bar graph and interpreting the results in the Try it Together section. Make sure to explain that we are coloring in the amount from the story. For example we are coloring 8 boxes in the dog section because 8 students picked dogs as their favorite animal. Graphs do not always have show favorites. Graphs can show totals of items.

Activity

Take a colorful beach ball that has three different colors. If you don’t have a beach ball, use an object that has equal sections with at least three different colors. For example, a beach ball that has 10 sections with 4 red, 3, white, and 3 yellow sections. Have students count how many total sections. Have them identify the colors of the beach ball with how many of each color. Allow students to draw their own bar graph on a sheet of paper using colorful crayons.

Struggling Learners

Provide students that are struggling with a handful of colorful objects. Have them sort the objects directly onto the bar graph using the dry-erase board as the base with an x-axis and a y-axis. For example, if student collect red, blue and yellow objects, sort them into 3 piles. Make a bar or column on the dry-erase board of these grouped items. All the red items in a row or column on the graph one on top of each other. All of the blue items in the next row or column, and so on.

Early Finishers

Provide students with a bin of pattern blocks. Work in pairs. Each student will pull out two hands full of pattern blocks and make a pile between them. Students will then sort the pattern blocks by color/shape. Then, the students will count the number of each and make a bar graph on their dry-erase board. Model the structure of the bar graph for students to copy onto their dry-erase boards.

Challenge and Explore

Provide students with a story problem to graph. For example, “Jacob has 3 red shirts, Jack has 4 yellow shirts, and Isaac has 7 blue shirts. Make a bar graph that shows the number of each color of shirts”. Have students draw the bar graph on their dry-erase boards.

Ask Students

1. Let’s create a bar graph as a class. What is everyone’s favorite color?

[create a bar graph on the board charting everyone’s favorite color and discuss.]

2. Why do we use bar graphs? How do they help us?

[Bar graphs help us see which thing is the most and which thing is the least. They use bars to show us, and it’s easy to understand.]

Assess

Provide students with a pre-filled bar graph about favorite shapes displaying the following information: Circle: 8, Square: 6, Triangle: 10, Star: 4

Ask students

5

1. Which shape is liked the most? [Triangle]

2. Which shape is liked the least? [Star]

3. How many students like the shape circle? [8]

4. How many students like the shape square? [6]

Common Errors

Students may switch up what should be named on the left side of the bar graph and place numbers instead of objects there. Be sure to model for them when they are making their own bar graphs.

Objective and Learning Goals

y Identify pennies.

y Add the value of pennies to find the sum.

Vocabulary

y Add - to bring two or more numbers together to make a total; counting up to make more

y Penny - a coin that has the value of 1 cent in the U.S.

y Sum - the answer, or result, when adding numbers

Materials

y Dominoes

y Dry-erase boards

y Dry-erase markers

y One-dollar bill

y Pencils or crayons (brown)

y Pennies (10 per student)

Pre-Lesson Warm-up Guiding Questions

Bring students to the center of the room and make a circle. Pass around a 2-3 bags of coins for them to look at. Ask them questions about what they notice about the coins. Lead them in recognizing that the penny is a different color. Introduce the general value of the coins that you use, but emphasize that pennies are worth 1 cent, like the number 1.

Guiding Questions

1. What does a penny look like? [larger than a dime, smaller than a nickel and quarter. Copper or brown in color]

2. What is the value of the penny? [1 cent]

3. When can you use a penny or pennies? [to buy items that do not cost a lot like a piece of candy]

Introduce the Lesson (Try it Together)

Say: “Look at the picture of the penny next to Flash. Underneath the penny is the number 1 and the cents sign. We use this sign when we write about coins less than a dollar.” Use of the cents sign will be explored more thoroughly in Level A. Then, take a look at the Let’s Learn and ask how many pennies does Flash have? [4] Emphasize that this is 4 cents.

Continue working in this section by counting on the number of pennies and tracing the number below the pennies. Continue practicing counting the pennies before tracing the numbers. In the Try it Together section, have students count and write the number of pennies. In the independent practice pages, students will need to circle pennies, color pennies and write the sum or total amount of pennies. Use a brown crayon to color. Review that the sum means the total when we add numbers together.

Activity

Provide a bag of pennies to each student. Allow them time to really examine the pennies. Then, have students use the pennies to count by 1s from 0 - 10, then count by 2s to from 0-10, and then to create 2 equal groups. Have students place their pennies back in their bag and remind them that each bag has 10 pennies in there. Ask students: “If we were to skip count by 10, we would have [start with 10], 20, 30, 40, 50, 60, 70, 80, 90, 100. What happens when we get to 100?” [the total would be 1 dollar, they may or may not be able to answer this, but show them a dollar bill]

1 2 2 2 3 3 3 4 4 4 5 5 6 6 7 7 8 9

Struggling Learners

Provide students with a bag of pennies. Have the students pull out 1 penny at a time. On their dry-erase board, they write 1, then 2, then 3 as they pull out each penny. Start with 1-9, then 10-19.

Early Finishers

Provide students with a bin of dominoes. Work in pairs. Students each pull out one domino and turn it horizontally. Look at the dots on the domino. The left set of dots is the first addend. The right set of dots is the second addend. Note that if there are no dots in one section, the addend is zero. Write their addition sentence on their dry-erase boards. Have students represent that addition sentence with pennies before finding the sum. Then find the sum. Compare the amount of dots on the domino to the amount of pennies.

Challenge and Explore

Place students in groups of 2. Provide each group with a bag of pennies. Have 1 student pull an amount from the bag and say, I have ___ pennies. If you have the same amount, we would have ___ altogether. Have students take turns repeating the process.

Ask Students

1. What did you learn about finding the sum of pennies? [Finding the sum means adding up all the pennies to see how many there are in total.]

2. Can you think of a real-life situation where you might use pennies or count them, like we did in our lesson? [We might use pennies to buy something from a vending machine or count them to save money in a piggy bank.]

Assess

Have students describe what a penny looks like, by asking the following question: Describe what a penny looks like. [brown, larger than a dime or smaller than a nickel in size, may describe images or dates of a penny]

Ask students to write on their dry-erase board, what is the value of 7 pennies? [7 cents]

Common Errors

Students may count the first penny as 0 instead of 1. They may wrongly identify a dime and penny since the dime is smaller.

Objective and Learning Goals

y Identify dimes.

y Add the value of dimes to find the sum.

Vocabulary

y Add - to bring two or more numbers together to make a total; counting up to make more

y Dime - a coin that has the value of 10 cents in the U.S.

y Sum - the answer, or result, when adding numbers

Materials

y Dimes (10 per student)

y Dry-erase boards

y Dry-erase markers

y Pencils or crayons

y Pennies (10 per student)

Pre-Lesson Warm-up Guiding Questions

Bring students to the center of the room and make a circle. Pass around a 2-3 bags of coins for them to look at. Ask them questions about what they notice about the coins. Lead them in recognizing that the dime is silver and is smaller than all other coins. Introduce the general value of the coins that you use, but emphasize that dimes are worth 10 cents as in the number 10.

Guiding Questions

1. What does a dime look like? [smallest coin. Silver in color] 2. What is the value of the dime? [10 cents]

Introduce the Lesson (Try it Together)

Then, take a look at the Let’s Learn. Say: “Look at the picture of the dime next to Flash. Underneath the dime is the number 10 and the cents sign. We use this sign when we write about coins less than a dollar.” Use of the cents sign will be explored more thoroughly in Level A. Now ask how many dimes does Flash have? [5] Emphasize that this is 50 cents, skip counting by 10. Write 50.

Continue working in this section by counting on the number of dimes and tracing the number below the dimes. Continue practicing counting the dimes before tracing the numbers. In the Try it Together section, have students count by 10s and write the numbers. In the independent practice pages, students will need to circle the dimes, color the dimes and write the sum of the dimes. Use a gray crayon to color. Review that the sum means the total when we add numbers together.

Activity

Provide a bag of dimes to each student. Allow them time to really examine the dimes. Then, have students use the dimes to count by 10s from 0 - 100. Have students place their dimes back in their bag and remind them that each bag has 10 dimes inside. Ask students: “If dimes are 10 cents each and we have 10 dimes in a bag, how much is that worth?” [the total would be 1 dollar, they may or may not be able to answer this, but show them a dollar bill]

Struggling Learners

Provide students with a bag of dimes. Have the students pull out 1 dime at a time. On their dry-erase board, they write 1 dime is 10 cents, then 2 dimes is 20 cents, then 3 dimes is 30 cents as they pull out each dime. This can be done for 1-9 dimes.

Early Finishers

Provide students with a deck of cards from 0-9 and a bag of 9 dimes. Allow students to work in pairs. Students each pull 1 card and this number represents the number of dimes. Each student starts at 0 and counts the value of that number of dimes. If the card says 3, then the student would write 10, 20, 30 to represent the value of 3 dimes.

Challenge and Explore

Place students in groups of 2. Provide each group with a bag of pennies and dimes. Have 1 student pull an amount from the bag and say, I have ___ pennies and ___ dimes, how much do I have? Have students take turns repeating the process.

Ask Students

Can you think of a real-life situation where you might use dimes or count them, like we did in our lesson? [We might use dimes to buy something from a store or count them to save money in a jar.]

Assess

Have students describe what a dime looks like, by asking the following question: Describe what a dime looks like. [silver or grey, smallest coin in size, may describe images or dates of a dime]

Ask students to write on their dry-erase board, what is the value of 7 dimes? [70 cents]

Common Errors

Students may count the value of the first dime as 0 or 1 instead of 10. Also, students may confuse the dime and penny since the dime is smaller and the penny is larger in size but not in value.

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