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F Level

Lighthouse

Math

Basic Edition

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LEVEL F

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©Copyright 2021 Lighthouse Curriculum Inc. All rights reserved. Lighthouse Math Level F • ISBN 978-1-955773-99-7 No part of this publication may be reproduced, stored in a retrieval system, stored in a database and/or published in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. To obtain permission to use portions of material from this publication, please contact Lighthouse Curriculum. 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 Color coded pages Easy to find tabs at the top and bottom of the Lesson Page and Exercise Page Daily review at the beginning of every lesson to provide review of previous skills Vocabulary at the bottom of the page with important terms and definitions Learn and Connect introduces the lesson with real life situations, illustrations and helpful hints Apply provides problems for the teacher and the students to practice together Practice is a full page of exercises for students to practice the skills and concepts they have learned Tabs on the top of each page allow you to find chapters and lessons easily

Say “AND” at the decimal point

Call outs and Hints help remind students of important steps and give them clues

1 2 Clear, worked out examples 21 3�32=3

Challenge

Challenge problem solving or challenges to extend and enrich student learning

Review for every chapter

Assessment provided for every chapter

Hi, my name is Flash! Welcome to the Lighthouse Math Curriculum! Here is a list of items that will help as you navigate through the book!

A better way to teach Dear Educator, Welcome to the Lighthouse Math Curriculum! What makes our curriculum so unique? Lighthouse Math uses a scaffolded approach to learning and mastering math skills. When provided with a solid foundation, students can retain more information and prepare for the next level of skills. Instead of separate workbooks and textbooks, students have everything they need built into one place: a soft covered book containing 14 chapters, comprised of 8 lessons per chapter, with each lesson containing review, new skills, and practice. All lessons include step by step instructions for clarity, giving all teachers neophyte as well as seasoned - the tools for success. The books are custom illustrated, providing a vibrant learning experience. They 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. We, at Lighthouse CurriculumTM, are committed to providing support and guidance to our educators. We look forward to hearing from you and are available to answer any questions that you may have.

Sincerely,

Lighthouse Curriculum Team

Table of Contents CHAPTER 1 W hole Number Operations Addition Facts and Properties..........................................................14 Subtraction Facts............................................................................ 16 Multiplication Facts........................................................................ 18 Division Facts.................................................................................20 Exponents.....................................................................................22 Order of Operations....................................................................... 24 Problem Solving.............................................................................26 Review..........................................................................................28

CHAPTER 2 Place Value through Trillions Place Value into the Trillions............................................................32 Expanded Notation........................................................................ 34 Compare and Order........................................................................36 Add Large Numbers.......................................................................38 Subtract Large Numbers................................................................. 40 Add and Subtract Money............................................................... 42 Estimate Sums and Differences....................................................... 44 Review......................................................................................... 46 Lighthouse Math

Table of Contents

CHAPTER 3 Multiplication of Whole Numbers Multiplication x 10..........................................................................50 Estimating Products........................................................................52 Multiply by One Digit.................................................................... 54 Multiply Up to Six Digits by One Digit..............................................56 Multiply by 2 Digit Factors..............................................................58 Multiply by 3 Digit Dactors..............................................................60 Multiply 3 and 4 Digit Factors..........................................................62 Review......................................................................................... 64

CHAPTER 4 Division of Whole Numbers Divide By Multiples of 10................................................................68 1 Digit Divisors...............................................................................70 Divide Up To 6 Digit Dividends........................................................ 72 Zero in the Quotients......................................................................74 Interpreting Remainders.................................................................. 76 Division Using Estimation................................................................ 78 Divide by One and Two Digits.........................................................80 Problem Solving Review..................................................................82

CHAPTER 5 Multiplication and Division of Larger Numbers Finding Averages............................................................................86 Multiplying 1, 2, 3 Digits.................................................................88 Divide By 1 and 2 Digit Divisors........................................................90 Mixed Multiplication and Division....................................................92 Inverse Operations: Multiplication and Division................................. 94 Order of Operations........................................................................96 Problem Solving: Division and Multiplication.....................................98 Review........................................................................................100 8

Table of Contents

Lighthouse Math

CHAPTER 6 Basic Fraction Concepts Factors and Greatest Common Factor (GCF).....................................104 Least Common Multiple (LCM)...................................................... 106 Prime Factorization....................................................................... 108 Equivalent Fractions...................................................................... 110 Simplest Form...............................................................................112 Improper and Mixed Fractions....................................................... 114 Order and Compare Fraction......................................................... 116 Problem Solving Review................................................................ 118

CHAPTER 7 Adding and Subtracting Fractions Estimating With Fractions............................................................. 122 Adding Fractions with Like Denominators....................................... 124 Adding Fractions with Different Denominators................................ 126 Add Mixed Numbers with Unlike Denominators.............................. 128 Subtract Fractions with Like Denominators...................................... 130 Subtract Fractions with Unlike Denominators.................................. 132 Subtract Mixed Numbers with Unlike Denominators........................ 134 Review........................................................................................ 136

CHAPTER 8 Multiplying and Dividing Fractions Multiply Fractions.........................................................................140 Multiply Fractions with Factoring................................................... 142 Multiply Mixed Numbers..............................................................144 Reciprocals.................................................................................. 146 Divide Fractions and Wholes......................................................... 148 Divide Fractions........................................................................... 150 Divide Mixed Numbers................................................................. 152 Review........................................................................................ 154 Lighthouse Math

Table of Contents

CHAPTER 9 Decimal Basics: Adding and Subtracting Decimals Decimal Place Value...................................................................... 158 Compare and Order Decimals........................................................ 160 Rounding Decimals....................................................................... 162 Estimate Decimal Sums and Differences.......................................... 164 Adding Decimals.......................................................................... 166 Subtracting Decimals.................................................................... 168 Subtracting Decimals - Add to Check Answers............................... 170 Review........................................................................................ 172

CHAPTER 10 Multiplying and Dividing Decimals Multiply Decimals by Whole Numbers........................................... 176 Multiplying Decimals by Decimals.................................................. 178 Multiplying Decimals with Zeros.................................................... 180 Dividing Decimals by Whole Numbers........................................... 182 Dividing Decimals with Zeros in the Quotient.................................. 184 Dividing Decimals by Decimals...................................................... 186 Extending Dividing Decimals......................................................... 188 Review........................................................................................ 190

CHAPTER 11 Geometry Converting Units of Length ........................................................... 194 Customary Units - Weight and Capacity......................................... 196 Using a Formula........................................................................... 198 Rectangles - Perimeter and Area...................................................200 Triangles - Perimeter and Area......................................................202 Circumference of a Circle.............................................................. 204 Find the Area of a Circle................................................................206 Review........................................................................................208 10

Table of Contents

Lighthouse Math

CHAPTER 12 Types of Shapes, Lines and Angles Basic Geometric Vocabulary........................................................... 212 Classifying Polygons..................................................................... 214 Classifying Triangles..................................................................... 216 Classifying Quadrilaterals............................................................... 218 Congruent Polygons......................................................................220 Parts of a Circle............................................................................ 222 Transformations...........................................................................224 Review........................................................................................ 226

CHAPTER 13 Fractions, Decimals and Percents Writing Ratios..............................................................................230 Equal Ratios................................................................................. 232 Proportions..................................................................................234 Similar Polygons........................................................................... 236 Percents...................................................................................... 238 Percents, Fractions, Decimals........................................................ 240 Compare and Order - Percents, Fractions, Decimals........................242 Review....................................................................................... 244

CHAPTER 14 Review of Concepts Learned Order of Operations......................................................................248 Multi-Digit Multiplication.............................................................250 Multi-Digit Division...................................................................... 252 Fractions and Mixed Numbers - Add/Subtract...............................254 Fractions and Mixed Numbers - Multiply/Divide............................ 256 Decimals - Add/Subtract/Multiply/Divide.................................... 258 Ratios and Percents......................................................................260 Geometry.................................................................................... 262 Lighthouse Math

Table of Contents

Chapter 1 NYS NG Standards NY-3.NBT.2 NY-3.OA.3 NY-3.OA.4 NY-3.OA.5 NY-3.OA.6 NY-3.OA.7a

NY-3.OA.8 NY-3.OA.8b NY-4.NBT.4 NY-5.OA.1 NY-6.EE.1

CC Standards 3.NBT.A.2 3.OA.A.3 3.OA.A.4 3.OA.B.5 3.OA.B.6 3.OA.C.7

3.OA.D.8 4.NBT.B.4 4.NBT.B.5 4.NBT.B.6 5.OA.A.1 6.EE.A.1

In Chapter 1 we review and learn about

Whole Number Operations We will learn the different properties for addition and multiplication. We will also review our basic addition, subtraction, multiplication and division facts, properties of exponents, the order of operations, and a four step problem solving strategy. • Addition facts and properties • Subtraction facts • Multiplication facts and properties © Lighthouse Curriculum. Copying strictly prohibited.

• Division facts • Exponents • Order of operations • Problem solving • Mixed review

Chapter 1-1 Addition Facts and Properties Daily Review

Solve.

1. 8 + 3 =

2. 4 + 5 =

3. 7 + 8 =

4. 9 + 9 =

Learn and Connect Frank left his apartment and walked 6 blocks to the library, then 5 more blocks to the market. If he returns home the same way, how many blocks will he have to walk from the market to his apartment?

Apply Find each sum. Check by adding in reverse order. 1. 8 +2 10

2 +8 10

6. 7 +4

2. 3 +9

3. 5 +7

4. 9 +2

5. 6 +6

7. 4 +0

8. 2 5 +4

9. 6 2 +8

10. 8 7 +2

Vocabulary Commutative Property - changing the order of the addends does not change the sum Associative Property - changing the grouping of addends does not change the sum Identity Property - the sum of zero and any number is that number 14

Level F

Chapter 1

Lesson 1

Lighthouse Math

Exercise 1-1 Name Find each sum. 1.

7+5=

4+8=

3+2=

6+0=

6+6=

8+5=

2+7=

9+4=

4+7=

10. 1 + 6 =

11. 3 + 9 =

12. 5 + 5 =

13. 7 + 8 =

14. 5 + 2 =

15. 0 + 5 =

16. 3 + 6 =

17.

18. 8 + 9 =

19. 6 + 5 =

20. 5 + 4 =

3+1=

21. 8 +8

22. 7 +9

23. 2 +7

24. 6 +2

25. 4 +6

26. 7 +7

27. 4 +9

28. 1 5 +3

29. 4 0 +6

30. 1 7 +5

31. 0 +0

32. 5 +6

33. 3 2 +9

34. 8 5 +1

35. 2 2 +2

Add. Check by adding in reverse order.

Challenge Solve each problem. 36. How can changing the order of the addends help with solving addition problems?

37. There were 6 apples, 5 oranges, and 2 bananas in the fruit bowl. How many pieces of fruit were there in all?

Lighthouse Math

38. James read 3 books last week. This week, he read 3 more books. How many total books did he read?

Level F

Chapter 1

Exercise 1

Chapter 1-2 Subtraction Facts Daily Review

Find each difference.

1. 8 – 3 =

2. 9 – 5 =

3. 8 – 7 =

4. 6 – 6 =

Learn and Connect Joshua is buying a new hammer for a project. He pays with a twenty-dollar bill. How much change will he receive? To find the difference, we subtract the cost of the hammer from the bill that Joshua gave the clerk. –

Joshua receives

in change.

Using inverse operations and fact families can help us check our answers: 20 – 7 = 13

13 + 7 = 20

20 – 13 = 7

7 + 13 = 20

Apply Solve. Check by using the inverse operation. 1. 7 –2 5

5 +2 7

6. 13 – 1

2. 19 – 3

3. 8 – 5

4. 6 – 3

5. 8 – 6

7. 7 –4

8. 15 – 4

9. 6 – 2

10. 9 – 6

Vocabulary Inverse Operation - opposite operations that “undo” each other; subtraction is the opposite of addition Fact Family - a group of math facts that use the same numbers and inverse operations such as addition and subtraction

Level F

Chapter 1

Lesson 2

Lighthouse Math

Exercise 1-2 Name Find each difference. 1.

12 – 5 =

14 – 8 =

3–2=

6–0=

16 – 6 =

8–5=

12 – 7 =

9–4=

14 – 7 =

10. 11 – 6 =

11. 13 – 9 =

12. 5 – 5 =

13. 17 – 8 =

14. 5 – 2 =

15. 10 – 5 =

16. 13 – 6 =

17.

18. 18 – 9 =

19. 16 – 5 =

20. 12 – 4 =

15 – 4 =

21. 18 – 6

22. 7 –5

23. 12 – 7

24. 16 – 8

25. 14 – 4

26. 7 –7

27. 9 –4

28. 15 – 3

29. 17 – 6

30. 11 – 5

31. 10 – 0

32. 13 – 6

33. 12 – 9

34. 8 –1

35. 8 –2

Challenge Solve each problem. 36. How can inverse operations help with solving addition or subtraction problems?

37. Mike had 6 coins and John had 13 coins. How many more coins did John have than Mike?

Lighthouse Math

38. Nathan had 16 math problems to complete for homework. He finished 8 before dinner. How many problems were left to complete?

Level F

Chapter 1

Exercise 2

Solve. Check by using the inverse operation.

Chapter 1-3 Multiplication Facts Daily Review

Find each product.

1. 8 � 3 =

2. 9 � 5 =

3. 8 � 7 =

4. 6 � 6 =

Learn and Connect Leo and his dad are planting a small garden. They plant 3 rows of beans with 12 bean plants in each row. How many bean plants did they plant altogether? 3 rows � 12 bean plants =

plants

or 12 bean plants � 3 rows =

plants

We can use the commutative property of multiplication to make it easier to find products.

Apply

Find each product. Check by multiplying the reverse order. 1. 3 �4 12

4 �3 12

6. 9 �1

2. 5 �4

3. 6 �6

4. 7 �3

5. 3 �6

7. 4 �4

8. 8 �0

9. 6 �2

10. 2 �5

Find each product. 11. 2 � (3 � 2) =

12. (6 � 3) � 1 =

13. 3 � (3 � 3) =

14. (5 � 2) � 5 =

Vocabulary Commutative Property - two factors can be multiplied in any order Associative Property - grouping the factors does not change the product Identity Property - the product of any factor multiplied by one is that number Zero Property - any factor multiplied by zero is zero 18

Level F

Chapter 1

Lesson 3

Lighthouse Math

Exercise 1-3 Name Find each product. 1.

2�5=

4�6=

3�2=

9�0=

5�5=

7�2=

10 � 8 =

3�6=

(2 � 7) � 2 =

10. 1 � (6 � 2) =

11. 8 � 9 =

12. 4 � 5 =

13. 9 � 8 =

14. 5 � 2 =

15. (2 � 5) � 5 =

16. 6 � (3 � 2) =

17.

18. 2 � (3 � 6) =

19. 2 � (8 � 5) =

20. 4 � 9 =

(5� 3) � 4 =

21. 7 �6

22. 4 �4

23. 8 �6

24. 2 �9

25. 3 �3

26. 7 �7

27. 8 �3

28. 4 �2

29. 5 �9

30. 6 �7

31. 4 �0

32. 3 �6

33. 4 �9

34. 8 �1

35. 5 �7

Challenge Solve each problem. 36. H ow can the commutative and associative properties help with solving multiplication problems?

37. One box contains 6 donuts. How many donuts are in 4 boxes?

Lighthouse Math

38 . A cake is cut into eight slices. Bob orders 5 cakes for 20 guests. Will he have enough cake for each guest to eat two slices?

Level F

Chapter 1

Exercise 3

Solve. Check by using the inverse operation.

Chapter 1-4 Division Facts Daily Review

Find each quotient.

1. 4 ÷ 2 =

2. 15 ÷ 5 =

3. 6 ÷ 3 =

4. 8 ÷ 8 =

Learn and Connect Jane is helping with a bake sale to raise money for new books. She baked 4 dozen cookies and plans to package 6 cookies per bag. How many bags will she need? First, we need to know the total number of cookies: 1 dozen = 12 cookies 12 � 4 = Now, divide the total number of cookies by the number of cookies per bag: 48 ÷ 6 = Check using the inverse operation: �

Jane will need 8 bags.

Apply Find each quotient. 1. 12 ÷ 2 =

2. 7 ÷ 1 =

3. 0 ÷ 9 =

4. 30 ÷ 5 =

5. 56 ÷ 7 =

Find each quotient. Check by using the inverse operation. 6.

6)18

5)35

4)24

2)16

10.

3)15

Write each missing factor. 11. 2 �

= 16

12.

� 5 = 25

13. 8 �

= 32

14. 3 �

= 21

15. 4 �

= 36

Vocabulary Inverse Operation - opposite operations that “undo” each other; multiplication is the opposite of division 20

Level F

Chapter 1

Lesson 4

Lighthouse Math

Exercise 1-4 Name Find each quotient. 1.

16 ÷ 4 =

24 ÷ 6 =

6 ÷2 =

9÷1=

16 ÷ 8 =

27 ÷ 3 =

20 ÷ 4 =

32 ÷ 8 =

36 ÷ 9 =

10. 12 ÷ 3 =

11. 72 ÷ 8 =

12. 24 ÷ 3 =

13. 56 ÷ 7 =

14. 35 ÷ 5 =

15. 42 ÷ 7 =

16. 18 ÷ 6 =

Divide. Check by using the inverse operation.

17.

7)49

18.

2)16

19.

6)42

20.

6)18

21.

9)45

22.

5)20

23.

8)64

24.

8)40

25.

7)7

26.

9)81

27. 5 �

= 30

28. 3 �

= 24

29.

� 8 = 56

30.

� 2 = 18

31. 9 �

= 27

32. 2 �

= 20

33.

� 4 = 16

34.

�6=6

Find the missing factor.

Challenge Solve each problem. 35. How can inverse operations help with solving division problems?

36. There are 48 chairs and 8 tables. How many chairs would be at each table if the tables all had the same amount?

Lighthouse Math

Level F

37. James wants to share 24 jelly beans evenly between his 3 friends and himself. How many jelly beans will each person get?

Chapter 1

Exercise 4

Chapter 1-5 Exponents Use the inverse operation to find the missing factor.

Daily Review 1. 9 �

= 36

3. 4 �

� 5 = 35

= 32

� 8 =56

Learn and Connect Adam has completed a model of the solar system as a science project. He wants to show the distance of each planet from the sun, but doesn’t have enough room on his labels to write out such large numbers. His teacher shows him a way to use exponents to write out the distances.

Exponents are a way to express a product, especially when the number is extremely large. Using a repeated factor, called a base, we can express numbers without having to write so many zeros. Let’s look at powers of 10 on the table below: FACTORED FORM

EXPONENT FORM

STANDARD FORM

10 x 10

102

100

10 x 10 x 10

103

1,000

10 x 10 x 10 x 10

10,000

10 x 10 x 10 x 10 x 10

100,000

Apply Write in exponent form. 1.

3�3=

2�2�2�2=

6 squared =

the 5th power of 7 =

33 =

4�4�4=

Write as standard form. 6.

42 =

23 =

5 x 102 =

10.

2 x 10 x 10 x 10 =

Vocabulary Exponent - shows how many times the same factor is multiplied by itself, also referred to as “power” (i.e the fourth power of “x” is x4) Base - the factor that is being multiplied Squared - refers to the second power exponent or x2 Cubed - refers to the third power exponent or x3 22

Level F

Chapter 1

Lesson 5

Lighthouse Math

Exercise 1-5 Name Write in exponent form. 1.

5 squared =

3. the fourth power of 6 =

9�9�9=

5. the 7th power of 9 =

4�4=

7. 5 to the fifth power =

2�2�2�2=

10. 12 squared =

11. 8 cubed =

12. the 6th power of 3 =

13. the 7th power of 7 =

14. 5 � 5 � 5 =

15. 6 to the 2nd power =

16. 2 � 2 � 2 � 2 � 2 � 2 � 2 =

17.

18. 45 � 45 =

3�3�3=

8�8�8=

16 cubed =

19. 62 =

20. 3 � 10 � 10 =

21. 43 =

22. 3 � 3 � 3 � 3 =

23. 9 � 104 =

24. 2 squared =

25. 103 � 4 =

26. 3 cubed =

27. 6 to the fourth power =

28. 4 � 101 =

29. 7 � 10 � 10 � 10 =

30. 82 =

Write in standard form.

Challenge Look at the examples below and identify the patterns for multiplying and dividing exponents with the same base: 24 � 22 = (2 � 2 � 2 � 2) � (2 � 2) = 26 = 64 25 ÷ 22 = (2 � 2 � 2 � 2 � 2) ÷ (2 � 2) = 23 = 8 Use the pattern of exponents to find the answer. 31. 2 2 � 23 = (2 � 2) � (2 � 2 � 2) =

Lighthouse Math

32. 24 ÷22 = (2 � 2 � 2 � 2) ÷ (2 � 2) =

Level F

Chapter 1

Exercise 5

Chapter 1-6 Order of Operations Daily Review

Write the following in exponent form.

1. 5 cubed =

2. 4 � 4 � 4 � 4=

3. 7 to the power of 5 =

4. 6 squared =

Learn and Connect Mrs. Morten wrote the following problem on the board: 2 � (12 – 3 ) + 42 Half of the class got 37 as the answer and the other half got 34. Which half was correct? The Order of Operations is a set of rules that tells you the order in which operations must be solved. To get the correct answer, you must follow these rules: First, do all operations in parentheses if there are any. Next, use the exponents if there are any.

2 � (12 – 3 ) + 42

Then, do all multiplication and division in order from left to right.

2 � 9 + 42 2 � 9 + 16

Last, do all of the addition and subtraction in order from left to right.

18 + 16 34

PEMDAS helps us remember the order of operations.

34 is the correct answer!

Apply Simplify the expression using the order of operations. 1.

(53 – 3) ÷ 2 + 32

4. (9 + 3)2 + (15 ÷ 3)

2. 4 � (13 – 5 ) + 22

3. (10 � 3 – 42) + 9

5. (10 – 3)2 + (20 ÷ 5 )

6. 5 + (4 – 2) + 32 – 4 � 2

Vocabulary Order of Operations - a set of rules that tells you the order in which operations must be solved PEMDAS - a way to remember the order of operations; Parentheses Exponents Multiply Divide Add Subtract

Level F

Chapter 1

Lesson 6

Lighthouse Math

Exercise 1-6 Name Simplify the expression using the order of operations. 1.

(17 – 4) � 14 – 5

(8 + 3) + 15 ÷ 3

(17 + 7) � 14 + 6

(15 + 21 – 6) ÷ 3

8 � ( 9 – 2 ) + 72

7 x (10 – 6 ) + 62

(12 – 4 )2 + 10 ÷ 5

(51 – 3 ) ÷ 6 + 62

(9 + 2 )2 + 20 ÷ 4

10. 6 � (9 + 6) + 32

11. 2 � ( 8 + 2 ) – 22

12. (75 – 52) ÷ (7 – 2)

13. 36 – 4 ÷ 8 + 52 = 29

14. 92 + 15 ÷ 5 = 84

15. 34 – 6 ÷ 14 + 72 = 51

16. 4 � 7 + 82 – 4 = 88

17.

18. 5 � 9 – 6 + 52 = 40

19. 28 – 22 ÷ 13 – 7 = 4

20. 5 � 3 + 32 ÷ 4 = 6

8 � 8 – 2 + 52 = 73

21. 8 +34 – 2 ÷ 8 + 52 = 30

Challenge Place the correct symbol (+, �, x, or ÷) to make the statement true. 22. (34 25. 4

2) ÷ 2 + 27 = 146

2 � ( 9 + 2 ) = 88

Lighthouse Math

23. (13 +21 � 4) 26. (14 � 5)

Level F

2 = 15

24. (11 +37

(6 � 3 ) = 16

15 ÷ 3 = 14

27. 7 � 23

( 5 + 10) = 840

Chapter 1

Exercise 6

Put the parentheses in the correct place to make the statement true.

Chapter 1-7 Problem Solving Daily Review 1.

Use order of operations to solve. 2. 62 – (3 � 2) – 4 =

(4 � 5) + 12 =

3. (12 ÷ 3)2 + (3 + 5) =

Learn and Connect Mason and Max went to the bakery. They bought 21 dozen donuts. How much did they spend at the bakery? Use a Four Step Plan: Understand: What do we know? What are you trying to find? Read the problem completely. Then, re-word the question as a statement: • We know that they bought

donuts.

• We know that donuts cost

Plan: How will you find it? What strategy will you use to help you answer the question? We can use multiplication. Do: Follow your plan or strategy.

1 2 dozen = 6 donuts

Donuts are $0.75 each 6 x $0.75 = $4.50. Answer: They spent $4.50 at the bakery.

Check: Does your answer make sense? You can rework the problem, use an inverse operation, check for reasonableness. Use the inverse operation: $4.50 ÷ 6 = $0.75

Apply Seth wants several different color plates for his birthday. Seth wants to get 108 green plates, 120 orange plates, and some amount of black plates. In total, Seth wants 312 plates, so how many black plates should he get? Understand: There are

green plates,

We want to know: Seth needs to buy

orange plates, and

total plates.

plates.

Plan: We can the number of green and orange plates, then total number of plates.

that from the

Do: 1 08 + 120 = 312 – 228 = Answer: Seth needs to buy black plates. Check: Add up each color of plate to see if it matches the total. 108 + 120 + 84 = 312

Level F

Chapter 1

Lesson 7

Lighthouse Math

Exercise 1-7 Name Four Step Problem Solving Strategy 1. Understand: What are your trying to find? 2. Plan: How can you find it?

3. Do: Follow your plan. 4. Check: Does your answer make sense?

Use the four step problem solving strategy to solve the following. 1. Mitchell has 26 books. Ben has 4 times more books than Mitchell. How many books does Ben have? 2. T here are 17 children in the classroom, and each student will get 3 pencils. How many pencils will the teacher have to give out? 3. M ason walks 6 blocks to the coffee shop, then 3 blocks to the library. After that, he walks 2 blocks to the market and 9 blocks back to his apartment. How many blocks did he walk in all?

4. Aaron and his family are planning to visit the Museum of Natural History. The admission price is $23 for each adult and $13 for each child. If there are two adults and three children going, how much is the total cost of admission? 5. Tom has eleven blue marbles. James has five times more blue marbles than Tom. How many blue marbles does James have? 6. A cake recipe calls for 4 eggs. Frank would like to make three cakes. If he buys one dozen eggs, will he have enough eggs to triple the recipe?

Challenge 7. Samuel earns $12.00 an hour cleaning houses. If he works from 8:00 am to 12:00 pm, how much money will he earn? If he works the same hours five days a week, how much will he earn in four weeks?

Lighthouse Math

Level F

Chapter 1

Exercise 7

Chapter 1-8 Review Use >, <, or = to make each statement true.

Daily Review 1. 2,399

3,299

2. 102

3. 2 + 3

100

4. 10000

3+2

10 � 10 � 10

Learn and Connect In this chapter, you have learned and reviewed whole number operations and properties for addition, subtraction, multiplication, and division. You have also learned about exponents and the order of operations, as well as problem solving strategies. Now it is time to review what you have learned. Reviewing and practicing what you learn will help your brain hold on to the new learning long term. Practicing old skills can also help prime your brain for the new skills you will be learning in the next lessons! As you work through this mixed review, refer back to examples in previous lessons if necessary.

Apply Add. Check using the reverse order (commutative property). 1. 23 + 15 38

15 + 23 38

4. 42 + 82

2. 6 +7

3. 12 + 8

5. 25 + 34

6. 10 + 26

Solve. Check by using the inverse operation. 7. 19 – 3 16

16 + 3 19

8. 8 –5

Level F

9. 27 – 12

Chapter 1

Lesson 8

10. 48 –24

11. 36 – 9

Lighthouse Math

Exercise 1-8 Name Find each product. Check using the reverse order (commutative property). 1.

8�7=

9�7=

12 � 10 =

4�8=

5. 5 �3

6. 12 �5

7. 2 �4

8. 12 �4

10. 2 � (3 � 3) =

11. (5 � 6) � 3 =

12. 2 � (6 � 5) =

(3 � 4) � 2 =

Find each quotient. Check using the inverse operation. 13.

7)42

14.

2)14

15.

6)60

16.

5)30

17.

9)45

18.

5)40

19.

8)72

20.

10)40

21.

12)60

22.

20)20

Write each of the following in exponent form. 24. 3 � 3 � 3 � 3 � 3 =

25. 2 � 2 � 2 =

Write each of the following in standard form. 26. 52 =

27. 25 =

28. 23 =

29. 3 � 103 =

Simplify the expression using the order of operations. 30. (42 - 3 ) ÷ 3 + 42

31. 3 � (22 - 4 ) + 32

32. (10 � 4 - 52) + 9

33. (5 + 2)2 + (15 ÷ 3)

Challenge Use the four step problem solving strategy to solve the following. 34. K ane buys a bag of apples for $3.00, eggs for $2.75, and a gallon of milk for $4.35. He pays with a $20 bill. How much change did he receive?

Lighthouse Math

Level F

Chapter 1

Exercise 8

23. 7 � 7 =

Chapter 2 NYS NG Standards NY-3.OA.8 NY-3.NBT.1 NY-3.NBT.2 NY-4.NBT.1 NY-4.NBT.2a

NY-4.NBT.2b NY-4.NBT.3 NY-4.NBT.4 NY-5.NBT.1 NY-5.NBT.7

CC Standards 3.0A.D.8 3.OA.D.9 3.NBT.A.2 4.NBT.A.1 4.NBT.A.2

4.NBT.A.3 4.NBT.A.4 5.NBT.A.1 5.NBT.B.7

In Chapter 2 we review and learn about

Place Value into the Trillions We will use place value to learn about expanded notation and to gain mastery of addition and subtraction with larger numbers.

• Place value into trillions • Expanded notation • Compare and order • Add larger numbers • Subtract larger numbers • Add and subtract money • Estimate sums and differences • Mixed review We will be solidifying the concept of place value as a foundation that we can apply to more complex operations. Fluently adding and subtracting money is an important life skill. These skills will help prepare students for more complex mathematics.

Chapter 2-1 Place Value into the Trillions Daily Review

Write the value of the bolded, blue digit.

1. 35,273,297

2. 792,172,990.029

3. 672,198,721. 123

Learn and Connect In space, we measure how far something is by using light-years. Even though the name sounds like it is a measurement of time, it is actually a measurement of distance. A light-year is the distance a beam of light travels in a single Earth year. One light-year equals 5,878,625,370,000 miles. To read this number correctly, start by writing the number in the place value chart below.

Therefore, a light-year is equal to five

six hundred twenty-five

, three hundred seventy

ONES

HUNDREDS

, eight hundred seventy-eight

TENS

ONES THOUSANDS

TEN THOUSANDS

HUNDRED THOUSANDS

THOUSANDS MILLIONS

TEN MILLIONS

HUNDRED MILLIONS

MILLIONS BILLIONS

TEN BILLIONS

HUNDRED BILLIONS

BILLIONS TRILLIONS

TEN TRILLIONS

HUNDRED TRILLIONS

TRILLIONS

Apply Write the standard form of each of the following numbers. 1. Thirty-four trillion, five hundred sixty-seven billion, eight hundred ninety-seven million, six hundred thirty thousand, ninety-seven 2. Fourteen trillion, eight hundred billion, nine hundred seventy-five million, four hundred twenty-one thousand, six hundred fifty-six Write the word form of each of the following numbers. 3. 3,729,816,273,124 4. 12,267,193,002,736

Level F

Chapter 2

Lesson 1

Lighthouse Math

Exercise 2-1 Name Complete the place value chart below.

Write the digit that is in the place value for each problem. 5. Millions place? 6. Ten Trillions place? 321,499,402 325,178,902,192,321

ONES

TEN MILLIONS

Write the place value of each digit in blue. 1. 543,998,082 2. 270,562,772 3. 457,110,032,762

TENS

ONES HUNDREDS

MILLION

HUNDRED TRILLIONS

TRILLION

4. 732,990,765,543,210

7. Hundred Billions place? 432,895,201,345,811

Write each number in standard form. 8. 789 billion, 234 million, 670 thousand, 021

9. 982 million, 554 thousand, 204 10. 87 trillion, 321 billion, 543 million, 712 11. 5 trillion, 289 billion, 119 million, 378 thousand, 298 Write the values for each group of numbers to complete the short word form. 12. 78,345,219,064 78

, 345

, 219

, 064

Challenge 13. Proxima Centauri, a yellow star in the night sky, is 5 trillion, 880 billion, 293 million, 734 thousand, 034 miles away. Write this number in standard form.

Lighthouse Math

Level F

14. Bernard’s star is a red dwarf that is approximately 987,459,113,543,500 miles from the sun. Write this number in short word form.

Chapter 2

Exercise 1

Chapter 2-2 Expanded Notation Daily Review

Write the value of the bolded, blue digit.

1. 922,378,164,238,243

2. 76,482,142,537,374

3. 6,741,028,471,323

Learn and Connect Mr. Johnson gave his students the following numbered cards. He asked his students to try to make the largest number possible with the cards. Write the digits into the place value chart to determine the largest possible number.

ONES

TENS

HUNDREDS

THOUSANDS THOUSANDS

HUNDRED MILLIONS

ONES

MILLIONS BILLIONS

HUNDRED BILLIONS

TEN THOUSANDS

BILLIONS TRILLIONS

TEN TRILLIONS

HUNDRED TRILLIONS

TRILLIONS

HUNDRED THOUSANDS

MILLIONS

TEN MILLIONS

TEN BILLIONS

What is this number written in expanded form?

,000,000,000,000 + 00,000,000 +

00,000,000,000 +

0,000,000 +

0,000,000,000 +

,000,000 +

00,000 +

,000,000,000 +

0,000 +

,000 +

00 +

Apply Write the standard form of each of the following numbers. 1. 1,000,000,000,000 + 300,000,000,000 + 20,000,000,000 + 3,000,000,000 + 400,000,000 + 80,000,000 + 3,000,000 + 200,000 + 90,000 + 8,000 + 200 + 70 + 1 : 2. 8 ,000,000,000,000 + 600,000,000,000 + 70,000,000,000 + 5,000,000,000 + 300,000,000 + 80,000,000 + 9,000,000 + 700,000 + 40,000 + 6,000 + 200 + 10 + 5 : Write the expanded form of each of the following numbers. 3. 12,908,412,735,462:

Level F

Chapter 2

Lesson 2

Lighthouse Math

Exercise 2-2 Name Write the standard form of each of the following numbers. 1. 3,000,000 + 400,000 + 50,000 + 2,000 + 300 +60 +5: 2. 200,000,000 + 30,000,000 + 2,000,000+ 300,000 + 40,000 + 2,000 + 700 +60 +6: 3. 5 ,000,000,000,000 + 200,000,000,000 + 40,000,000,000 + 6,000,000,000 +700,000,000 + 40,000,000 + 3,000,000 + 200,000 + 30,000 + 4,000 + 100 +70 +8: 4. 3 00,000,000,000 + 20,000,000,000 + 4,000,000,000 + 500,000,000+ 60,000,000 +4,000,000 + 300,000 + 50,000 + 7,000 +10: 5. 2 ,000,000,000,000 + 400,000,000,000 + 5,000,000,000 + 400,000,000 + 20,000,000 + 1,000,000 + 300,000 + 60,000 + 7,000 + 600 + 80 +9: 6. 7 0,000,000,000 + 5,000,000,000 + 300,000,000 + 40,000,000 + 2,000,000 +500,000 +400 + 30 + 5: 7. 2 00,000,000,000,000 +30,000,000,000,000 + 2,000,000,000,000 + 500,000,000,000 +90,000,000,000 + 9,000,000,000 + 600,000,000 + 50,000,000 + 5,000,000 + 400,000 + 20,000 + 5,000 + 600 + 70 + 1: 8. 8 0,000,000,000 + 4,000,000,000 + 700,000,000 + 60,000,000 + 5,000,000 + 400,000 + 30,000 + 6,000 + 800 +90 + 7:

Write the expanded form of each of the following numbers. 9. 23,412,346,786:

10. 4 96,684,305,245,754:

11. 3 ,999,875,453,232:

12. 9 8,988,899,999:

Lighthouse Math

Level F

Chapter 2

Exercise 2

Chapter 2-3 Compare and Order Daily Review

Write the standard form of the number.

1. 4 ,000,000,000,000 + 200,000,000,000 + 10,000,000,000 + 3,000,000,000 + 600,000,000 + 40,000,000 + 1,000,000 + 200,000 + 30,000 + 8,000 + 500 + 30 + 4:

Learn and Connect Four students wrote down numbers on a card and held them up. If the students were placed in order from greatest to least, what would be the order of the students?

To compare, write the numbers on top of each other making sure to line up each place value. STEVE:

JAKE:

RYAN:

TIM:

Then, start at the greatest place value to the left. Decide which number is greatest. Then, continue to the next place value until all numbers are compared. Therefore, the order of the students would be:

Apply Compare the following numbers using the symbols: <, >, or =. 1. 1,345,602,346,431

1,345,723,456,210

2. 87,182,982.231

3. 21,345,602,346,431

89,343,134,112

4. 4,145,234,053,134.5

4,145,234,053,134.52

5. 43,281,273,083,172

142,837,173,002,721

6. 6,261,189,098,631

9,362,009,372

Level F

Chapter 2

Lesson 3

87,182,982.08

Lighthouse Math

Exercise 2-3 Name Compare the following numbers using the symbols: <, >, or =. 1. 5,642,357,432,193

2. 99,859,325,326,452

564,235,743,219,328

99,859,325,326,872

3. 254,342,567,892,395

254,342,567,891,236

4. 844,256,389,325

489,436,432,345

5. 65,432,739,293,342

5,432,739,293,342

6. 56,434,456,432

56,894,543

7. 7,845,276,342,109

7,845,276,342,109

8. 8,543,435

8,543,435,453

9. 645,382,394,593,235

645,382,222,436,890

10. 765,434,549,765

11. 543,546,345,287,497

543,546,345,287,497 12. 83,432,536,742

765,343,426,436 85,432,536,742

Write the number sets in order. 13. Least to Greatest: 435,423,456,786; 657,456,389,675; 214,567,348,789; 432,345,654,789 ,

14. G reatest to Least: 748,543,679,324,342; 34,432,345,432,786; 563,465,786,593,567; 67,543,679,899,453 ,

15. L east to Greatest: 342,345,567,435,346; 342,345,567,323,147; 342,345,845,678,352; 342,345,567,435,783 ,

16. G reatest to Least: 743,425,356,234,198; 743,546,432,784,937; 743,425,589,435,652; 743,645,789,547 ,

Challenge Order the following planets according to their distance from sun from least to greatest.

Lighthouse Math

Saturn = 886,700,000 miles Uranus = 1,784,000,000 miles Neptune = 2,794,400,000 miles Mars = 141,600,000 miles Jupiter = 483,600,000 miles

Level F

Chapter 2

Exercise 3

Chapter 2-4 Add Large Numbers Daily Review

Compare the following numbers using the symbols: <, >, or =.

1. 5,273,003,173,272

2. 12,672,839,298,730

5,272,643,123,489

9,984,426,102

Learn and Connect A small library has fiction books, nonfiction books, and magazines. What is the total amount of books and magazines in the library? To solve, we have to add all of the amounts. Start by lining up the digits by their place value. Then, add the numbers starting with the smallest place value to the right. 9 8 2, 8 9 2 9 7 8, 2 8 1 + 2 8, 9 7 2

Therefore, the small library has books and magazines.

Apply Add. 1. 658,306 + 132,001

2. 932,697 + 226,811

3. 883,076 + 95,216

Set up the addition problem, then add. 4. 736,283 + 372,298 =

5. 463,287 + 31,783 =

6. 389,108 + 2,893 =

7. 892,281 + 28,982 =

Level F

Chapter 2

Lesson 4

Lighthouse Math

Exercise 2-4 Name Add. 1.

732 + 84

2,718 + 695

65,920 + 8,045

25,832 + 19,554

43,284 + 65,613

384,057 + 5,872

492,713 + 62,003

632,942 + 91,274

146,979 + 329,741

10.

856,559 + 437,715

Set up the addition problem, then add. 11.

349 + 82 =

12.

759 + 548 =

13.

6,175 + 665 =

14.

59,382 + 9,793 =

15.

167,943 + 56,345 =

16.

693,874 + 582,557 =

17.

492,621 + 832,705 =

18.

1,045,783 + 568,327 =

19. What is the distance around Mars and Jupiter combined? 20. What is the distance around Mars and Neptune? 21. What is the combined distance around Mars, Saturn, and Neptune?

PLANET

DISTANCE AROUND THE PLANET

Mars

13,263 miles

Jupiter

272,946 miles

Saturn

235,298 miles

Neptune

96,685 miles

22. Would it take longer to fly a rocket around Jupiter or to get around Saturn and Neptune combined?

Challenge Add these numbers together by writing them vertically and regrouping as necessary. 23.

15,692 + 367,904 + 732,596 + 54,725 =

Lighthouse Math

Level F

Chapter 2

Exercise 4

Use the chart below to solve the problems.

Chapter 2-5 Subtract Large Numbers Daily Review

Add.

1. 782,182 + 263,821 =

2. 782,082 + 89,291 =

3. 892,108 + 27,192 =

Learn and Connect A company called You-Pick-It allows people to pick tulips for a fee. On the first day it was open, 24,928 tulips were picked. How many tulips are left in the field? To solve, we have to subtract the tulips removed from the total amount of tulips in the field. Start by lining up the digits by their place value. Then, subtract the numbers starting with the smallest place value to the right.

�

2 4 0, 2 7 2 2 4, 9 2 8

tulips.

Therefore, the field has

Apply Subtract. 1. 909,081 � 128,118

2. 960,701 � 872,461

3. 845,087 � 34,534

Set up the subtraction problem, then subtract. 4. 582,818 � 169,227 =

5. 738,283 � 37,271 =

6. 836,273 � 3,278 =

7. 727,279 � 27,182 =

8. 378,283 � 1,203 =

9. 382,928 � 12,389 =

Level F

Chapter 2

Lesson 5

Lighthouse Math

Exercise 2-5 Name Subtract and check with addition. 1.

8,956 � 987

Check

19,604 � 7,058

Check

89,664 � 38,758

Check

23,042 � 8,437

Check

98,003 � 23,994

Check

678,294 � 473,905

Check

359 � 62 =

609 � 328 =

3,192 � 568 =

10.

9,382 � 5,611 =

11.

178,940 � 84,375 =

12.

88,504 � 9,655 =

13.

328,703 � 287,098 =

14.

500,280 � 298,367 =

Set up the subtraction problem, then subtract.

Solve each problem. 15. If rockets need a velocity of 25,000 miles per hour to break through Earth’s atmosphere, how much faster does a rocket going 18,975 miles per hour need to go to break through?

16. In 1967, the fastest rocket could go 4,520 miles per hour. Today, the Solar Probe can go 153,454 miles per hour. What is the difference in these two speeds?

Challenge One way to subtract from a round number easily without regrouping is to subtract one from the round number. Study the example and then try it on your own.

Lighthouse Math

Subtract 1 49,999 � 26,499 23,500 Add 1 back = 23,501

50,000 � 26,499

Level F

Chapter 2

Exercise 5

17. Your Turn 100,000 � 75,496

Chapter 2-6 Add and Subtract Money Daily Review

Subtract.

1. 163,281 � 123,927 =

2. 361,297 � 56,875 =

Learn and Connect Ken needs a new pair of shoes. He found a pair that he likes. If he pays for the shoes with a $100 bill, how much money will he have left before tax? To solve, we have to subtract the cost of the shoes from the money Ken has. Start by lining up the numbers by their place value. Because the hundred dollars does not have a decimal, add it on at the end followed by placeholder zeros. 100.00 � 52.28

left.

Therefore, Ken will have

Apply Set up the problem by lining up the place values, then solve. 1. $35.28 � $0.24 =

2. $8.20 � $0.05 =

�

4. $35.27 � $14.27 =

7. $60.40 + $24.17 =

�

Level F

Chapter 2

6. $75 � $2.45 = �

8. $18 � $1.27 =

5. $19 + $3.78 =

�

3. $132+ $2.45 =

9. $213.25 + $7.98 = +

Lesson 6

Lighthouse Math

Exercise 2-6 Name Solve. 1.

$5.24 + $4.73

$9.74 � $2.52

$8.13 + $3.10

$8.34 � $5.85

$3.17 + $2.84

$94.21 � $73.75

$53.55 + $23.54

$95.80 � $46.72

$56.63 + $13.33

10.

$71.00 � $51.24

11.

$856.30 + $667.15

12.

$734.89 � $202.88

13.

$311.05 + $160.22

14.

$229.76 � $199.19

15.

$684.54 + $388.21

18. $7,424.98 � $2,987.07

19.

$6,425.54 + $5,423.98

20.

$4,434.46 � $3,581.44

16. $5,319.61 � $4,567.83

17. $2,037.35 + $1,999.59

Set up the problem to line up place value and solve.

+ 24. $5.10 � $2.49 = �

22. $9.08 � $3.66 =

23. $8.41 + $3.48 =

�

25. $74.16 + $32.36 = +

26. $42.54 � $30.11 = © Lighthouse Curriculum. Copying strictly prohibited.

21. $5.26 + $2.30 =

�

27. $19.59 + $10.79 =

28. $96.24 � $27.60 =

�

29. $361.82 � $196.28 =

30. $6,721.90 + $1,721.95 =

�

Challenge 31. O n Saturday, Ryan paid $14.34 each for two books. He also bought a set of pens for $6.54. Ryan paid with two $20 bills. How much change did he receive?

Lighthouse Math

Level F

Chapter 2

Exercise 6

Chapter 2-7 Estimate Sums and Differences Daily Review

Solve.

1. $35 - $7.84 =

2. 5.40 - $3.78 =

3. $52 + $9.83 =

Learn and Connect Kennedy is looking at two lawn mowers to buy. He can’t decide between the blue or red lawn mower. About how much more money would he pay for the blue lawn mower than the red lawn mower? To solve, we have to round each price. Then, we should subtract the estimated price of the red lawn mower from the blue lawn mower. Red: 317

320

Blue: 578

580

580 � 320

Therefore, Kennedy would pay about $ more for the blue lawn mower.

Apply Estimate by rounding to the nearest hundred. 1. 528 � 376 =

2. 892 + 347 =

3. 824 � 748 =

4. 1,283 � 728 =

5. 2,182 + 2,762 =

6. 3,271 + 1,283 =

Estimate by rounding to the nearest thousand. 7. 12,398 � 10,237 =

8. 45,829 � 22,298 =

9. 62,128 + 26,127 =

10. 17,209 � 1,372 =

11. 28,781 + 2,742 =

12. 39,621 + 12,328 =

Level F

Chapter 2

Lesson 7

Lighthouse Math

Exercise 2-7 Name Estimate by rounding to the nearest hundred. 1. 562 + 357 =

2. 987 � 435 =

3. 1,246 + 3,478 =

4. 6,754 � 4,530 =

5. 878 + 235 =

6. 1,325 � 657 =

7. 563 + 4,572 =

8. 6,750 � 3,245 =

9. 4,857 + 7,862 =

10. 19,323 � 6,435 =

11. 23,789 + 3,426 =

12. 53,672 � 43,673 =

13. 23,486 + 12,325 =

14. 126,458 � 82,465 =

15. 342,523 + 34,527 =

16. 1,233 + 2,435 =

17. 3,248 � 2,546 =

18. 1,547 + 4,526 =

19. 7,834 � 7,284 =

20. 12,546 + 3,458 =

21. 21,567 � 3,452 =

22. 34,567 + 23,435 =

23. 46,574 � 34,987 =

24. 14,785 + 85,683 = © Lighthouse Curriculum. Copying strictly prohibited.

Estimate by rounding to the nearest thousand.

Estimate by rounding to the nearest ten thousand. 25. 34,578 + 89,432 =

26. 78,423 � 45,887 =

27. 67,459 + 12,354 =

28. 233,567 � 34,500 =

29. 453,574 + 78,932 =

30. 78,564 � 58,434 =

Challenge 32. Anthony's school sold 672 boxes of 31. S heldon picked 456 apples and Dennis picked 312 apples from the apple tree. chocolate for a fundraiser this year. He sold About how many apples did they pick 157 boxes. About how many boxes were together? Round your answer to the nearest sold by the rest of the students? Round hundred. your answer to the nearest ten.

Lighthouse Math

Level F

Chapter 2

Exercise 7

Chapter 2-8 Review Daily Review

Estimate the solution by rounding to the nearest hundred.

1. 3,567 � 578 =

2. 2,457 + 1,893 =

3. 829 + 762 =

Learn and Connect Jonah estimated the cost of three items by rounding to the nearest dollar. He then bought all three of the items. What is the difference between the estimated cost and the actual cost of all three items? The difference between the estimate and the actual is ______ .

To solve, we need to first find the estimated cost of all three items by rounding to the nearest dollar and adding the total.

$12.75 $5.98 $4.17

$13.00 $6.00 $4.00

Then, we need to find the actual cost of the items by adding the three prices.

13 6 + 4 $23

Last, we need to subtract the actual cost from the estimated cost.

12.75 5.98 + 4.17 22.90

23.00 � 22.90

Apply Complete the chart. EXPANDED FORM

STANDARD FORM

WORD FORM

COMPARE: >,<, OR =

1,000,000,000,000 + 200,000,000,000 + 30,000,000,000 + 7,000,000,000 + 800,000,000 + 30,000,000 + 9,000,000 + 200,000 + 70,000 + 1,000 + 300 + 70 + 3

1,378,281,922

Solve. Estimate to check your answer. 1.

345,689 + 23,784

Level F

872,689 � 37,884

Chapter 2

Lesson 8

$342.15 234.17

Lighthouse Math

Exercise 2-8 Name Write the place value of each digit in blue. 1. 634,542,675,138

2. 232,543,762

3. 532,476,568,501,469

4. 754,342,786,101

Complete the chart. EXPANDED FORM

STANDARD FORM

WORD FORM

COMPARE: >,<, OR =

seven trillion, one hundred eighty-nine billion, two hundred eight million, three hundred seventy-two thousand, two hundred ninety-seven

7. 982,389,234

221 + 83

431 + 421

10.

15.

672 � 597

16.

2,336 432

11.

3,751 + 2,586

12.

10,111 + 6,491

13.

25,478 + 43,543

�

3,756 582

17.

8,436 � 2,349

18.

36,232 � 8,931

19.

98,673 � 56,478

Subtract. 14.

436 � 76

Set up each problem by lining up the place value. Then, solve. 20. $3.35 + $4.35 = +

21. $12. 43 � $4.59 =

22. $15.42 + $21.68 =

�

Estimate by rounding each number to the greatest place value. 23. 578 + 432 =

Lighthouse Math

24. 784 � 458 =

Level F

25. 7,465 + 2,534 =

Chapter 2

Exercise 8

Add.

Chapter 3 NYS NG Standards NY-4.NBT.5 NY-4.NBT.6 NY-5.NBT.2 NY-5.NBT.5

NY-3.NBT.3 NY-3.OA.4 NY-3.OA.8b

CC Standards 3.NBT.A.3 3.OA.A.4 3.OA.C.7 3.OA.D.8

4.OA.B.4 4.NBT.B.5 5.NBT.A.2 5.NBT.B.5

Chapter 3 focuses on

Multiplication of Whole Numbers We will start with multiplying by 10, as well as estimating products, then move into multiplying larger numbers and multi-digit factors. • Multiplication x 10 • Estimating products • Multiply by 1 digit • Multiply up to 6 digit numbers by 1 digit © Lighthouse Curriculum. Copying strictly prohibited.

• Multiply by 2 digit factor • Multiply 3 x 3 digit factors • Multiply 4 x 3 digit factors • Review Building on the understanding of place value, students will gain mastery of not only their basic multiplication facts, but they will also be able to apply those foundational skills to more challenging computation.

Chapter 3-1 Multiplication x 10 Daily Review

Solve.

1. 5 � 3 =

2. 2 � 12 =

3. 3 � 8 =

4. 6 � 9 =

5. 7 � 8 =

Learn and Connect Some teachers went to the store to buy packs of paper. Mr. Elizandro bought 2 packs. Mr. McCale bought 20 packs. Mr. Benedict bought 200 packs. How many individual pieces of paper did each teacher have?

To solve, we have to multiply the amount of pages per pack by the amount of packs bought. Because we are multiplying by multiples of 10, we can use this trick. Start by multiplying the nonzero numbers.

Then, place the same amount of zeros in the factors at the end of the product.

2 × 50 = 2 × 5 = 10 20 × 50 = 2 × 5 = 10 200 × 50 = 2 × 5 = 10

2 × 50 = 2 × 5 = 100 20 × 50 = 2 × 5 = 1,000 200 × 50 = 2 × 5 = 10,000

Therefore, Mr. Elizandro has 100 pieces of paper, Mr. McCale has 1,000 pieces of paper, and Mr. Benedict has 10,000 pieces of paper.

Apply Solve using the multiplying with zeros trick. 1.

40 × 300 =

10 × 10 =

5 × 30 =

4. 60 × 400 =

20 × 100 =

80 × 200 =

Find the missing factor. 7. 11.

5×

= 500

× 100 = 2,500

× 200 = 1,200

12.

× 400 = 2,000

13. 6 ×

Level F

Chapter 3

Lesson 1

7×

= 1,400

10.

= 180

14. 8 ×

× 40 = 200 = 1,600

Lighthouse Math

Exercise 3-1 Name Solve. 1. 50 × 5 =

30 × 30 =

70 × 4 =

4. 60 × 10 =

5. 14 × 20 =

6. 30 × 12 =

40 × 50 =

8. 7 × 200 =

9. 300 × 40 =

10. 3,000 × 30 =

11. 3,300 × 200 =

12. 52 × 20 =

13. 25 × 400 =

14. 4,000 × 7,000 =

15. 230 × 20 =

16. 600 × 300 =

17. 9,000 × 40,000 =

18. 4 ×

= 120

19.

× 140 = 1400

20. 50 ×

= 200

21. 32 ×

= 640

22.

× 10 = 400

23. 12 ×

= 360

24. 200 ×

= 2800

25. 30 ×

= 9000

26. 300 ×

= 21,000

28. 250 ×

= 50,000

29. 1,500 ×

27.

× 400 = 80,000

30. 5,000 ×

= 15,000,000

31.

× 110 = 440,000

32. 600 ×

= 450,000

= 420,000

Challenge 33. A concentrated bottle of a cleaning solution claims to have 200 times more uses in one bottle than a regular bottle. If the regular bottle has 300 uses, how many uses would the concentrated bottle have?

Lighthouse Math

Level F

34. An ant can carry up to 5,000 times its body weight. If an ant weighs 2 mg, how much can it carry?

Chapter 3

Exercise 1

Find the missing factor.

Chapter 3-2 Estimating Products Solve each multiplication problem.

Daily Review 1.

8 �9

3. 492 � 3

64 � 5

74 � 56

Learn and Connect There are 896 people that come to the aquarium each day. If about the same number of people come each day to the aquarium, approximately how many people come to the aquarium in a week? This problem uses “approximately” and “about” to show we need to estimate the answer. First, round 896 to the nearest 100: Second, multiply 900 � 7. About

people come to the aquarium each week.

Apply

Complete the chart by rounding to the nearest 10, 100, or 1000. Round to the nearest 10

983

7,845

3,392

Round to the nearest 100

Round to the nearest 1,000

Round to the highest place value. 4. 893

5. 45

6. 9,304

Round to the highest place value and then solve. 7. 13 � 56 =

�

8. 532 � 45 =

�

9. 89 � 178 =

�

10. 7 � 1368 =

�

Level F

Chapter 3

Lesson 2

Lighthouse Math

Exercise 3-2 Name Complete the chart by rounding to the nearest 10, 100, or 1000. Round to the nearest 10

561

5,297

6,078

13,509

Round to the nearest 100

Round to the nearest 1,000

Round each decimal to the underlined place. 5.

4.5 =

13.67 =

9.341 =

82.984 =

Round to the highest place value. 9.

592

10. 4.3

11. 7,305

12. 12,593

13. 15.67

14. 0.509

Round to the highest place value and then solve.

17. 7.8 � 793 = 19. 10.56 � 171 =

�

= �

16. 492 � 28 =

�

18. 51 � 362 =

�

20. 8,394 � 68 =

= = �

Challenge 21. There are 345 people that attend each dolphin show. If there are two shows a day, about how many people attend the shows in a week?

22. Rodney watched the tropical fish exhibit. There were 1,562 fish in one tank. If there were about the same amount in each tank. How many fish would be in the 8 tanks?

23. A mako shark weighs approximately 1,750 pounds. If there are three mako sharks in the shark exhibit, about how much do they weigh combined?

24. Tickets for the dolphin show are $3.75 and ten friends want to go. About how much will it cost them to attend?

Lighthouse Math

Level F

Chapter 3

Exercise 2

15. 83 � 19 =

Chapter 3-3 Multiply by One Digit Estimate the products by rounding to the greatest common place value.

Daily Review 1. 325 × 45 =

2. 132 × 345 =

3. 765 × 453 =

4. 56 × 72 =

Learn and Connect James and Robert are working together to create a report about their local aquarium. They love to watch the 5 sea lions as they play in their exhibit. The trainers always have a bucket of fish. Each sea lion eats 135 fish in one week. How many fish do all of the sea lions eat in total? Multiply 135 × 5, using the area model.

100

500

150

Add your partial products for the total product: 500 + 150 + 25 = Therefore, the sea lions eat

fish in a week.

Apply Solve each problem using the area model and then check your work using the standard algorithm. 1.

78 � 6 70

300

384 � 7 80

1000

400

Algorithm Check: 78 � 6

1,459 � 4

Algorithm Check: 384 � 7

Algorithm Check: 1,459 � 4

Vocabulary Area Model - a strategy that allows for each place value to be multiplied separately and the products added together at the end to reach the total product

Level F

Chapter 3

Lesson 3

Lighthouse Math

Exercise 3-3 Name Solve each problem using the area model and then check your work using the standard algorithm. 1.

82 � 9

Algorithm Check: � 00

648 � 8

9,705 � 3

Algorithm Check: � 00

Solve each problem using the strategy of your choice. 4.

45 � 9

804 � 2

10. 197 � 5

11. 899 � 6

12. 415 � 4

13. 936 � 9

14. 6,711 � 5

15. 4,169 � 8

16. 4,621 � 8

17. 5,932 � 5

18. 8,606 � 7

68 � 7

37 � 5

92 � 3

18 � 8

Challenge 19. The sea lions at the local aquarium put on three shows a day for 256 days out of the year. How many shows total do the sea lions put on in a year?

Lighthouse Math

Level F

20. The sea lions can weigh up to 2,500 pounds. About how much do the 5 sea lions at the aquarium weigh combined?

Chapter 3

Exercise 3

Chapter 3-4 Multiply Up to Six Digits by One Digit Daily Review

Set up and multiply.

1. 123 × 5 =

2. 1,372 × 4 =

3. 472 × 3 =

Learn and Connect Eric and Victor are going on a road trip. As they are entering a town called Mittenville, Eric explains that his hometown has exactly 5 times as many people as Mittenville. What is the population of Eric’s hometown? To solve, we have to multiply the population of Mittenville by 5. Start by setting up the problem, placing the number with the most digits at the top. Then, multiply each digit by the bottom digit starting from the right. 203,562 � 5

Therefore, Eric’s hometown has a population of

Apply Multiply. 1.

211,194 � 2

626,340 � 2

547,938 � 8

545,561 � 5

922,402 � 9

652,459 � 4

652,459 � 7

460,901 � 2

547,938 � 8

10.

357,300 � 7

11.

671,318 � 3

12.

506,824 � 8

Level F

Chapter 3

Lesson 4

Lighthouse Math

Exercise 3-4 Name

25 � 3

342 � 2

3,487 � 5

23,453 � 3

154,376 � 4

76 � 4

794 � 5

5,727 � 6

75,345 � 5

10.

324,567 � 2

11.

32 � 7

12.

618 � 4

13.

4,523 � 2

14.

15,678 � 7

15.

702,342 � 6

16.

38 � 5

17.

452 � 6

18.

6,218 � 8

19.

95,673 � 4

20.

273,847 � 3

21.

98 � 2

22.

783 � 7

23.

5,412 � 5

24.

56,211 � 2

25.

453,724 � 6

26.

15 � 7

27.

713 � 8

28.

4,861 � 4

29.

54,555 � 2

30.

613,245 � 8

31.

45 � 7

32.

378 � 6

33.

2,583 � 4

34.

34,654 � 5

35.

532,645 � 5

Challenge 36. The city of Los Angeles has about 7 times the population of the entire state of Wyoming. The population of Wyoming is 576,851. What is the population of of the city of Los Angeles, California?

Lighthouse Math

Level F

37. Alaska is about 6 times larger than Nevada. If Nevada has an area of 110,571 mi2, what is the area in square miles of Alaska?

Chapter 3

Exercise 4

Multiply.

Chapter 3-5 Multiply by 2 Digit Factors Solve each multiplication problem.

Daily Review 1.

6 � 8

37 � 4

178 � 6

7,403 � 2

Learn and Connect The local aquarium has a new baby dolphin. James and Robert are hoping to get some pictures for their report for school. There are 125 people allowed in the observation room with reserved passes. If the baby dolphin has been in the aquarium for 14 days, how many people have been able to see the dolphin? Use the area model to multiply 125 � 14 100

10 4

Add your products: +

people have seen the baby dolphin.

Apply Practice multiplying 683 x 24 using three different strategies. 1.

683 � 24 +

Algorithm

Partial Products 683 � 24

4 � 683 0 then 2 � 683

4�3 4 � 80 4 � 600 20 � 3 20 � 80 20 � 600

Area Model 600

20 4

Vocabulary Algorithm - a set pattern of steps that can be repeated to solve problems 58

Level F

Chapter 3

Lesson 5

Lighthouse Math

Exercise 3-5 Name Solve using any strategy. 1.

54 � 19

86 � 45

73 � 25

129 � 33

810 � 18

607 � 32

179 � 56

1,290 � 62

4,153 � 48

10.

7,942 � 95

Rewrite and solve. 11.

17 � 49 =

14. 763 � 21 =

12. 67 � 44 =

13. 99 � 14 =

15.

16. 594 � 76 =

405 � 82 =

Use the admission prices chart to solve the problems below. The Paulsen family has two adults and three children. How much would it cost for the children to get into the aquarium?

18. How much would it cost all of the adults to get into the aquarium?

19.

ADMISSION PRICES Child

Adult

$ 15

Large Family

$ 55

What is the total cost for their family? Is it a better deal to buy the large family ticket?

Challenge Fill in the missing digits.

20.

135 � 21 135 + 2700 2835

Lighthouse Math

Level F

Chapter 3

Exercise 5

17.

Chapter 3-6 Multiply by 3 Digit Factors Daily Review

Multiply.

1. 15 � 6 =

2. 32 × 15 =

3. 16 × 21 =

4. 18 × 321 =

Learn and Connect A double decker bus is a bus with two levels. A double decker bus is used to pick up and drop off passengers at an event that lasts all day long. If each trip the bus makes is at full capacity, how many passengers did the bus drop off after 113 trips? To solve, we have to multiply the total capacity of the bus and the amount of stops the bus makes to release all of the passengers. First, multiply the ones digit in the second factor by all three digits of the first factor. 125 � 113 375

Next, multiply the tens digit in the second factor by all three digits of the first factor. 125 � 113 375 1250

125 113 375 1250 + 12,500

Last, add all of the numbers to find the product.

�

people.

Therefore, the double decker bus transferred © Lighthouse Curriculum. Copying strictly prohibited.

Then, multiply the hundreds digit in the second factor by all three digits of the first factor.

Apply Multiply. 1.

234 � 425

345 � 564

324 � 345

567 � 128

572 � 431

425 � 504

372 � 236

545 � 137

118 � 104

10.

783 � 212

Level F

Chapter 3

Lesson 6

Lighthouse Math

Exercise 3-6 Name

312 � 231

573 � 352

834 � 532

978 � 568

357 � 892

612 � 124

413 � 253

634 � 348

784 � 554

10.

318 � 642

11.

941 � 111

12.

716 � 218

13.

223 � 455

14.

988 � 554

15.

875 � 215

16.

413 � 632

17.

358 � 781

18.

433 � 344

19.

999 � 101

20.

213 � 356

21.

878 � 226

22.

523 � 756

23.

286 � 234

24.

655 � 316

25.

877 � 578

Multiply.

Challenge 26. A museum has an average daily attendance of 342 visitors. The museum is open 245 days per year. How many people visit the museum per year?

Lighthouse Math

Level F

27. A dictionary has 175 pages. Each page has 125 words. How many total words are in the dictionary ?

Chapter 3

Exercise 6

Chapter 3-7 Multiply 3 and 4 Digit Factors Daily Review

Multiply.

1. 231 � 432 =

2. 234 × 532 =

3. 234 × 156 =

Learn and Connect A local apple farmer picks 545 apples from each of his apple trees over six months. If he has 1,456 apple trees, how many total apples does he pick in six months? To solve, we have to multiply the number of apples he picks from each tree by the amount of trees. First, multiply the ones digit in the second factor by all four digits of the first factor.

Next, multiply the tens digit in the second factor by all four digits of the first factor.

1,456 � 545 7,280

1,456 � 545 7,280 58,240

Therefore, the apple farmer picks

Then, multiply the hundreds digit in the second factor by all four digits of the first factor. 1,456 545 7,280 58,240 + 728,000

Last, add all of the numbers to find the product.

�

apples over 6 months.

Apply Multiply. 1.

2,345 � 123

3,321 � 258

2,346 � 742

5,891 � 456

8,653 � 125

2,895 � 235

1,234 � 368

8,902 � 234

3,864 � 234

10.

6,732 � 124

Level F

Chapter 3

Lesson 7

Lighthouse Math

Exercise 3-7 Name

2,345 � 465

5,632 � 115

7,435 � 223

4,563 � 756

5,678 � 213

6,316 � 714

9,314 � 542

1,218 � 143

3,342 � 418

10.

2,673 � 564

11.

1,798 � 156

12.

2,139 � 796

13.

7,341 � 824

14.

4,967 � 415

15.

3,999 � 682

16.

6,241 � 365

17.

8,312 � 734

18.

9,134 � 385

19.

2,325 � 466

20.

3,556 � 542

21.

2,896 � 232

22.

9,572 � 875

23.

6,734 � 918

24.

1,984 � 526

25.

3,009 � 515

Challenge 26. There are 243 condominiums in a subdivision. Each condominium is 1,323 sq ft. What is the total square footage of all of the condominiums?

Lighthouse Math

Level F

27. The city is building a new park. The park is 1,435 ft. long by 684 ft. wide. What is the total area of the new park?

Chapter 3

Exercise 7

Multiply.

Chapter 3-8 Review Daily Review

Multiply.

1. 2,346 × 163 =

2. 1,253 × 145 =

3. 625 × 156 =

Learn and Connect A flight is completely booked for a trip to Paris. The flight holds 123 passengers. How much money did the airline make for this one trip to Paris? To solve, we need to multiply the cost of the flight by the amount of passengers on the flight. Cost of the flight: Amount of passengers:

�

Therefore, the airline made $

Apply

Estimate by rounding to the highest place value. 1. 24 � 78 =

2. 423 � 62 =

3. 895 � 372 =

Multiply. 4.

123,467 � 5

362,127 � 3

24 � 35

45 � 26

872 � 24

562 � 26

10.

352 � 368

11.

912 � 273

12.

7,932 � 175

13.

2,831 � 105

Level F

Chapter 3

Lesson 8

Lighthouse Math

Exercise 3-8 Name Multiply. 1. 40 � 12 =

2. 400 � 30 =

3. 2,000 � 3,200 =

Find the missing factor. 4. 5 ×

= 150

× 20 = 300

50 ×

= 350

= 480

× 40 = 2,000

8×

= 720

16 ×

Round to the highest place value and then solve. 10. 43 × 16 =

11. 378 × 42 =

12. 6.2 × 235 =

13. 21 × 869 =

14.

34 � 4

15.

465 � 6

16.

3,782 � 5

17.

23,487 � 7

18.

463,623 � 8

19.

82 � 53

20.

814 � 81

21.

625 � 37

22.

3,465 � 89

23.

1,425 � 46

24.

372 � 215

25.

851 � 313

26.

1,823 � 472

27.

5,378 � 634

28.

8,042 � 301

Lighthouse Math

Level F

Chapter 3

Exercise 8

Multiply.

Chapter 4 NYS NG Standards NY-3.OA.8b NY-4.OA.2 NY-4.OA.3

NY-4.NBT.6 NY-5.NBT.6 NY-6.NS.2

CC Standards 3.OA.D.8 4.OA.A.2 4.OA.A.3

4.NBT.B.6 5.NBT.B.6 6.NS.B.2

In Chapter 4 we focus on

Division of Whole Numbers We will start with understanding division patterns and dividing by 10, then move into dividing larger numbers and working with 2 digit divisors. • Division patterns, divide by multiples of 10 • 1 digit divisors • Larger dividends, up to 6 digits, divide by 1 digit • Zeros in quotient © Lighthouse Curriculum. Copying strictly prohibited.

• Interpreting remainders • Estimating and dividing • Dividing by 2 digits • Review Understanding factor patterns, building on place value, using estimation and interpreting remainders are foundational skills that help students develop confidence in working with division problems.

Chapter 4-1 Divide By Multiples of 10 Solve.

Daily Review 1. 5 × 10 =

3. 6 × 10 =

3 × 100 =

4. 4 × 200 =

Learn and Connect When dividing by zeros, you can use the following tricks to divide quickly in your head. Dividing With Zeros in the Dividend Start by dividing the first few factors.

Then, place the same amount of zeros in the dividend at the end of the quotient.

160 ÷ 4 = 16 ÷ 4 = 4 1,600 ÷ 4 = 16 ÷ 4 = 4 16,000 ÷ 4 = 16 ÷ 4 = 4

160 ÷ 4 = 16 ÷ 4 = 40 1,600 ÷ 4 = 16 ÷ 4 = 400 16,000 ÷ 4 = 16 ÷ 4 = 4000

Try it: 360 ÷ 9 = 3,600 ÷ 9 = 36,000 ÷ 9 =

Dividing With Zeros in the Dividend and Divisor

Start by dividing the first few factors.

Then, remove the same amount of zeros in the divisor from the dividend. Add any remaining zeros to the quotient.

160 ÷ 40 = 16 ÷ 4 = 4 1,600 ÷ 400 = 16 ÷ 4 = 4 16,000 ÷ 4,000 = 16 ÷ 4 = 4

160 ÷ 40 = 16 ÷ 4 = 4 1,600 ÷ 40 = 16 ÷ 4 = 40 16,000 ÷ 400 = 16 ÷ 4 = 40

Try it: 350 ÷ 50 = 3,500 ÷ 50 = 35,000 ÷ 50 =

Apply Solve using the division with zero strategy. 1. 180 ÷9 =

2. 1,600 ÷ 80 =

3. 490 ÷ 70 =

4. 40 ÷ 20 =

5. 450 ÷ 90 =

6. 9,000 ÷ 90 =

7. 180 ÷ 3 =

8. 500 ÷ 100 =

9. 3,600 ÷ 120 =

10. 2,400 ÷ 6=

11. 3,600 ÷ 60 =

12. 800 ÷ 40 =

16. 6,000 ÷

Find the missing divisor or dividend. 13. 2,500 ÷ 17.

= 500

÷ 30 = 20

14. 700 ÷

= 70

15. 40 ÷

18.

÷ 300 = 5

19.

Level F

Chapter 4

Lesson 1

= 20

÷ 80 = 6

20.

= 300 ÷ 350 = 4

Lighthouse Math

Exercise 4-1 Name Solve using the dividing with zeros strategy. 1.

240 ÷ 6 =

120 ÷ 4 =

420 ÷ 60 =

600 ÷ 120 =

2,400 ÷ 300 =

5,600 ÷ 70 =

2,500 ÷ 500 =

48,000 ÷ 60 =

27,000 ÷ 900 =

10. 8,100 ÷ 90 =

11. 6,300 ÷ 700 =

12. 150,000 ÷ 500 =

13. 120,000 ÷ 300 =

14. 360,000 ÷ 6,000 =

15. 720,000 ÷ 80,000 =

16. 540,000 ÷ 90,000 =

17.

18. 280,000 ÷ 40,000 =

49,000 ÷ 700 =

Find the missing divisor or dividend.

22.

= 11

÷ 1,200 = 400

31. 140,000 ÷

= 200

26.

24.

= 8,000

÷ 6,000 = 70

÷ 50 =70

27. 2,800 ÷

÷ 40 = 900

29. 64,000 ÷ 32.

21. 540 ÷

÷ 5 = 30

23. 2,400 ÷

÷ 60 = 5

25. 66,000 ÷ 28.

20.

30.

= 700

÷ 200 = 800

33. 720,000 ÷

Challenge Solve each problem. 34. A farmer needed to transport 1,500 bales of hay using 3 semi-trucks. How many bales of hay were on each semi-truck?

Lighthouse Math

35. How long will it take to fill a 5,000 gallon swimming pool at 500 gallons per hour?

Level F

Chapter 4

Exercise 1

19. 320 ÷

Chapter 4-2 1 Digit Divisors Daily Review

Solve.

1. 1,800 ÷ 9 =

2. 180 ÷ 60 =

3. 2,400 ÷ 40 =

4. 3,600 ÷ 120 =

Learn and Connect At the zoo, they have 3 baby elephants in a pen. The zookeepers place the same total amount of food into the pen each day. If each elephant eats the same amount, how many pounds of food does each baby elephant eat in one day? To solve, we have to divide the amount of food given to the baby elephants per day by the number of baby elephants. Number of baby elephants

= Amount per elephant

)

Total amount of food

Therefore, each elephant eats day.

pounds per

Apply Divide. 1.

5)324

4)456

3)367

8)175

3)469

6)631

2)568

7)896

10. 6)234

Level F

Chapter 4

Lesson 2

4)853

Lighthouse Math

Exercise 4-2 Name Divide. 3)210

4)444

5)645

6)742

9)990

7)707

6)720

2)302

3)413

10. 6)234

11. 3)720

12. 4)945

13. 2)752

14. 5)905

15. 8)944

16. 8)3,416

17. 4)3,070

18. 2)1,327

19. 3)2,301

20. 4)2,860

21. 5)3,845

22. 5)1,882

23. 8)2,152

24. 2)327

25. 8)848

26. 9)967

27. 4)900

28. 3)462

29. 5)836

30. 7)799

Challenge Solve each problem. 32. Mr. Merriweather bought 125 pencils for his class. The pencils came in packages of 5. How many packages of pencils did he buy?

31. At a bake sale, there were 324 cookies donated. If there are 6 cookies in a bag, how many bags of cookies are there?

Lighthouse Math

Level F

Chapter 4

Exercise 2

Chapter 4-3 Divide Up To 6 Digit Dividends Daily Review 1.

Divide.

3)637

6)287

2)148

5)195

Learn and Connect Richard wants to buy a motorcycle from a used car lot. The owner says he can pay off the motorcycle in small payments. If he pays off the motorcycle in 9 equal payments, how much will each payment be? To solve, we need to divide the cost of the motorcycle by 9 equal payments. Number of payments

)

= each payment Total cost of motorcycle

Therefore, each payment will be $

Apply Divide. 1.

3)17,272

5)62,162

3)17,382

8)82,728

5)278,182

3)372,382

2)378,372

4)172,732

10. 6)283,837

Level F

Chapter 4

Lesson 3

4)28,271

Lighthouse Math

Exercise 4-3 Name Divide. 3)13,542

4)34,412

5)42,355

6)32,145

9)76,459

7)54,354

6)86,345

2)34,256

3)43,153

10. 2)45,352

11. 3)78,467

12. 4)89,435

13. 2)134,267

14. 5)143,905

15. 8)674,944

16. 8)314,352

17. 4)307,674

18. 2)132,357

19. 3)230,121

20. 4)286,980

21. 5)384,625

22. 5)161,882

23. 8)283,152

24. 2)415,327

25. 8)538,484

Challenge Solve. 26. The total area of a piece of land is 174,240 ft2. The owner of the land wants to divide it into 8 equal size lots. How many square feet will each lot be?

Lighthouse Math

Level F

Chapter 4

Exercise 3

Chapter 4-4 Zero in the Quotients Daily Review 1.

Divide.

3)637

6)287

2)12,532

5)15,305

Learn and Connect Jason wants to read a new book in 3 days. He looked at the last page of the book to see how many pages there are in total. If he reads an equal amount of pages each day, how many pages will he have to read to finish the entire book in 3 days? To solve, we need to divide the total number of pages by 3 days. Because you cannot make a group of 3 with 2, place a zero in the quotient and bring down the next digit. 10

3)324

–3 02

Complete the division problem to solve.

Therefore, Jason must read

pages per day.

Apply Divide. 1.

3)3,612

5)2,530

3)6,294

8)3,248

5)6,500

3)4,209

2)4,090

4)12,036

10. 6)33,654

Level F

Chapter 4

Lesson 4

4)4,412

Lighthouse Math

Exercise 4-4 Name Divide. 3)312

5)532

6)4,235

2)2,122

9)3,634

7)5,112

6)3,652

2)1,814

3)7,522

10. 2)4,104

11. 3)2,311

12. 4)8,923

13. 2)4,167

14. 5)5,112

15. 8)6,452

16. 8)32,152

17. 4)36,424

18. 2)32,157

19. 3)230,121

20. 4)272,314

21. 5)523,467

22. 3)362,348

23. 6)363,111

24. 2)415,327

25. 8)483,213

Challenge Solve. 26. Mason and Billy were trying determine how many containers they would need to evenly divide 436 crayons into groups of 4. Mason said they would need 19, but Billy said they would need 109. Who is correct? Write a division problem that supports your answer.

Lighthouse Math

Level F

Chapter 4

Exercise 4

Chapter 4-5 Interpreting Remainders Daily Review 1.

Divide.

3)1,215

6)1,848

4)2,564

5)5,425

Learn and Connect As a reward, a school principal wants to buy popsicles for every student at the school. If there are 357 students in the school, how many boxes of popsicles does he need to buy to have enough for each student? To solve, we need to divide the number of popsicles needed by the number of popsicles in each box.

Popsicles in each box

044 8)357 – 32 037 – 32 5

= Boxes of popsicles Number of popsicles needed Popsicles still needed

The remainder in this problem is important because it indicates that 5 students would not receive popsicles if the principal bought 44 boxes. Therefore, the principal needs to buy 45 boxes.

Interpreting Remainders Drop It: Not all remainders are important. If we are looking for only the equal groups, we only need the quotient and not the remainder.

Add It: If we need to include every piece of the dividend, then we need to add one extra to the quotient to make up for the missing piece.

Keep It: If the question wants the remaining pieces or the leftover portion; it only wants the remainder.

Apply For each of the word problems, decide if you need to drop the remainder, add one to the quotient, or only use the remainder by writing “drop it”, “add it”, or “keep it.” Then, solve. 1. Arnold has 326 business cards. He wants to put the cards in an album that holds 5 cards per page. How many pages will he use of the album if he wants to put all the cards in the album?

Level F

Chapter 4

2. Nathan has 4,238 flowers to put into bouquets. If he puts 15 flowers into each bouquet, how many full bouquets can he make?

Lesson 5

Lighthouse Math

Exercise 4-5 Name

1. Steven's family is taking a trip to his aunt's house in another state. The total distance to his aunt's house is 1,321 miles. Their car uses one gallon of gas for every 16 miles driven. How many gallons will they need?

2. The bakery made 134 scones. Scones are sold in boxes of 4. Any extra scones are not sold to customers. How many boxes will the baker need?

3. R iley has 343 stickers. He is going to share the stickers with his friends, Josh and Archer. How many stickers will each of them get?

4. Jeff and his mom are putting old pictures into a photo album. They have 217 photos. Each page holds two pictures. How many pages will they need?

5. A community group is having a fundraiser dinner with 500 people attending. Each table will seat 8 guests. How many tables will they need?

6. Mr. Rhodes purchased 85 highlighters for his class. He plans to give each student three highlighters in a bag. How many bags will he need?

Challenge Solve each problem. 7. A restaurant had an order for 130 slices of pizza. Each pizza is divided into 8 slices. How many pizzas did they have to make to fill the order?

Lighthouse Math

Level F

8. The 5th grade class is going on a field trip. There are 116 students and 10 adults. If each bus can hold 50 passengers, how many buses will they need?

Chapter 4

Exercise 5

Interpret the remainder for each word problem by writing “drop it”, “add it” or “ keep it”. Solve each problem using the interpretation you chose.

Chapter 4-6 Division Using Estimation Daily Review 1.

Divide.

3)263

12)378,261

7)13,289

7)8,327

Learn and Connect Eli has 147 cookies. He wants to make little snack packs with 12 cookies inside using small bags. If each bag has the same amount of cookies, about how many full bags can he make? To solve, we will estimate using compatible numbers. Then, we will divide to find the quotient. The goal when using compatible numbers is to choose numbers that would make it easier to solve in your head. Think of the multiples of 12. What number is close to 147? ÷ 12 = Therefore, Eli can make about

small bags of cookies.

Apply Use compatible numbers to estimate the quotients. 1.

3,023 ÷ 15 =

2. 4,008 ÷ 10 =

272 ÷ 9 =

4. 359 ÷ 6 =

6,389 ÷ 8 =

6. 8,789 ÷ 8 =

5,429 ÷ 5 =

8. 3602 ÷ 5 =

Divide and estimate to check if your answer is reasonable. 9.

5)4,482

10.

Estimated answer:

4)2,034

Estimated answer:

Level F

Chapter 4

Lesson 6

11.

3)6,599

Estimated answer:

Lighthouse Math

Exercise 4-6 Name Use compatible numbers to estimate the quotients. 1.

362 ÷ 6 =

478÷ 80 =

239 ÷ 3 =

1,211 ÷ 40 =

2,715 ÷ 90 =

3,492 ÷ 700 =

2,099 ÷ 30 =

4,480 ÷ 50 =

31,879 ÷ 400 =

10. 19,000 ÷ 5,000 =

11. 17,600 ÷ 6 =

12. 47,925 ÷ 100 =

14. 43,234 ÷ 110 =

15. 42,653 ÷ 60 =

16. 13,975 ÷ 2000 =

13. 71,333 ÷ 800 =

Use compatible numbers to estimate the quotients. 3)157

Estimate:

20.

7)412

Estimate:

23.

8)647

Estimate:

18.

5)234

19.

Estimate:

21.

Estimate:

5)607

22.

Estimate:

24.

4)325

17.

5)512

Estimate:

3)622

25.

Estimate:

4)2,439

Estimate:

Challenge Solve the problem by estimating. 26. J ulius and George picked 358 apples. The apples were divided between 3 bushel baskets. About how many apples are in a bushel?

Lighthouse Math

Level F

Chapter 4

Exercise 6

Chapter 4-7 Divide by One and Two Digits Use compatible numbers to estimate the quotients.

Daily Review 1. 7,193 ÷ 8 =

2. 2,098 ÷ 7 =

Learn and Connect Liam bought a large bag of baking flour to make some bagels. If he needs 8 ounces of flour for every batch of bagels, how many batches of bagels can he make with this bag of flour? To solve, we need to divide the total ounces of flour by the amount needed for each batch.

Amount per batch

= Number of batches of bagels

)

Total ounces of flour in the bag

Therefore, Liam can make batches of bagels using the flour from this bag.

Apply Divide. 1.

3)3,612

5)2,530

3)6,294

8)3,248

4)4,412

20)342

15)342

12)687

34)514

10.

45)457

Level F

Chapter 4

Lesson 7

Lighthouse Math

Exercise 4-7 Name

5)6,500

3)4,209

2)4,090

4)12,036

5. 6)33,654

16)782

52)831

24)869

36)139

10. 36)942

11. 71)541

12. 25)375

13. 56)682

14. 18)426

15. 78)849

16. 36)1,237

17. 62)3,452

18. 43)2,434

19. 76)6,114

20. 22)8,476

21. 54)3,871

22. 67)2,918

23. 38)3,219

24. 26)3,423

25. 17)6,150

Challenge 26. T he maintenance staff was setting up chairs for an event. They had 644 chairs and enough room for 23 rows. How many chairs were in each row?

Lighthouse Math

Level F

27. A truck driver drove on the interstate at an average speed of 65 mile per hour. How many hours did it take for him to drive 845 miles?

Chapter 4

Exercise 7

Divide.

Chapter 4-8 Problem Solving Review Daily Review

Set up and divide.

1. 1,283 ÷ 15 =

2. 2,787 ÷ 21 =

Learn and Connect A local restaurant bought some items at the store and recorded the total costs. Find the cost of one of the items by dividing the total cost of the item by the number of items.

ITEM

TOTAL COST

NUMBER OF ITEMS

A. Glass Bowls

$1,449

B. Fabric Napkins

$144

C. Microwaves

$1,872

D. Wood Tables

$21,756

)

PRICE PER ITEM

)

Apply For each of the word problems, decide if you need to drop the remainder, add one to the quotient, or only use the remainder by writing “drop it”, “add it”, or “keep it.” Then, solve. 1. R andy is collecting shells to make necklaces. He collected a total of 1,289 shells. If each necklace uses 8 shells, how many necklaces can he make?

Level F

Chapter 4

2. Abe is giving out an equal amount of candies to his friends and keeping the remainder. If he passes out a total of 3,278 candies to his 12 friends, how many will he get to keep?

Lesson 8

Lighthouse Math

Exercise 4-8 Name Solve using the dividing with zeros strategy. 1.

320 ÷ 4 =

160 ÷ 40 =

3,600 ÷ 60 =

4,800 ÷

800 ÷ 200 =

Find the missing divisor or dividend. 5.

640 ÷

÷ 60 = 3

÷ 120 = 30

Divide. 9. 3)635

10. 6)3,160

11. 4)63,467

12. 2)267,134

13. 9)1,872

14. 5)431,509

15. 25)382

16. 13)278

17. 73)278

18. 38)6,325

Use compatible numbers to estimate the quotients. 20. 638 ÷ 80 =

21. 184 ÷ 3 =

22. 1,667 ÷ 40 © Lighthouse Curriculum. Copying strictly prohibited.

19. 257 ÷ 5 =

Use compatible numbers to estimate the quotients. 23.

3)598

Estimate:

24.

4)417

25.

6)544

Estimate:

Challenge Interpret the remainder for each word problem by writing “drop it”, “add it” or “keep it”. Solve each problem using the interpretation you chose. 26. A bakery made 1,234 bagels. They put the bagels in boxes of 12. Each remaining bagel was sold for $1.25 each. How much money did they make selling the remaining bagels?

Lighthouse Math

Level F

Chapter 4

Exercise 8

Chapter 5 NYS NG Standards NY-4.OA.2 NY-4.OA.3 NY-4.NBT.5 NY-4.NBT.6 NY-5.NBT.5

NY-5.NBT.6 NY-6.NS.2 NY-6.SP.3 NY-6.SP.5c

CC Standards 4.OA.A.2 4.OA.A.3 4.NBT.B.5 4.NBT.B.6 5.NBT.B.5

5.NBT.B.6 6.NS.B.2 6.SP.A.3 6.SP.B.5.C

In Chapter 5 we will take a deeper dive into

Multiplication and Division of Larger Numbers We will use division to find averages, and review multiplying larger numbers with multi-digit factors as well as dividing larger numbers up to two-digit divisors. • Finding averages • Multiplying larger numbers by 1, 2, and 3 digits • Dividing by 1 and 2 digits (with and without remainders) • Multiply & divide mixed problems

• Using multiplication and division inverse to check answers • Order of operations, properties (distributive property for larger number multiplication) • Problem solving including money • Review Real world application of the skills learned in this chapter will be explored through problem solving and problems involving money. Students will also begin to apply the order of operations to solving more complex math problems.

Chapter 5-1 Finding Averages Daily Review

Solve using order of operations.

1. (53 - 5) ÷ 6 =

2. (7 + 7 + 7) ÷ 3 � 5 =

3. 3 + 5 + 6 � 4 � 8 =

Learn and Connect Jason

Ben

Wyatt

1st Race

91 seconds

135 seconds

96 seconds

2nd Race

82 seconds

128 seconds

99 seconds

3rd Race

85 seconds

141 seconds

90 seconds

4th Race

122 seconds

140 seconds

119 seconds

Three friends decided to race against each other. Each time, they had their parents time them to see how long it took them to run to the end of the block. What is the average time it took Jason to complete the race? When we need to find the average, or middle number, of a set of data, we add up all the values and then divide this total by the number of values.

First, add all of Jason’s times:

91 82 85 + 122

Then, divide the total by 4 races: = average # of Races

Total of Jason’s times

Apply Use the chart above to answer the following questions. 1.

What is the average time it took all three boys to run the last race?

2. Which boy had the lowest average race time for all four races?"

Vocabulary Average - the middle value in a set of data 86

Level F

Chapter 5

Lesson 1

Lighthouse Math

Exercise 5-1 Name

2. 4, 3 , 7, 6:

3. 12, 27, 34, 15:

4. 45, 62, 73, 82, 18:

5. 78, 78, 69, 54, 66:

6. 13, 12, 24, 21, 20:

8. 33, 22, 26, 33, 43, 23:

9. 67, 45, 35, 54, 55, 62:

10. 43, 22, 15, 20:

11. 15, 15, 17, 18, 15:

12. 45, 42, 43, 46:

13. 7, 7, 5, 8, 8:

14. 12, 34, 56, 74:

15. 15, 18, 15:

16. 23, 15, 38, 48:

17. 65, 62, 64, 67, 62:

18. 46, 47, 52, 50, 51, 48:

2, 4, 2, 8: 2 16 ÷ 4 = 4 4 Average: 4 2 +8 16

6, 12, 8, 8, 6:

Find the average for each data set.

Challenge Use the table to right to solve. 19. Four friends each had a stack of books they checked out from the library. What is the average number of books the friends checked out?

Lighthouse Math

Level F

Chapter 5

Exercise 1

Joy

Shawna

Michelle

Darla

Chapter 5-2 Multiplying 1, 2, 3 Digits Daily Review

Find the average of the data set.

1. 12, 6, 5, 8, 6, 5 =

2. 11, 7, 12, 11, 15, 10 =

3. 22, 24, 21, 25 =

Learn and Connect A post office began keeping track of how many letters they delivered for the month. If they continue to deliver the same amount of letters each month, how many letters will they have delivered after 12 months? To solve, we have to multiply the number of letters delivered by 12 months. Start by multiplying all the digits in the first factor by the ones digit in the second factor. Then, multiply all the digits in the first factor by the tens digit in the second factor.

12,345 � 12

Last, add both of the products to find your answer.

Therefore, after 12 months, the post office would have delivered

letters.

Apply Solve. 1.

234,213 � 2

34,738 � 8

670,782 � 9

1,234 � 21

2,345 � 13

34,089 � 22

2,346 � 345

34,567 � 267

1,294 � 876

10.

7,293 � 456

Level F

Chapter 5

Lesson 2

Lighthouse Math

Exercise 5-2 Name Solve. 1.

4,532 � 4

6,582 � 6

5,213 � 2

7,491 � 3

14,322 � 3

8,218 � 4

6,113 � 4

9,642 � 2

10. 212,201 � 8

11.

2,345 � 12

12.

8,218 � 23

13.

6,113 � 46

14.

9,642 � 53

15.

16.

22,314 � 42

17.

39,435 � 26

18. 262,451 � 15

19. 447,130 � 29

20. 312,441 � 56

21.

3,355 � 314

22.

6,654 � 522

23.

24.

25.

2,992 � 324

47,131 � 71

56,413 � 648

Challenge Solve. 26. Rent for a three bedroom apartment is $2,375 per month. How much does one tenant pay for 12 months? If there are 225 apartments in the complex with the same rent amount, how much rent is collected in the complex each month?

Lighthouse Math

Level F

Chapter 5

Exercise 2

7,324 � 219

36,184 � 5

Chapter 5-3 Divide by 1 and 2 Digit Divisors Daily Review

Solve.

1. 123,456 × 6 =

2. 2,234 × 22 =

3. 8,234 × 15 =

Learn and Connect The train station has 3 trains that arrive every 52 minutes. If it has been 1,356 minutes since the trains started running, how many times have the 3 trains stopped in the train station? To solve, we have to divide the total number of minutes by the number of minutes it takes for the three trains to arrive. = Number of times the trains have stopped in the station Minutes it takes for the trains to arrive

52 1,356

Total minutes passed

Therefore, the trains have been in the station

times.

Apply

Solve. 1. 5)327,298

2)273,823

3. 4)38,932

4. 12)28,398

6. 16)2,398

30)28,380

8. 14)89,824

9. 7)38,298

10. 3)12,289

Level F

Chapter 5

Lesson 3

15)22,070

Lighthouse Math

Exercise 5-3 Name Divide. 3)4,562

5)1,378

6)3,674

4. 4)2,663

2)23,413

4)12,877

7)44,573

7)2,781

5)65,789

10. 3)52,231

11. 6)134,425

12. 8)324,337

13. 26)3,421

14. 54)6,542

15. 37)1,874

16. 23)26,541

17. 42)61,423

18. 36)247,534

19. 14)328,546

20. 67)682,436

Challenge Solve. Round your answer to the nearest tenth of a mile. 21. U.S. Route 20 covers 3,365 miles from Boston, Massachusetts to Newport, Oregon. It is currently the longest highway in the country. A cyclist plans to ride the entire route in 28 days, not including rest days. How many miles will the cyclist need to ride each day to meet his goal?

Lighthouse Math

Level F

Chapter 5

Exercise 3

Chapter 5-4 Mixed Multiplication and Division Daily Review

Solve.

1. 1,352 ÷ 5 =

2. 2,736 ÷ 12 =

3. 12,382 ÷ 21 =

Learn and Connect Elon drives to his new job each day. After some time working at his new job, Elon calculated that he traveled a total of 1,950 miles to and from work. How many times did Elon drive to and from work during this time? To solve, we have to divide the total miles he drove by the number of miles he lives from work. = Times he drove to and from work Miles from work

15 1,950

Total miles driven

Therefore, Elon drove

times to and from work.

Apply

Solve. 1.

14)128,291

234 � 276

6. 9)3,177

372,981 � 4

Level F

Chapter 5

28,198 � 15

4. 23)27,289

14)21,278

Lesson 4

7,987 � 15

Lighthouse Math

Exercise 5-4 Name Solve. 1.

45,367 � 23

6. 25)5,472

2. 5)34,762

8. 42)135,562

65,739 � 28

532,346 � 416

4. 13)47,513

10. 8)342,376

987,342 � 9

213,225 � 36

Solve. There are 1,043 students at a school. If each classroom holds 30 students, how many classrooms are needed at the school?

13. A wedding reception plans to have 227 guests. If 12 guests can be seated around a table, how many tables will there need be at the reception?

12. The library has 52 bookcases in the fiction section. Each case holds 234 books. How many books are in the fiction section?

14. It takes 680 minutes to fly from San Francisco to Beijing, China. What is this time in hours and remaining minutes? Hint: 1 hour is 60 minutes

Challenge Solve. 15. A florist creates 270 flower arrangements in 6 days. Each arrangement contains 12 flowers. How many flowers does the florist use in 6 days? How many arrangements does the florist make each day?

Lighthouse Math

Level F

Chapter 5

Exercise 4

11.

Chapter 5-5 Inverse Operations: Multiplication and Division Daily Review

Solve.

1. 4,348 ÷ 4 =

2. 2,736 × 12 =

3. 87,632 ÷ 21 =

Learn and Connect Rick decided to buy some coffee for his employees. He spent $325 on large plain coffees. How many cups of coffee did he buy for his employees? To solve, we have to divide the total cost by the price of each cup of coffee.

Divisor

First, divide to find the answer.

Quotient

065 5 325 � 300 25 � 25 0

Dividend

Therefore, Rick bought

Then, check your answer by using multiplication. Multiply the quotient by the divisor.

65 � 5 325

Last, add any remainders and check if the answer equals the dividend.

cups of coffee.

Apply Solve. 1.

34,583

2. 45

�

3,226 � 45

Level F

Chapter 5

Lesson 5

67,860

�

23,654 � 9

Lighthouse Math

Exercise 5-5 Name Solve and check each problem using the inverse operation. 1.

3,425 � 23

Check:

5,153 � 38

Check:

342 � 25

Check:

4,662 � 83

Check:

32,431 � 45

Check:

55,642 � 14

Check:

43,521 � 58

Check:

324,486 � 3

Check:

873,229 � 4

Check:

10. 3)465

13.

5)14,587

16. 43)678

Check:

11.

2)582

Check:

12. 6)3,742

Check:

14. 7)314,544

Check:

15.

22)473

Check:

17.

78)58,897

Check:

18. 63)87,452

Check:

Challenge Solve. Round your answer to the nearest tenth. 19. A hotel is 23 stories tall. Each floor is 15,413 square feet. What is the total square footage of the hotel?

Lighthouse Math

20. If there are 48 rooms on each floor, what is the approximate square footage of each room? Round your answer to the nearest tenth.

Level F

Chapter 5

Exercise 5

Solve and check each problem using the inverse operation.

Chapter 5-6 Order of Operations Daily Review

Solve.

1. 5,685 ÷ 5 =

2. 4,219 × 7 =

3. 94,562 ÷ 32 =

Learn and Connect Kevin has $545. He spent $239 at the store. Then, he divided the remaining money up into three equal parts for himself and his two siblings. Later, his mother gives him an additional $20 for mowing the lawn. Write an expression to help find the money he has left. Then, solve. To solve, consider the order of operations. First, we solve operations in parentheses, then exponents, followed by multiplication and division from left to right. Last, we solve addition and subtraction from left to right. Consider what happens first in the story and, therefore, needs to be in parentheses. Then, provide the additional information. ( Therefore, Kevin has $

�

)�

left.

Note: The symbol “∙” can be used in place of the “×” for multiplication.

Apply Use the order of operations to solve. 1.

12,323 + (234 ∙ 22) ÷ 2 =

2. 5,437 ∙ 6 + (9 ∙ 234) =

3. 152 + (12,374 + 17,289) � 5 =

4. (3 + 2352) � (5 ∙ 123) =

Level F

Chapter 5

Lesson 6

Lighthouse Math

Exercise 5-6 Name Use the order of operations to solve. 2. 28 � (6 ∙ 3) ÷ 2 =

4. 49 ÷ (3 + 4) ∙ 5 =

(42 � (9 ÷ 3)) ∙ 20 =

6. (37 + 5) ∙ 3 � 52 =

45 ÷ 9 + (5 ∙ 7) =

8. 82 + (21 ∙ 453) � 1,822 =

9. 542 ÷ 2 + 62 =

10. (17 � 234) � 834 ÷ 3 =

11. 7 � 8 + (16 ÷ 2) � 42 =

12. (62 ∙ 40) � 144 ÷ 12 =

13. 81 ÷ 3 + (52 � 6) =

14. 32 + 8 � 32 ∙ 4 =

15. (16 ∙ 5 � 2) ÷ 3 =

(4+5) ∙ 62 � 9 =

6 + 12 ∙ 2 � (32 � 1) =

Challenge Solve. 16. Roan buys 2 coffees for $4.00 each, a tea for $3.00, and 3 muffins for $3.00 each at the coffee shop. Write a numerical expression to represent this situation and then find the total cost of the meal.

Lighthouse Math

Level F

Chapter 5

Exercise 6

Chapter 5-7 Problem Solving: Division and Multiplication Daily Review

Solve using the order of operations.

1. (532 · 22) + 8 · 2 =

2. (3,840 ÷ 12) · 5 =

Learn and Connect A carnival has a ticket booth at the entrance. If a customer buys a pack of 20 game tickets and 5 adult admission tickets, how much will their total be? To solve, we have to first multiply the cost of the admission tickets by the number of tickets. Then, we have to add the additional pack of game tickets. Cost of admission tickets Number of tickets

�

Total cost of admission tickets Cost of 1 pack of 20 game tickets

Total price paid

Therefore, the customer would pay $

for the game tickets and admission tickets.

Apply Solve using the information from the ticket booth. 1.

How much do you save per ticket by buying a pack of 20 game tickets instead of single tickets?

2. If a customer bought 4 packs of ride tickets, how much would they have to pay?

HINT: Find the price of one ticket in the pack of 20 by dividing by the total cost

3. If a customer wanted 1 admission ticket for a kid that is 14 years old and three packs of ride tickets, how much would they have to pay?

Level F

Chapter 5

Lesson 7

Lighthouse Math

Exercise 5-7 Name Solve. John and his friends collect unique rocks. John has 234 rocks, Toby has 1 as 2 many rocks as John, Justin has 212 rocks more than John, and Elijah has 3 times as many rocks as Toby.

The local thrift store wants to send some of the extra clothes and shoes to another charity in town. They want to donate 1,548 shirts, 986 pairs of pants, and 326 pairs of shoes.

A. H ow many rocks does Toby have?

A. A single box can hold up to 100 items. How many boxes will they need?

B. How many rocks does Elijah have?

B. There are twice as many kid shirts as there are adult shirts. How many shirts are adult shirts?

C. W hat is the average number of rocks between the four boys?

C. Half of the shoes are for men. How many shoes are for women?

Challenge A store is having a sale on furniture. For every sofa purchased, they will give you 21 off of a loveseat or recliner. The regular price of each item is as follows: Sofa - $2,543 Recliner - $834 Loveseat - $1,892 End table - $165 3. H ow much would you pay for a sofa, recliner and two end tables? How much would you save?

Lighthouse Math

Level F

4. How much would you pay for a sofa, love seat, and two end tables? How much would you save?

Chapter 5

Exercise 7

Chapter 5-8 Review Solve using the order of operations.

Daily Review

1. (617 · 48) - 37 · 21 =

2. (731 ÷ 17) · 8 =

Learn and Connect John is comparing the prices of cupcakes at four local bakeries. Help John compare the prices by completing the chart. To find the price of one cupcake, divide the cost of 12 cupcakes by a dozen. To find the price of a dozen cupcakes, multiply the price per cupcake by 12. STORE

PRICE PER CUPCAKE

Hailey’s Cupcakes

$ 1.25

Mr. Kim’s Cupcakes

$14.52

Butterfly Bakery

$17.76

B & B Bakery © Lighthouse Curriculum. Copying strictly prohibited.

CUPCAKES PER DOZEN (12)

$1.58

Apply Use the completed chart above to answer the following questions. 1.

100

What is the average cost of a single cupcake?

Level F

If a large company ordered 235 cupcakes from Mr. Kim’s Cupcakes, how much would they pay for all of the cupcakes?

Chapter 5

Lesson 8

A customer paid $33.88 for 28 cupcakes. Which store did she get the cupcakes from? Hint: Determine the price of one cupcake and compare to the listed prices.

Lighthouse Math

Exercise 5-8 Name Find the average for each data set. 1. 4, 10 , 18, 12:

2. 56, 72, 34, 14, 89:

3. 34, 34, 25, 67, 45, 77:

Multiply. 4.

14,356 � 6

65,342 � 31

254,347 � 28

5,214 � 325

63,158 � 632

10. 24)2,145

11.

7)53,563

12. 35)34,326

13.

13)563,452

Divide. 9.

4)3,568

Solve. Check using the inverse operation. 5,423 � 51

Check:

15.

23)32,145

Check:

16.

16,237 � 35

18. 6 � 4 + (8 ÷ 2) � 22 =

19.

(52 ∙ 20) � 72 ÷ 8 =

Check:

14.

Solve using the order of operations. 17.

(24 � 315) � 652 ÷ 2 =

Challenge 20. A stadium can hold 15,450 people. Each section has 515 seats. How many sections are there in the stadium?

Lighthouse Math

Level F

21. The lumber yard just received a large shipment of tiles. There were 12 pallets delivered. Each pallet has 81 boxes of tiles. How many boxes of tiles were delivered?

Chapter 5

Exercise 8

101

Chapter 6 NYS NG Standards NY-4.NF.1 NY.4.NF.2 NY.4.NF.3c

NY-5.NF.2 NY-6.NS.4

CC Standards 4.NF.A.1 4.NF.A.2 4.NF.B.3.C

102

5.NF.A.2 6.NS.B.4

In Chapter 6 we will explore

Basic Fraction Concepts We will learn how to determine the greatest common factor and least common multiple of two numbers. We will explore prime and composite numbers and utilize prime factorization. We will create equivalent fractions and simplify fractions including rewriting improper fractions and mixed numbers.

Multiples Least Common Multiples (LCM) •W e will find the least common multiple of two numbers by listing the multiples of each number Prime, composite, and prime factorization •W e will discover the difference between prime and composite numbers by determining their factor pairs

Equivalent fractions • We will use GCF to determine equivalent fractions Simplest form • We will reduce fractions to simplest form by dividing the numerator and denominator by their GCF Rewrite improper fractions and mixed numbers • We will practice turning improper fractions into mixed numbers and turning mixed numbers back into improper fractions

Greatest Common Factors (GCF) •W e will find the greatest common factor of two numbers by listing all of their factors

Ordering and comparing fractions • We will compare fractions using benchmark numbers

103

Chapter 6-1 Factors and Greatest Common Factor (GCF) Daily Review Solve.

1. 6 × 2 =

2. 3 × 4

3. 5 × 6 =

4. 3 × 10 =

Learn and Connect Morris is planting flowers in his backyard. He has 30 red flowers, 15 blue flowers, and 45 yellow flowers. He wants to make rows of flowers with the same number of flower plants in each row. If each row holds the same color flower, what is the greatest number of plants he can put in each row? To solve, we have to find the greatest common factor of 30, 15, and 45. A factor is a number that, when multiplied by another number, equals a product. For example, 2 and 5 are factors of 10 because they equal 10 when multiplied together. 1 is a factor of all numbers because when a factor is multiplied by 1, it always equals itself. List all the factors for 30, 15, and 45. Then, circle the greatest common factor (GCF), or the largest factor they have in common. The factors of 15 are: ,

Therefore, Morris can put

The factors of 30 are: ,

The factors of 45 are: ,

plants of the same color in each row.

Apply List all the factors of each number. Then, list the greatest common factor. 1. 1 2:

2. 3 0:

3. 2:

24:

15:

GCF:

4. 2 0:

5. 1 0:

6. 15:

15:

30:

40:

GCF:

Vocabulary Factor - a number, when multiplied by another number, equals a product Greatest Common Factor (GCF) - the greatest factor that both numbers have in common

104

Level F

Chapter 6

Lesson 1

Lighthouse Math

Exercise 6-1 Name

1. 18:

2. 30:

3. 3:

24:

20:

10:

GCF:

4. 25:

5. 12:

6. 27:

15:

32:

45:

GCF:

7. 16:

8. 21:

9. 6:

26:

GCF:

10. 13:

11. 28:

12. 14:

36:

35:

GCF:

13. 22:

14. 34:

15. 4:

33:

40:

44:

GCF:

List all the factors of each number. Then, list the greatest common factor (GCF).

Challenge Solve each problem. 16. Kevin is making identical gift bags for his friends. He has 18 balloons and 12 pieces of candy. What’s the largest number of gift bags he can make to have no leftover balloons and candy?

Lighthouse Math

17. Isaac wants to display his trophies and medals on shelves in his room. Each shelf will have the same number of trophies and medals on them. Isaac has 20 trophies and 15 medals to display. How many shelves will Isaac need?

Level F

Chapter 6

Exercise 1

105

Chapter 6-2 Least Common Multiple (LCM) Find the Greatest Common Factor (GCF) of each of these pairs.

Daily Review 1. 22, 18:

2. 40, 24:

3. 10, 8:

Learn and Connect Jason is having a small event at his home to celebrate his graduation. He wants to buy the same number of cups and plates for the event. If the cups come in packs of 6 and the plates come in packs of 8, what is the least number of cups and plates that Jason needs to buy to have the same amount of each? To solve, we need to find the least common multiple of 8 and 6. Multiples are the result of the same factor being repeatedly added together. When you divide a multiple by one of its factors, you don’t get a remainder. Write out the multiples of 8 and 6. Then, determine which is the least common multiple (LCM), or the smallest number they have in common. Multiples of 8:

Therefore, Jason will have

Multiples of 6:

of each. He will need to buy

packs of cups and

, packs of plates.

Apply List the first five multiples of each of the numbers. 1.

21:

2. 22:

3. 15:

4. 41:

List the multiples of each number and determine the least common multiple (LCM). 5. 8 :

6. 7 :

7. 2:

LCM:

Vocabulary Multiple - the result of the same factor being repeatedly added together; when you divide a multiple by one of its factors, you don’t get a remainder Least Common Multiple (LCM) - the smallest multiple that both numbers have in common 106

Level F

Chapter 6

Lesson 2

Lighthouse Math

Exercise 6-2 Name

1. 3:

2. 4:

3. 6:

10:

LCM:

4. 9:

5. 6:

6. 3:

14:

18:

LCM:

7. 12:

8. 21:

9. 10:

LCM:

10. 8:

11. 12:

12. 14:

21:

LCM:

13. 15:

14. 5:

15. 7:

28:

LCM:

List the multiples of each number and determine the least common multiple (LCM).

Challenge Solve each problem. 16. At 9am, two buses arrive at a bus stop. One bus returns every 6 minutes and the other returns every 8 minutes. How many minutes will pass before both buses are at the stop at the same time again?

Lighthouse Math

17. One student is stacking blocks that are 12 inches tall. Another student is stacking blocks that are 10 inches tall. How many inches tall will the stacks be when they are both the same height?

Level F

Chapter 6

Exercise 2

107

Chapter 6-3 Prime Factorization Find the greatest common factor (GCF) of each of these pairs.

Daily Review 1. 18, 24:

2. 3, 12:

3. 9, 15:

Learn and Connect Prime Versus Composite Numbers A prime number is a number with only one factor pair, itself and one.

A composite number is a number that has more than one factor pair.

For example: The number 5 can only be made by multiplying 1 × 5. Therefore, 5 is a prime number.

For example: The number 10 can be made by multiplying 1 × 10 and 2 × 5. Therefore, the number 10 is composite.

Prime factorization Prime factorization is a way of expressing a number as a product of its prime factors. 48 6

�

� 2

Therefore, the prime factorization of 48 can be represented by:

8 2

�

2 × 2 × 2 × 2 × 3 OR 24 × 3

Apply Identify the number’s factor pairs, then circle if it is prime or composite. 1. Factor pairs for 3:

2. F actor pairs for 12:

Prime or Composite

3. Factor pairs for 9:

Prime or Composite

Complete the factor tree and write the prime factorization using exponents. 4. P rime factorization for 24:

5. Prime factorization for 90:

�

45 3

� �

108

Level F

Chapter 6

Lesson 3

Lighthouse Math

Exercise 6-3 Name Identify the number’s factor pairs, then circle if it is prime or composite. 2.

Prime or Composite

Factor pairs for 6:

3. Factor pairs for 8:

Prime or Composite

4. Factor pairs for 4:

Prime or Composite

Factor pairs for 7:

Prime or Composite 6. Factor pairs for 10:

Prime or Composite

7. Factor pairs for 13:

Prime or Composite

Factor pairs for 20:

Prime or Composite 9. Factor pairs for 15:

Prime or Composite

10. Factor pairs for 11:

11. Factor pairs for 16:

Prime or Composite

Prime or Composite 12. Factor pairs for 21:

Prime or Composite

13. Factor pairs for 18:

14. Factor pairs for 14:

Prime or Composite

Prime or Composite 15. Factor pairs for 17:

Prime or Composite

Complete the factor tree and write the prime factorization using exponents. 16. Prime factorization for 81:

17. Prime factorization for 100:

100

�

Lighthouse Math

�

Level F

Chapter 6

Exercise 3

109

1. Factor pairs for 5:

Chapter 6-4 Equivalent Fractions Determine if the number is prime or composite.

Daily Review 1. 12:

2. 100:

3. 7:

4. 19:

Learn and Connect Alexander is cooking using his mother’s recipe. He noticed that he needs 1 cup of sugar. However, he only had a 1 cup 2 8 measuring cup. How many scoops of sugar does he need to add using the 1 cup measuring cup to equal 1 ? 8

To solve, we need to find an equivalent fraction to 1 that 2 has a denominator of 8. An equivalent fraction is a fraction that is equal to another fraction. To make an equivalent fraction you have to divide or multiply the numerator and the denominator by the same number. First, consider: 2 ×

Numerator

Then, multiply the numerator by the same number. Therefore, 1 is equivalent to 2 with the 1 measuring cup.

1 × 2 ×

Denominator

= =

. This means that Alexander needs to add

scoops of sugar

Apply Write two equivalent fractions that can represent the shaded part of the figure. 1.

Fill in the boxes to make an equivalent fraction. 4.

110

7 × 8 ×

= =

5 ÷ 5. 20 ÷

Level F

= =

Chapter 6

3 × 6. 12 ×

Lesson 4

= 12 =

÷ 7. 20 30 ÷

= =

Lighthouse Math

Exercise 6-4 Name Write two equivalent fractions that can represent the shaded part of the figure. 1.

10.

3 × 7 ×

= =

13.

15 25

� �

= =

11.

12 � 18 �

= =

14.

7 × 15 ×

= = 30

12.

5 × 11 ×

= 20 =

15.

35 � 63 �

= =

Find the equivalent fraction.

Challenge Solve. 17. Samuel put a book that weighs 5 6 of a pound on one end of a seesaw. How many 1 pound weights 12 should he put on the other end to balance the seesaw?

16. One lap around a certain track is 1 of a mile. After 16 running 12 laps, what fraction of a mile have you run? Write two equivalent fractions. Lighthouse Math

Level F

Chapter 6

Exercise 4

111

Chapter 6-5 Simplest Form Complete the equivalent fraction.

Daily Review 1.

1 × 5 ×

= =

6 ÷ 2. 30 ÷

= =

4 × 8 ×

= =

÷ 4. 18 45 ÷

= =

Learn and Connect Blake made a cheesecake for his family on Monday. He cut the cake into 16 equal pieces. By Friday, his family had eaten a lot of the cheesecake. What fraction of the cheesecake remains? To solve, we need to create a fraction by making the numerator the number of cheesecake pieces that remain and the denominator being the total number of pieces that made up the entire cheesecake. Remaining pieces Total pieces To write this number in simplest form, we need to find the greatest common factor (GCF) of both the numerator and the denominator. Then, we divide both numbers by the greatest common factor.

Factors of numerator:

Factors of denominator: Therefore, there is

, ,

of the cheesecake remaining.

Apply Simplify Each Fraction. 1.

1 ÷ 5 ÷

= =

30 ÷ 60 ÷

= =

5 ÷ 25 ÷

= =

4. 24 ÷ 36 ÷

= =

6 ÷ 9 ÷

= =

8 ÷ 14 ÷

= =

8 ÷ 40 ÷

= =

8. 18 ÷ 45 ÷

= =

Vocabulary Greatest Common Factor (GCF) - the greatest factor that both numbers have in common 112

Level F

Chapter 6

Lesson 5

Lighthouse Math

Exercise 6-5 Name

15 ÷ 40 ÷

= =

20 ÷ 60 ÷

= =

15 ÷ 25 ÷

= =

16 ÷ 18 ÷

= =

18 ÷ 24 ÷

= =

12 ÷ 40 ÷

= =

27 ÷ 45 ÷

= =

35 ÷ 49 ÷

= =

6 ÷ 100 ÷

= =

10.

24 ÷ 54 ÷

= =

11.

22 ÷ 77 ÷

= =

12.

25 ÷ 55 ÷

= =

13.

6 ÷ 39 ÷

= =

14.

28 ÷ 64 ÷

= =

15.

36 ÷ 42 ÷

= =

16.

22 ÷ 50 ÷

= =

17.

54 ÷ 60 ÷

= =

18.

64 ÷ 84 ÷

= =

Simplify each fraction.

Challenge Solve each problem. 19. S teven is running a 24 mile race. He has already run 10 miles. How much of the race has he completed? Express your answer as a simplified fraction.

Lighthouse Math

20. Nathan is working on a worksheet that is 20 problems long. He has finished 12 of the problems. How much of the worksheet has he completed? Express your answer as a simplified fraction.

Level F

Chapter 6

Exercise 5

113

Chapter 6-6 Improper and Mixed Fractions Reduce to simplest form.

Daily Review 1. 15 ÷ 20 ÷

= =

÷ 2. 4 8 ÷

= =

÷ 3. 24 36 ÷

= =

9 4. 36

÷ ÷

= =

Learn and Connect Mr. Stevens ordered some pizzas for his children and their friends. After eating, the children had some slices of pizza left. If each slice was 1 of a 6 pizza, how much of the pizza was left over? To solve, we need to create a fraction by making the numerator the number of remaining slices of pizza and the denominator the size of the slices. Number of slices left Size of slices

8 6

The fraction of pizza remaining is an improper fraction. This means that the numerator is bigger than the denominator, which indicates we have more than one whole. We need to change the fraction into a mixed number. To turn improper fractions into mixed numbers:

To turn mixed numbers into improper fractions:

Turn the fraction into a division problem. The denominator becomes the divisor and the numerator becomes the dividend.

Multiply the denominator times the whole number. Then, add the numerator.

8 6

1 6)8 –6 2 2 16

Number of wholes

New numerator

+ �

2 6

6�1=6+2=8

New numerator Denominator stays the same

Denominator stays the same

8 6

Therefore, there is 1 whole pizza and 2 slices remaining. 6

Apply Turn the improper fractions into mixed numbers and the mixed numbers to improper fractions. 1. 13 3 =

114

2. 45 =

3. 19 2 =

Level F

Chapter 6

4. 6 37 =

Lesson 6

5. 9 31 =

2 6. 2 11 =

Lighthouse Math

Exercise 6-6 Name Turn the improper fractions into mixed numbers. Simplify if necessary. 1.

17 3 =

7 5=

21 = 2

18 8 =

13 4 =

16 6 =

75 20 =

50 11 =

30 7 =

10. 58 10 =

11. 85 9 =

12. 27 12 =

13. 33 8 =

14. 45 6 =

15. 27 7 =

16. 76 9 =

3 17. 4 12 =

18. 8 47 =

19. 7 32 =

20. 6 45 =

5 21. 3 11 =

22. 5 21 =

23. 2 65 =

24. 9 97 =

25. 2 27 =

26. 10 83 =

7 27. 6 10 =

28. 11 43 =

29. 6 87 =

30. 4 45 =

11 31. 12 12 =

32. 3 98 =

Challenge Solve the problems. 33. T he art teacher has students cut pieces of paper into identical strips for a project. Each piece of paper makes 10 strips. How many pieces of paper will be needed to make 45 strips? Express your answer as both an improper fraction and as a mixed number.

Lighthouse Math

Level F

34. For a certain set of blocks, 12 stacked on top of each other will be 1 foot high. For a science project, you will stack 50 of these blocks. How many feet high will your stack reach? Express your answer as both an improper fraction and as a mixed number.

Chapter 6

Exercise 6

115

Turn the mixed numbers into improper fractions.

Chapter 6-7 Order and Compare Fractions Turn the improper fractions into mixed numbers.

Daily Review 1. 17 2 =

2. 79 10 =

3. 65 11 =

4. 37 4 =

Learn and Connect A tailor is adding ribbon to a customer's dress. He wants to use the thickest ribbon he has. Which size ribbon should he use? To solve, we need to compare the thickness of both ribbons. However, we cannot compare fractions with different denominators. Therefore, we need to rewrite the fractions with common denominators. List the multiples of the denominator of each fraction. Multiples of 4:

Multiples of 5:

Then, create equivalent fractions using the new denominator. Compare the new fractions by determining which fraction has the largest numerator. 4 × 5 ×

3 × 4 ×

= =

Therefore, the tailor should use the ribbon that is

in thick.

Apply Compare the fractions by rewriting them using a common denominator. Then place a <, > or = inside the circle. 1. 51

3 8

3 2. 11

2 5

3. 97

5 6

6 4. 11

5 8

5. 98

4 5

Put the fractions in order from least to greatest. 6. 97

116

1 3

1 18

7. 43

Level F

1 2

Chapter 6

2 8

8. 31

Lesson 7

2 5

4 15

Lighthouse Math

Exercise 6-7 Name Compare the fractions by rewriting them using a common denominator. Place <, > or = inside the circle. 1.

2 5

5 6

6 11

3 7

2 9

1 6

7 12

9 10

3 4

4 9

2 9

3 10

4 7

2 3

2 5

3 13

7 10

4 5

10. 43

5 6

11. 35

5 7

12. 51

2 15

13. 83

2 7

14. 85

7 11

15. 87

9 10

16. 35

5 7

1 2

17. 32

3 7

19. 83

5 6

7 10

3 20. 10

5 11

22. 45

2 3

7 8

2 23. 12

3 15

3 4

18. 61

2 5

4 9

2 9

21. 35

2 3

5 11

1 8

24. 35

8 15

7 10

Challenge 25. T hree friends calculated how tall

26. T hree students were comparing different

they were. Lenny was 5 83 ft, Jeremy

quizzes from different classes. One student

7 was 5 12 ft, and Ken was 5 4 9 ft.

18 8 got 20 right, one student got 10 right, and

one got 16 18 right. Put the students’ grades in

Who was the tallest?

order from least to greatest.

Lighthouse Math

Level F

Chapter 6

Exercise 7

117

Put the fractions in order from least to greatest.

Chapter 6-8 Problem Solving Review Daily Review Compare the fractions by rewriting them using a common denominator. Place a <, > or = sign inside the circle. 1. 85

2 6

7 12

5 2. 15

Learn and Connect Two students chose a numbered card. They then used the numbers to fill out the chart below. Complete the chart using the same numbers to check their answers. 18

List the factors and circle the GCF List the multiples and circle the LCM

3 × 18 ×

Create an equivalent fraction

= =

5 × 27 ×

= =

Prime or Composite?

18 =

Complete a prime factor tree and write the prime factorization in exponents in the box on the top right

27 =

18 3

�

Apply Turn the improper fractions to mixed numbers and reduce each fraction to the simplest form. 1.

÷ ÷

28 12 =

= =

21 6 =

÷ ÷

= =

10 4 =

÷ ÷

= =

Compare the fractions by rewriting with a common denominator. Place a <, > or = sign inside the circle. 4. 93

118

10 50

5 5. 60

16 20

Level F

18 6. 48

Chapter 6

10 30

Lesson 8

1 7. 10

1 4

8. 21

1 12

Lighthouse Math

Exercise 6-8 Name List all the factors of each number. Then, list the greatest common factor. 1. 32:

2. 15:

3. 9:

48:

28:

36:

GCF:

List the multiples of each number and determine the least common multiple. 4. 4:

5. 6:

6. 12:

15:

20:

LCM:

Identify the number’s factor pairs, then circle if it is prime or composite. 8.

7. Factor pairs for 23:

Prime or Composite

Factor pairs for 24:

9. Factor pairs for 35:

Prime or Composite

10.

30 ÷ 54 ÷

= =

11.

30 ÷ 74 ÷

= =

12.

28 ÷ 44 ÷

Simplify each fraction. = =

Turn the improper fractions into mixed numbers and the mixed numbers into improper fractions. 13. 23 4 =

14. 7 65 =

15. 57 5 =

16. 1232 =

Put the fractions in order from least to greatest. 17. 92 47 31

Lighthouse Math

13 18. 45 43 16

Level F

3 4 19. 25 10 15

Chapter 6

Exercise 8

119

Chapter 7 NYS NG Standards NY-4.NF.2 NY-4.NF.3a NY-4.NF.3c

5.NF.1 5.NF.2 6.NS.4

CC Standards 4.NF.A.2 4.NF.B.3.A 4.NF.B.3.C

120

5.NF.A.1 5.NF.A.2 6.NS.B.4

In Chapter 7 we practice

Adding and Subtracting Fractions We will use our knowledge of LCD and GCF to make equivalent fractions and simplify. We will also practice rewriting mixed numbers and improper fractions.

Estimate with fractions • We will use benchmark numbers to estimate the sum and difference of fractions Add fractions with the same denominator • We will practice adding fractions with the same denominator Find a LCF and add a different denominator • We will find the least common factor to create equivalent fractions and add Add mixed numbers with LCD and regrouping • We will add mixed numbers and regroup fractions and mixed numbers Subtract fractions with the same denominator review • We will practice subtracting fractions with the same denominator Subtract numbers with different denominator • We will find the least common factor to create equivalent fractions and subtract Subtract from whole number or mixed numbers with regrouping • We will subtract mixed numbers and regroup fractions and mixed numbers

121

Chapter 7-1 Estimating with Fractions Simplify the fractions.

Daily Review 1.

1 � 4 �

= =

2. 45 � 54 �

= =

3. 20 � 40 �

= =

4. 21 � 28 �

= =

Learn and Connect Abel is weighing fruit at the grocery store. He noticed that the watermelon 6 ounces and the cantaloupe weighed 225 1 ounces. weighed 230 10 12 About how much more did the watermelon weigh than the cantaloupe? To solve, we need to estimate the size of each fruit and then subtract. When estimating fractions, we use benchmark numbers. The denominator in the fraction tells us how many pieces we need to make 1 whole. Determine how many pieces you need to make 1 whole and half for each fraction. Then, decide if the numerator is closer to 0, 1 , or 1 whole. 2

1 whole: 10 pieces 6 10 half: 5 pieces

1 whole: 12 pieces half: 6 pieces

1 12

Notice that 6 is closer to 1 because

Since 1 is closer to zero than 6, 1 is

6 is closer to 5 than 10. This means,

closer to the lesser whole. This means,

we estimate 230 6 to 230 1 .

we estimate 225 1 to 225.

12 1 Next, we subtract 225 from 230 2 . Therefore, the watermelon weighs 5 21 ounces more than the

cantaloupe.

Apply Determine if each fraction is closer to 0, 1 , or 1. 2

1. 21

8 2. 18

9 3. 10

2 4. 10

8 5. 10

Estimate the solution to each problem using benchmark numbers. 2 7 10 =

6. +

3 51 =

12 9 24 =

7. +

5 2 12 =

2 6 15 =

8. �

3 3 13 =

9. +

12 10 11 =

10.

4 67 =

4 45 =

�

3 61 =

Vocabulary Benchmark numbers - numbers against which other numbers or quantities can be estimated and compared 122

Level F

Chapter 7

Lesson 1

Lighthouse Math

Exercise 7-1 Name Determine if each fraction is closer to 0, 1 , or 1. 2

4 6

5 14

3 8

1 6

4 6. 30

5 6

8. 30 50

7 8

10. 62

11. 20 24

12. 85

13. 63

15 14. 30

15. 93

1 7

Estimate the solution to each problem using benchmark numbers.

8 5 10 =

20.

4 67 =

9 51 =

17. +

21. +

5 7 12 =

18.

5 9 16 =

5 12 14 =

17 2 20 =

�

31 3 40 =

5 85 =

24 6 =

22.

5 20 25 =

23.

13 98 =

1 83 =

�

7 5 18 =

5 57 =

19.

Challenge 24. A student weighs the contents of his

25. The art teacher has one box of clay that

backpack and finds a textbook that

weighs 3 10 pounds. He combines the

weighs 5 of a pound and another

clay with another box that weighs 2 1

textbook that weighs 8 of a pound.

pounds. Using benchmark numbers,

Using benchmark numbers, estimate the

estimate the total weight of the clay.

weight of the two books together.

Lighthouse Math

Level F

Chapter 7

Exercise 1

123

6 81 =

16.

Chapter 7-2 Adding Fractions with Like Denominators Daily Review

Determine if each fraction is closer to 0, 1 , or 1. 2

1. 42 =

8 2. 18 =

9 3. 10 =

2 4. 10 =

8 5. 10 =

Learn and Connect There are some ducks in a pond. After an hour, 4 of the ducks flew away. Thirty minutes later, 12 an additional 2 of the original ducks flew away. 12

What fraction of the ducks flew away over the past hour and a half?

To solve, we have to add the amount of ducks that flew away after an hour and the amount of ducks that flew away after another thirty minutes. To add fractions with the same denominator, first you add the numerators.

4 2 2 12 + 12 = 12

Then, keep the denominator the same.

Last, reduce the fraction to simplest form.

4 2 12 + 12 =

6 �6 12 = �6

6 12

1 2

Therefore, 1 of the original ducks flew away. 2

Apply Add and simplify answers if necessary. 4 7

1. +

1 7

5 3 10

6. +

124

3 2 10

3 8

2. +

4 8

2 11 12

7. +

Chapter 7

2 45

Lesson 2

1 2

7 9

7 51

6 8 12

Level F

7 9

1 2

5 12 10

9. +

3 8 10

11 16

5. +

12 16

4 31

10. +

4 32

Lighthouse Math

Exercise 7-2 Name Add and simplify answers if necessary.

1 3

6 4 11

6. +

7 98

5 65

8 20

6 2 15

10.

8 43

9 10

14.

5 9

7 10

4 9

24 25

5 7 16

20.

1 1 10

7 5 16

9 8 10

5 4 16

18.

1 4

10 42

15 20

2 47

13.

1 5

1 63

17.

6 37

3 4

8 12

7 4 13

3 5

12.

9 12

4 6

4 9 13

1 8

5 97

16.

4 6 11

5 8

11.

1 6

19.

11 2 16

9 4 15

6 25

15.

2 3

Challenge Solve and simplify if necessary. 21. Eli brings 3 82 pizza to a birthday party,

22. Caleb and Samuel are training for a relay

and Ezra brings 2 7 of a pizza. How much

race. Caleb can run 3 of the race, Samuel

pizza combined did the two boys bring?

can run 5 of the race. Together, how

much of the race can they complete?

Lighthouse Math

Level F

Chapter 7

Exercise 2

125

Chapter 7-3 Adding Fractions with Different Denominators Daily Review

Add and simplify answers if necessary.

5 2 + = 8 8

4 3 + = 5 5

2 3 + = 11 11

Learn and Connect Roger’s baby brother has a toy train. The train has a total length of 7 ft. Roger bought his brother a new piece that connects to the 8

train that is 6 ft long. When the new train piece is connected, 7

what will be the full length of the toy train? To solve, we need to add the length of the current toy train and the length of the additional new piece. Numbers with different denominators cannot be added or subtracted as is because the denominators represent different size pieces. Therefore, you must use equivalent fractions. First, find the least common multiple for each denominator.

+ 87

7, 14, 21, 28, 35, 42, 49, 56 8, 16, 24, 32, 40, 48, 56, 64 © Lighthouse Curriculum. Copying strictly prohibited.

Then, create your new, equivalent fractions by multiplying the numerators by the same factor.

6 = 56 7 �8

= �7 56

The full length of the toy train will be

Finally, add the numerators and simplify if necessary.

6 �8 48 = 56 7 �8 �7 + 87 = 49 �7 56 97 41 56 = 1 56

Apply Add and simplify answers if necessary. 1 5

1. +

126

3 4

1 7

1 3

1 2

2. +

2 5

2 8

7. +

Chapter 7

1 5

Lesson 3

1 8

1 4

1 6

3 5

Level F

2 3

1 7

3 7

9. +

3 8

3 5

5. +

1 4

10. +

3 6

Lighthouse Math

Exercise 7-3 Name Add and simplify answers if necessary.

1 5

1 2

5. +

13. +

1 6

1 4

1 6

1 4

3 5

14.

2 4

2 9

3 8

1 2

16.

2 7

3 7

2 3

15.

2 5

12.

3 5

1 5

1 3

11.

1 4

2 5

3 8

2 6

2 5

1 7

1 2

10.

2 4

1 3

3 4

1 3

1 2

1 6

Challenge Solve and simplify if necessary. 17. Two students are working on a project.

18. Noah is baking a cake and measuring the

One student finishes 5 of the project,

flour. First he adds 1 of a cup of

the other finishes 2 of the project. How 5

flour, then adds another 2 cup. How

much of the project have they finished?

Lighthouse Math

Level F

much total flour has he added?

Chapter 7

Exercise 3

127

Chapter 7-4 Add Mixed Numbers with Unlike Denominators Daily Review

Add and simplify answers if necessary.

6 6 12 + 8 =

7 1 9 + 5 =

2 6 3 + 9 =

Learn and Connect Elijah is making a floral arrangement for his mother. He originally cut off 1 3 in. of the 4

stems of each flower. He realized that the flowers were still too tall so he cut off some more. How many total inches did Elijah cut off of the stem? To solve, you must add the lengths of both pieces that Elijah cut off the stem. However, numbers with different denominators cannot be added or subtracted as is because the denominators represent different size pieces.

Therefore, you must use equivalent fractions. First, find the least common multiple for each denominator. 4, 8, 12, 16 6, 12, 18, 24

1 43

�3

+ 1 62

�2

= 1 12 = 1 12

Then, create your new, equivalent fractions by multiplying the numerators by the same factor.

1 43

Finally, add the numerators. Then, add the wholes and simplify if necessary.

�3

= 1 9 �3 12 �2 4 + 1 62 = 1 12 �2 13 1 2 12 = 3 12

Apply Add and simplify answers if necessary. 1.

1 31 + 4 83

128

2 51

2. +

6 62

Level F

1 31

3. +

Chapter 7

3 35

Lesson 4

1 51

4. +

5 27

2 4 4

5. +

2 9 8

Lighthouse Math

Exercise 7-4 Name Add and simplify answers if necessary. 1 2 +

3 3 + 4 67

3 4 +

2 5

13.

4 4 +

8 8

10.

+ 4 65

14.

+ 10 31

4 5 +

7 3

2 7

16.

4 6 +

1 5 +

1 8

2 9

12.

15.

1 4 +

3 3 +

5 2

1 5

1 9

11.

4 2

2 5 +

1 6 +

5 2

2 7

1 4 +

6 4

4 3 +

3 5

9 3

Challenge Solve and simplify if necessary. 17. A flag is raised from the ground 2 2 feet 5

18. Samuel started a new book and read

up a flagpole, then it is raised another

3 1 chapters of his book. After dinner,

4 1 feet. How many feet up the pole is 4

he read another 2 2 chapters. How many

the flag?

Lighthouse Math

Level F

chapters has he read in total?

Chapter 7

Exercise 4

129

Chapter 7-5 Subtract Fractions with Like Denominators Daily Review

Add and simplify answers if necessary.

1. 10 91 + 7 65 =

4 87 + 1 68 =

Learn and Connect When David first began mowing his lawn, his battery was 5 full. By the time he was done 6

mowing the lawn, the battery was 1 full. What 6

fraction of the battery did it take to mow the lawn? To solve, we need to subtract the amount the battery is at after David mows the lawn from the amount that he started with. To subtract fractions with the same denominator, first you subtract the numerators. 5 6

4 � 61 = 12

Then, keep the denominator the same.

Last, reduce the fraction to simplest form.

5 6

4 6

� 61 = 4 6

�2 = �2

2 3

Therefore, mowing the lawn used 2 of David’s lawn mower’s battery. © Lighthouse Curriculum. Copying strictly prohibited.

Apply Subtract and simplify answers if necessary. 2 12

1. �

1 12

3 4

5. �

130

1 4

5 10 �

2 6 �

Level F

3 6

Chapter 7

9 4 �

2 10

�

Lesson 5

1 10

5 8 �

1 4

6 10

4 8

3 12 �

4 12

Lighthouse Math

Exercise 7-5 Name Subtract and simplify answers if necessary.

�

3 14

� 3 41

�

4 13

10.

9 11

� 2 61

�

4 11

14.

7 5

13.

5 16 �

7 16

9 10

5 1 10

1 2

11 12

16.

8 10 �

3 2 �

15.

� 4 25

1 15

8 7

12.

6 15 �

9 7 �

11.

1 9

7 10

�

8 9 �

1 4

4 13

7 4 �

2 8

6 8 �

�

2 12

9 14

Challenge Solve and simplify if necessary. 17. Your neighbor came to borrow flour. You

18. A runner is running a course that is 9 13

have 4 5 cups of flour. The neighbor

miles long. The runner has already run

borrowed 2 3 cups. How many cups of

3 3 miles. How many miles are left

flour do you have left?

before the runner has reached the end of

the course?

Lighthouse Math

Level F

Chapter 7

Exercise 5

131

Chapter 7-6 Subtract Fractions with Unlike Denominators Daily Review

Subtract and simplify answers if necessary.

2 1 3 � 3 =

3 2 5 � 5 =

6 1 10 � 10 =

Learn and Connect Micah and Noah are making milkshakes. Micah used a 2 cup ice cream scooper to get his ice cream. 3

Noah used a 3 cup ice cream scooper to get his ice cream. 4

How much more ice cream did Noah use than Micah? To solve, we have to subtract the amount of ice cream Micah is using from the amount of ice cream Noah is using. First, find the least common multiple for each denominator.

Then, create your new, equivalent fractions by multiplying the numerators by the same factor.

3 = 12 4 �3

�

3, 6, 9, 12, 15 4, 8, 12, 16

2 = 12 3 �4

Finally, subtract the numerators and simplify if necessary.

3 �3 9 = 12 4 �3

�

2 �4 8 = 12 3 �4 1 12

Therefore, Noah used 1 cup more ice cream than Micah. © Lighthouse Curriculum. Copying strictly prohibited.

Apply Subtract and simplify answers if necessary. 2 3

1. �

�

132

1 4

6 15

1 8

1 2

2. �

2 6

7 8

6. �

Level F

2 3

3. �

1 3

�

Chapter 7

1 4

13 16

Lesson 6

1 6

4 9

4. �

1 4

9 11

8. �

3 5

Lighthouse Math

Exercise 7-6 Name Subtract and simplify answers if necessary.

�

1 4

4 5

5. �

9. �

13. �

1 2

2. �

2 5

1 4

�

1 3

3 4

10.

6 7

1 3

�

1 2

7 9

14.

7 8

1 4

�

1 4

�

5 6

7. �

�

5 8

�

2 3

15. �

3 8

5 6

16.

2 9

1 4

4 5

12.

1 6

5 7

3 4

11.

4 9

1 5

�

2 3

�

4 7

Challenge Solve and simplify if necessary. 17. A share of 43 of a pie is divided up and

18. Before class today, you had used 1 of

given to the guests. There is 5 of the full

the pages in your notebook. After taking

pie remaining. What fraction of the full

notes in class, you had used a total of

pie was eaten?

2 of the pages in your notebook. What 9

fraction of the pages of your notebook were used by today’s notes?

Lighthouse Math

Level F

Chapter 7

Exercise 6

133

1 2

Chapter 7-7 Subtract Mixed Numbers with Unlike Denominators Daily Review

Subtract and simplify answers if necessary.

2 1 3 � 5 =

3 1 6 � 3 =

Learn and Connect Oliver and his brother were racing toy cars. Oliver’s car traveled 5 ft less than his brother’s. If Oliver’s brother’s 8

car traveled the entire length of their backyard swimming pool, how far did Oliver’s car travel? To solve, we need to subtract 5 from the total length 8

Oliver’s brother’s car traveled.

Numbers with different denominators cannot be added or subtracted because the denominators represent different size pieces. Therefore, you must use equivalent fractions.

First, create equivalent fractions by finding the least common multiple for each denominator.

6 31 �

3, 6, 9, 12, 15, 18, 21, 24 8,16, 24, 32, 40, 48, 56

�8

8 = 6 24

�8

5 �3 = 8 �3

15 24

Notice, you cannot subtract the numerators because 8 is smaller than 15. Therefore, you have to borrow a whole in fraction form.

Therefore, Oliver’s toy car traveled

6 31 �

�8 5 8 +24 32 = 6 24 4 �8

5 �3 = 8 �3

15 24 17 5 24

ft.

Apply Subtract and simplify answers if necessary. 1

2 8 �

134

5 6

2. �

3 4

Level F

5 2

Chapter 7

6 9 �

Lesson 7

1 5

3 10 �

2 6

Lighthouse Math

Exercise 7-7 Name Subtract and simplify answers if necessary.

5 6 �

1 7

9 4

1 1 3

�

2 6

�

7 10

6 2

10.

9 3

� 4 27

�

1 5

9 8

14.

7 10

�

7 15

�

13. �

5 4

11.

�

1 12

5 4

12.

7 2

�

3 9

2 7

8 9 �

1 12

16.

6 6 �

5 8

5 6

15.

2 3

3 9 �

4 4

3 2

8 5

8 5 �

3 7

2 3

Challenge 17. A student is making a project using

fabric. The student has 9 43 feet of fabric.

7 After using 6 8 feet of the fabric, how

1 18. A cook is bringing a pot filled with 4 6

pints of water to a boil. After heating the 9 water, there are 3 10 pints of water left

in the pot. How many pints of the water

many feet of fabric are left?

were lost to steam?

Lighthouse Math

Level F

Chapter 7

Exercise 7

135

Chapter 7-8 Review Daily Review 1.

Subtract and simplify answers if necessary.

5 43 � 2 81 =

1 44 6 � 2 3 =

Learn and Connect A gardener measured the height of the trees growing in his yard. He made the chart below to keep track of how tall each tree was. Tree Type

Oak Tree

Maple Tree

Papaya Tree

Mango Tree

Height (feet)

4 42 ft

3 45 ft

7 32 ft

1 ft 5 12

What is the difference between the height of the tallest tree and the shortest tree? To solve, we need to subtract the height of the shortest tree from the height of the tallest tree. Multiples of tallest tree denominator:

Multiples of shortest tree denominator:

Tallest tree

7 32

Shortest tree

� 3 45

6 +15 25 = 7 10 15 15 = 3 12 15

3 13 15 Therefore, the difference between the tallest and shortest tree is

ft.

Apply Use the chart above to answer the questions. Simplify your answers if necessary. 1.

A month later, the

Two months later, the

The gardener bought a

gardener noticed that

oak tree was a total

new mango tree that was

ft. How tall is the papaya

much did it grow in two

much taller is the new

the papaya tree grew 1 43 tree now?

height of 6 43 ft tall. How months?

7 98 ft tall. About how

mango tree than the old one?

136

Level F

Chapter 7

Lesson 8

Lighthouse Math

Exercise 7-8 Name Estimate the solution to each problem nearest half or whole. 7 71

8 4 9

9 + 4 11

10 85

17 1 30

�

7 14 15

3 2 24

� 4 4 6

Add and simplify answers if necessary. 1 3

5. +

1 5

6 3

1 3

6. +

10.

+ 2 41

2 7

1 6

1 2

11.

8 2 + 3 35

3 4

8. +

12.

4 6 + 1 43

1 8

5 7 + 9 31

Subtract and simplify answers if necessary. 1

8 8 � 1 65

14.

15.

9 3 � 4 41

16.

6 2 � 2 57

13.

5 10 � 3 45

Challenge 17. A recipe calls for 5 43 cups of flour.

5 A baker has 2 12 cups of flour. How many

more cups of flour does the baker need to complete the recipe? Simplify if necessary.

Lighthouse Math

Level F

18. A student is coloring in shapes for a math 1 shapes project. The student colored 6 15

3 yesterday and 10 10 shapes today. How

many shapes did the student color?

Chapter 7

Exercise 8

137

Chapter 8 NYS NG Standards NY-4.NF.1 NY-5.NF.4a NY-5.NF.7a NY-5.NF.7b

NY-5.NF.7c NY-6.NS.1 NY-6.NS.4

CC Standards 4.NF.A.1 5.NF.B.4.A 5.NF.B.7.A 5.NF.B.7.B

138

5.NF.B.7.C 6.NS.A.1 6.NS.B.4

In Chapter 8 we will practice

Multiplying and Dividing Fractions We will multiply and divide fractions by fractions and mixed numbers. We will also use the concepts of reciprocals to help divide fractions more easily. Multiply fractions • We will multiply fractions by other fractions and simplify at the end

Reciprocals • We will work with reciprocals which are fractions that are flipped over to equal one

Divide wholes and Simplify and multiply (factor before multiplying) fractions • We will divide whole • We will learn how numbers by fractions to factor numbers and fractions by whole before multiplying numbers to make the process easier and limit Divide fractions the amount of • We will divide two simplifying we fractions by each other have to do Divide mixed numbers Multiply mixed numbers • We will divide mixed • We will multiply numbers by rewriting mixed numbers them as improper by rewriting them fractions as improper fractions Review

139

Chapter 8-1 Multiply Fractions Simplify the fractions.

Daily Review 1. 5 � 10 �

� �

2. 10 � 12 �

� �

3. 6 � 15 �

� �

4. 4 � 10 �

� �

Learn and Connect Jason found a container of ice cream in his refrigerator. The container was 3 filled with ice 4 cream. If he ate 2 of the ice cream, how much of the total container did Jason eat? 3

To find out what fraction of something else we are using, we multiply. We know this because the word “of” in “ 2 of the ice cream” means multiply. 3

To solve, first multiply the numerators followed by the denominators. Then, simplify. 6 � 6 1 = 2 12 � 6

3 2 6 4 � 3 = 12

Apply

Solve. 1. What is 43 of 12? �

2. What is 32 of 41 ?

�

4. What is 41 of 6? �

5. What is 87 of 32 ?

�

3. What is 62 of 18? �

6. What is 4 8 of 20? �

Multiply the fractions and simplify if necessary. 3 � 10 7. 10 11 =

8 � 51 = 8. 12

4 � 61 = 9. 10

3 = 10. 68 � 12

11. 45 � 83 =

3 � 32 = 12. 10

13. 42 � 87 =

14. 61 � 41 =

140

Level F

Chapter 8

Lesson 1

Lighthouse Math

Exercise 8-1 Name Solve. 1. What is 31 of 24? �

�

4. What is 21 of 67 ? �

�

9. What is 83 of 16?

4 6. What is 43 of 15 ?

11. What is 57 of 28?

3. What is 4 6 of 30?

5 8. What is 45 of 12 ?

10. What is 61 of 83 ?

5. What is 35 of 15?

7. What is 45 of 20? �

2. What is 35 of 85 ?

�

7 12. What is 95 of 10 ?

�

Multiply the fractions and simplify if necessary. 13. 31 � 32 =

14. 21 � 32 =

16. 31 � 45 =

17.

19. 65 � 31 =

20. 21 � 67 =

21.

22. 43 � 25 =

23. 25 � 35 =

24. 57 � 45 =

15.

18. 43 � 61 =

1 4 2 � 5 =

1 3 3 � 4 =

1 3 2 � 4 =

Challenge 3

25. A student lives 4 of a mile from school. He has walked 3 of the 7 way to school. What fraction of a mile has he walked?

Lighthouse Math

26. A teacher has 8 of a package of paper. The teacher uses 25 of the paper to make an assignment. What fraction of the package of the paper was used to make the assignment?

Level F

Chapter 8

Exercise 1

141

Chapter 8-2 Multiply Fractions with Factoring Daily Review

Multiply and simplify if necessary.

9 � 21 = 1. 10

11 = 2. 83 � 12

8 � 31 = 3. 12

4. 45 � 45 =

Learn and Connect A local airport had flights to Europe and the United States. Of the flights to Europe, 4 of them were to the Paris, France airport. If 3 of the flights at the 9 8 airport were to Europe, what fraction of the total flights were to Paris, France? To find out what fraction of something else we are using, we multiply. We know this because the word “of” in “ 3 of the flights” means multiply. 8

Instead of reducing the fraction at the end of the problem, we can also use factoring before we multiply. Divide one number in the numerator and one in the denominator by the same divisor to reduce.

To solve, first multiply the numerators followed by the denominators. Then, reduce.

3 4 12 8 � 9 = 72

3�3= 4�4= 1 1

12 � 12 1 = 6 72 � 12

1 3 4 8 � 9 = 6

8�4= 9�3= 2 3

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Multiply by using factoring. 1. What is 85 of 12?

2. What is 41 of 87 ?

3. What is 82 of 17?

5 of 36? 4. What is 12

5. What is 43 of 24?

6. What is 37 of 18?

Multiply and use factoring if possible. 3 � 32 = 7. 10

8. 31 � 43 =

7 = 9. 32 � 10

3 = 10. 68 � 12

11. 32 � 21 =

2 � 32 = 12. 10

13. 42 � 21 =

14. 41 � 25 =

142

Level F

Chapter 8

Lesson 2

Lighthouse Math

Exercise 8-2 Name Solve. 1. What is 43 of 32?

4 2. What is 15 of 85 ?

7 3. What is 10 of 30?

6 ? 4. What is 83 of 10

5. What is 32 of 15?

4 9 6. What is 15 of 10 ?

7. What is 45 of 25?

9 5 8. What is 10 of 12 ?

9. What is 83 of 40?

21 3 of 14 ? 10. What is 24

9 11. What is 14 of 28?

7 12. What is 95 of 10 ?

13. 63 � 4 9 =

5 3 � 10 = 14. 12

22 14 � 33 = 15. 35

8 9 � 20 = 16. 15

7 5 � 21 = 17. 10

8 18. 10 12 � 15 =

3 = 19. 65 � 10

14 20. 20 21 � 15 =

12 21. 6 9 � 14 =

22. 83 � 92 =

23. 95 � 35 =

18 15 � 16 = 24. 25

Multiply the fractions and simplify if necessary.

Challenge 15 25. A field is 28 miles long. A student walks 7 of the field. 10 What fraction of a mile did the student walk?

Lighthouse Math

33 26. Last year, a fruit tree produced 40 of a bushel of fruit. This year, the tree produced 6 as much fruit. What fraction 11 of a bushel did the tree produce this year?

Level F

Chapter 8

Exercise 2

143

Chapter 8-3 Multiply Mixed Numbers Daily Review

Multiply and use factoring if possible.

6 = 1. 93 � 12

2. 81 � 47 =

3. 27 � 98 =

4. 63 � 47 =

Learn and Connect Yesterday, Randy’s Donut Shop sold 2 4 8 times as many strawberry donuts displays as chocolate donuts displays. If they sold 2 2 packs of chocolate displays, how many 10 displays of strawberry donuts did they sell? To solve, we need to multiply the number of chocolate donut displays sold by 2 4 . 8

1. To multiply, we must turn the mixed numbers into an improper fractions. + 2 4 = 20 8 �8

2. Then, factor to reduce the fractions. 20 � 10 = 22 � 2 = 2 11

+2 = 22 � 10 10

20 22 8 � 10 =

8�2= 4 3. Next, multiply the numerators and denominators.

2 11 4 � 1 =

10 � 10 = 1

4�2= 2

4. Last, change the improper fraction back to a mixed number and simplify if necessary. 5

1 11 11 2 � 1 = 2 © Lighthouse Curriculum. Copying strictly prohibited.

2 � 2= 1

11 �10

5 1 2

1 Therefore, Randy’s Donut Shop sold 5 1 displays of strawberry donuts. 2

Apply Multiply and use factoring if possible. 2

1. 1 5 � 4 =

2. 3 11 � 10 =

3. 10 12 � 6 =

5. 2 68 � 3 37 =

9 = 6. 4 45 � 1 11

144

Level F

Chapter 8

Lesson 3

6 25 � 2 85 =

4. 2 11 � 5 =

2 � 6 35 = 8. 3 11

Lighthouse Math

Exercise 8-3 Name

1. 1 3 � 2 4 =

2. 2 4 � 1 5 =

3. 3 3 � 2 6 =

1 4. 3 4 �4 2 =

5. 3 5 � 5 6 =

6. 4 3 � 2 5 =

7. 3 2 � 4 7 =

8. 3 8 � 2 3 =

9. 1 7 � 3 4 =

4 10. 4 2 7 � 5 =

11. 1 6 � 5 4 =

12. 4 3 � 2 5 =

13. 3 10 � 3 11 =

14. 3 10 � 2 9 =

15. 2 9 � 2 6 =

17. 1 11 � 4 5 =

1 3 = � 10 18. 4 12

16. 5 6 � 3 7 =

Multiply. Use factoring to reduce, if possible.

Challenge 19. An oak tree is 11 91 feet tall. A pine tree is 2 1 times as 40 tall as the oak tree. How tall is the pine tree?

Lighthouse Math

20. The art teacher has 10 27 feet of ribbon for the next project. The project needs 2 3 times as much ribbon for 8 the whole class to be able to participate. What is the total length of ribbon the teacher needs for the project?

Level F

Chapter 8

Exercise 3

145

Chapter 8-4 Reciprocals Multiply and use factoring if possible.

Daily Review 1. 5 42 � 3 21 =

3 2. 1 95 � 2 12 =

Learn and Connect Solve the four problems below. 5 12 12 � 5 =

15 20 20 � 15 =

1 9 9 � 1 =

7 10 10 � 7 =

Notice, each of the problems results in 1 as an answer. What do you notice about the fractions being multiplied? How are they similar? How are they different? The factors are reciprocals of each other. To find the reciprocal of a fraction, we exchange the position of the numerator and the denominator. Fraction

Reciprocal

3 4

4 3

Check

3 4 12 4 � 3 = 12 = 1

To find the reciprocal of a mixed number or whole number, first rename the mixed number as an improper fraction. Mixed Number

Improper Fraction

Reciprocal

3 2 12

+3 2 12 = 27 12 �

12 27

Check

12 27 324 27 � 12 = 324 = 1

Apply Write the reciprocal. 9 = 1. 10

2. 1 8 =

3. 3 4 =

4. 7 8 =

5. 6 9 =

1 = 6. 12

Write the missing factor. 7. 6 �

8. 3 4 �

9. 1 9 �

13. 3 1 2 �

14. 4 3 �

12. 2 �

146

Level F

Chapter 8

10. 2 5 �

11. 8 �

15. 8 �

16. 3 6 �

Lesson 4

Lighthouse Math

Exercise 8-4 Name Write the reciprocal. 1. 1 = 4

2. 2 = 3

3. 3 = 5

4. 5 = 6

5. 4 = 7

6. 5 = 8

7. 7 = 9

8. 3 = 10

9. 8 = 11

10. 11 =

11. 9 = 13

12. 5 = 14

13. 1 = 15

14. 9 = 16

15. 2 = 17

Write the missing factor. 16. 2 5 7 �

3 � 17. 1 10

18. 5 1 8 �

19. 4 4 9 �

20. 6 4 5 �

21. 3 2 3 �

22. 8 5 6 �

6 � 23. 9 11

24. 7 3 4 �

25. 5 2 5 �

9 � 26. 7 10

7 � 27. 4 12

Draw a line to the missing fraction that completes the expression. � 12 21 = 1

12 31

7 29. 2 12 �

30.

3 1 3

6 � 20 =1

13 4

31. 2 7 8 �

28.

8 23

Challenge 32. Explain what a reciprocal is and how we can check if a number is the reciprocal of another number.

Lighthouse Math

Level F

33. What is the reciprocal of 12? Write your answer below and explain using what you know about reciprocals.

Chapter 8

Exercise 4

147

Chapter 8-5 Divide Fractions and Wholes Daily Review

Write the reciprocal of each fraction.

1. 1 2 =

2. 3 4 =

3. 8 2 5 =

4. 3 2 3 =

Learn and Connect Micah works at a bakery. He needs to cut the freshly baked cakes to place in the display case. If Micah divides each cake into 1 pieces, how many total pieces of cakes can Micah put 6 in the display case? To solve, we have to divide the number of cakes by 1 pieces. 6

First, you need to create a multiplication problem by using the reciprocal of the second fraction. The reciprocal of a fraction is the same fraction but “flipped” over. The numerator becomes the denominator and the denominator is now on top.

6 � 1 6

Next, turn the whole into a fraction by placing a 1 as the denominator. Then, multiply the numerators and denominators.

6 6 36 1 � 1 = 1 = 36

Therefore, Micah will put 36 pieces of cake in the display case.

Because the answer has a 1 as the denominator, we know it is a whole number.

Apply Divide. Simplify your answers. 1. 8 � 3 4 =

2. 7 � 3 5 =

3. 4 5 �8 =

4. 5 � 1 4 =

5. 3 � 1 2 =

6. 6 � 2 8 =

6 7. 10 �4 =

8. 5 � 5 6 =

9. 1 3 �9 =

10. 2 4 �6 =

7 �9 = 11. 10

12. 1 3 �8 =

13. 1 2 �6 =

14. 2 3 �4 =

15. 2 5 �7 =

8 �1 = 16. 12

148

Level F

Chapter 8

Lesson 5

Lighthouse Math

Exercise 8-5 Name

1. 2 � 1 2 =

2. 8 � 2 3 =

3. 4 5 �6=

4. 3 8 �7=

5. 3 4 �4=

6. 9 � 1 4 =

7. 5 9 �5=

8. 4 � 3 5 =

9. 9 5 �5=

10. 3 � 6 7 =

11. 6 � 1 6 =

12. 2 3 �7=

13. 1 2 �4=

5 �9= 14. 11

15. 5 � 7 8 =

16. 3 � 4 9 =

17. 6 � 3 4 =

18. 7 6 �2=

3 19. 4 � 10 =

20. 5 7 �8=

21. 7 � 5 6 =

22. 1 4 � 10 =

23. 2 � 1 9 =

9 �3= 24. 10

25. 15 � 2 3 =

26. 22 � 1 2 =

27. 2 5 � 5 =

28. 3 8 �9=

Challenge 29. Timmy has 4 pies. He wants to cut each pie into 1 slices. 8 How many slices will he have in total?

30. Max wants to make biscuits with dough that weighs 5 ounces. If each biscuit uses 1 ounces of 6dough, how many biscuits 5 can he make?

31. If 3 loaves of bread need to be divided into 1 slices, how many 10 slices of bread will there be?

32. A 7 8 mile track is going to be divided into three evenly spaced sections. What fraction of a mile will each section be in length?

Lighthouse Math

Level F

Chapter 8

Exercise 5

149

Divide. Simplify your answers.

Chapter 8-6 Divide Fractions Daily Review

Divide. Simplify your answers.

1. 5 6 �2=

2. 2 7 �3=

3. 5 � 1 7 =

4. 30 � 1 5 =

Learn and Connect Caleb is painting some chairs. Each chair he paints uses 1 quarts of paint. How many chairs 8 can he paint before he needs to buy more paint?

To solve, we have to divide the total amount of paint Caleb has by the amount of paint it takes to paint one chair. First, you need to create a multiplication problem by using the reciprocal of the second fraction. The reciprocal of a fraction is the same fraction upside down.

1 1 2 � 8

Next, multiply the numerators and denominators.

1 8 8 2 � 1 = 2

Last, simplify or turn the improper fraction into a mixed 2 number. So, 8 needs to be simplified. Remember to 2 divide the numerator by the denominator.

4 8 = 4 �8 0

Therefore, Caleb can paint 4 chairs.

Apply Divide. Simplify your answers. 2 1. 1 5 � 6 =

9 2. 11 � 2 3 =

2 3. 3 7 � 3 =

2 4. 11 � 3 6 =

1 5. 3 8 � 2 =

1 6. 1 2 � 2 =

8 7. 6 7 � 9 =

1 8. 4 9 � 11 =

2 9. 4 7 � 12 =

1 10. 3 7 � 4 =

1 � 3 11. 12 7 =

2 12. 7 8 � 9 =

150

Level F

Chapter 8

Lesson 6

Lighthouse Math

Exercise 8-6 Name

1 1. 2 5 � 2 =

2 2. 3 7 � 3 =

1 3. 4 5 � 4 =

5 4. 3 8 � 6 =

1 5. 3 4 � 3 =

7 � 1 6. 10 4 =

2 7. 5 9 � 7 =

9 � 3 8. 10 5 =

9 � 1 9. 10 2 =

6 10. 1 5 � 7 =

1 11. 7 9 � 6 =

4 12. 2 3 � 5 =

1 13. 1 2 � 8 =

5 � 3 14. 11 4 =

7 15. 6 7 � 8 =

4 16. 5 6 � 9 =

9 � 3 17. 10 4 =

2 18. 7 6 � 7 =

3 19. 3 5 � 10 =

1 20. 5 7 � 3 =

5 21. 5 8 � 6 =

2 22. 4 4 � 5 =

7 � 1 23. 10 9 =

9 � 2 24. 10 3 =

1 25. 2 3 � 5 =

3 26. 5 8 � 7 =

4 27. 1 6 � 15 =

4 28. 11 � 2 9 = © Lighthouse Curriculum. Copying strictly prohibited.

Divide. Simplify your answers.

Challenge 29. The art class is 4 5 an hour long. If the students needs to pick a new paint color for their projects every 1 of an hour, 10 how many different colors will they use?

30. Andrew has a string that is 3 foot 4 long. If he cuts the string into 1 8 pieces, how many pieces will he have?

of a cup of sugar to 31. It takes 1 3 make a cake. You have 7 cups 8 of sugar. How many cakes could you bake?

32. A student needs to make 1 9 inch strips of paper by cutting up a 2 inch 3 strip of paper. How many strips can he make?

Lighthouse Math

Level F

Chapter 8

Exercise 6

151

Chapter 8-7 Divide Mixed Numbers Daily Review

Divide. Simplify your answers.

5 1. 3 4 � 6 =

1 2. 1 4 � 2 =

1 3. 2 3 � 5 =

2 4. 3 5 � 7 =

Learn and Connect Asher wants to build a tower made out of cups. He is planning to place the cups on top of each other vertically. If he wants to build a tower that is 29 3 inches tall, how 4 many cups will he need to use? To solve, we have to divide the total height of the tower by the height of each cup.

First, we must turn the mixed numbers into improper fractions.

+3 29 4 = 119 4 � +3 51 4 12 = 12 �

Next, we make a multiplication problem by using the reciprocal of the second fraction. Then, we multiply the numerators and denominators.

Last, we change the improper fraction back to a mixed number and simplify if necessary.

119 � 51 4 12

7 204

119 � 12 1,428 4 51 = 204

1,428 = 7 � 1,428 0

Apply Divide. Simplify your answers. 3 1. 7 2 3 �2 4 =

2 2. 1 1 3 �5 5 =

2 3. 2 4 5 � 7 =

1 4. 9 1 7 �3 4 =

2 5. 2 1 4 �2 6 =

6. 2 1 2 �5=

1 7. 1 1 4 � 3 =

1 8. 6 2 5 �2 4 =

1 9. 1 5 6 �2 3 =

3 10. 3 2 3 � 5 =

1 11. 4 1 6 �3 4 =

7 12. 1 4 5 � 8 =

152

Level F

Chapter 8

Lesson 7

Lighthouse Math

Exercise 8-7 Name

1 1. 1 3 5 �3 4 =

2 2. 2 4 7 �5 5 =

1 3. 4 3 5 �6 2 =

3 4. 8 1 8 �7 4 =

2 5. 2 3 5 �5 3 =

5 6. 6 3 4 �1 6 =

1 7. 8 2 3 �3 7 =

9 �4 1 8. 7 10 5 =

7 �5 1 9. 4 10 2 =

2 10. 3 1 5 �2 7 =

1 11. 8 3 7 �1 6 =

1 12. 6 2 3 �7 5 =

1 13. 5 1 2 �6 8 =

2 �8 3 14. 3 11 4 =

7 15. 2 2 6 �1 8 =

4 16. 7 5 6 �4 9 =

1 17. 5 1 2 �1 5 =

1 18. 6 5 8 �2 4 =

9 19. 8 1 3 � 2 10 =

1 20. 10 1 5 � 3 15 =

Challenge 21. At the bakery, each cake requires 2 1 cups 2 sugar. How many cakes can the bakery cups sugar ? bake if they have 12 1 2

22. A soup bowl holds a serving size of 1 1 3 cups. How many full servings of soup can cups of soup? you serve if you make 12 1 2 Do you have any soup left?

23. You want to make 6 1 2 servings out of 3 3 pizzas. What fraction of a pizza will 4 be a serving?

24. For a chemistry experiment, students will take a 2 4 gallon container and 5 divide it into 7 gallon sections. How 10 many sections will the container hold?

Lighthouse Math

Level F

Chapter 8

Exercise 7

153

Divide. Simplify your answers.

Chapter 8-8 Review Daily Review

Write the reciprocal of each fraction.

1. 2 1 3 =

2. 3 4 5 =

3. 4 1 2 =

4. 5 2 8 =

Learn and Connect Jason is putting frosting on some of the brownies he is making and leaving the others plain. He frosts 3 of the brownies in the 4 pan. Of the frosted brownies, 1 of them have chocolate frosting 3 and the rest have vanilla. What fraction of the brownie pan has chocolate frosting? To solve, we have to multiply the amount of chocolate frosted brownies and the total amount of frosted brownies.

Amount of frosted chocolate brownies

�

Total amount of frosted brownies

1 3

�

3 4

Fraction of pan with chocolate frosted brownies 3 1 12 = 4

Don’t forget to simplify!

Apply Multiply and use factoring if possible. 6 1. 12 5 � 5 =

3 2. 2 3 � 8 =

4 3. 3 6 � 5 =

3 4. 2 7 � 14 =

1 5. 3 1 7 � 3 =

6 6. 2 2 8 � 12 =

2 7. 2 3 9 � 5 =

8 � 2 8. 2 12 6 =

Divide. Simplify your answers. 9. 4 � 3 4 =

10. 3 � 3 5 =

11. 4 5 �5 =

12. 10 � 1 4 =

3 13. 2 4 6 �2 4 =

2 14. 2 1 5 �1 6 =

2 15. 3 2 5 � 4 =

1 16. 4 1 3 �3 3 =

154

Level F

Chapter 8

Lesson 8

Lighthouse Math

Exercise 8-8 Name Multiply and use factoring if possible. 1.

3 12 5 �2 4 =

3 21 4 �1 8 =

1 31 4 �2 6 =

3 1 4 �4 3 =

1 �5 5 3 10 6 =

2 42 3 �2 9 =

2 31 4 �4 7 =

1 33 8 �2 5 =

3 15 6 �3 4 =

5 11 =

14.

Write the reciprocal. 10.

3 4 =

11.

2 9 =

12.

3 7 =

13.

4 5 =

3 15. 1 1 5 �3 4 =

4 16. 2 5 7 �1 5 =

1 17. 4 2 5 �6 3 =

1 18. 8 3 8 �7 4 =

2 19. 2 1 6 �5 3 =

5 20. 6 1 4 �2 6 =

4 21. 8 1 3 �1 7 =

7 �2 1 22. 7 10 5 =

9 �4 1 23. 4 10 2 =

2 24. 3 4 5 �1 5 =

5 25. 5 5 8 �1 6 =

5 26. 6 2 9 �7 9 =

ft wide and 8 2 ft 27. A wall is 4 1 4 6 tall. What is the area of the wall? Hint: Area = Length × Width

Lighthouse Math

Divide. Simplify your answers.

28. It takes Mike 3 of an hour to do his math 8 homework each day. If he does his math homework every day for five days, how much time did he spend doing math homework?

Level F

Chapter 8

Exercise 8

155

Chapter 9 NYS NG Standards NY-5.NBT.1 NY-5.NBT.3 NY-5.NBT.3a NY-5.NBT.3b

NY-5.NBT.4 NY-5.NBT.7 NY-6.NS.3

CC Standards 5.NBT.A.1 5.NBT.A.2 5.NBT.A.3 5.NBT.A.3.A

156

5.NBT.A.3.B 5.NBT.A.4 5.NBT.B.7 6.NS.B.3

In Chapter 9 we will learn

Decimal Basics: Adding and Subtracting Decimals Decimals are important because we use them every day in different situations, such as counting money, looking at price tags, calculating test scores or reading temperatures. • Decimal place value • Compare and order decimals • Rounding decimals • Estimate decimal sums and differences • Adding decimals • Subtracting decimals • Subtracting decimals - adding to check your answer

DECIMALS

DT H OU SA N

RE D TH

RE D ND HU

OU SA N

ONES

HO US AN

THOUSANDS

We can name the place value of a digit to the right of the decimal point. We can use place value to order and compare decimal values. We can line up the decimal point correctly to add or subtract given amounts. We can apply our previous learning of rounding to decimals. We can use the inverse operation to check our addition and subtraction problems.

157

Chapter 9-1 Decimal Place Value Daily Review

Name the place value of the underlined digit.

1. 3,409

2. 239,007

3. 1,502,183

TENTHS

HUNDREDTHS

THOUSANDTHS

When saying a decimal number, the decimal point is said as the word “and.” We end saying the number with the last place value name.

ONES

We can use a place value chart to understand how to read decimals and know the number’s value.

TENS

THOUSANDS

A scientist is carefully measuring the amount of liquid for an experiment. He needs 32.079 milliliters in the beaker to ensure the experiment works correctly. If we were to estimate to the nearest whole number, that would be 32 milliliters.

HUNDREDS

Learn and Connect

32.079 This number is said as: thirty-two and seventy-nine thousandths.

What place is the 0 in? What place is the 7 in?

Apply Write as a decimal. 128 1. 1000 =

5 2. 12 10 =

72 3. 1000 =

7 4. 3 10 =

5. twenty-three and six tenths 6. seven thousand two hundred eighteen and nine hundredths Write the word form. 7. 54.75 8. 993.042

Vocabulary Tenths - one place to the right of the decimal point Hundredths - two places to the right of the decimal point Thousandths - three places to the right of the decimal point 158

Level F

Chapter 9

Lesson 1

Lighthouse Math

Exercise 9-1 Name Write the decimal. 1. 5 2 = 100

2. 32 = 1000

3. 28 5 = 10

4. 215 =

48 1000 =

6. 62 = 100

8. 243 =

205 1000 =

10.

11. 56 3 = 1000

4 100 =

1000

4 5 = 100

1000

12.

6 1000 =

13. Twenty-four thousandths 14. Thirteen and three hundredths 15. Eight and one hundred twenty-two thousandths 16. Two hundred and three tenths 17. Seven and forty-four hundredths 18. Six and eighty-nine thousandths Write the decimal number in words.

19. 8.732 20. 25.004 21. 6.03 22. 1.851 23. 5.025 24. 75.009

Challenge 25. Mr. Cohen drove 1,000 miles. He had to stop after 542 miles to get gas. What decimal represents the part of the whole trip that Mr. Cohen drove before he stopped for gas?

Lighthouse Math

Level F

26. In a survey of 100 people, 78 said that they like chocolate ice cream. What decimal represents the number of people who did not like chocolate ice cream?

Chapter 9

Exercise 1

159

Chapter 9-2 Compare and Order Decimals Daily Review

Name the place value of the underlined digit.

1. 8.201

2. 510.12

3. 68.3279

Learn and Connect Students are participating in a track and field event for school. Tim, Josh, Noah, and Sam all ran the times shown in the table. Let’s put those times in order from least to greatest.

400 METER TIME IN SECONDS

When we order decimals, we want to compare each number starting from the largest place value to the right. Because all of the numbers have a 6 in the tens place, we can move to compare the next largest digit. 61.25

60.38

61.52

Tim

61.25

Josh

60.38

Noah

61.52

Sam

60.4

Who ran the fastest?

Who ran the slowest?

Apply Write >, <, or =. 1. 0.3522

0.3571

2. 8.260

8.26

3. 4.931

4.391

4. 24.06

24.60

5. 32.181

32.183

6. 6.050

6.05

Order the numbers from least to greatest. 7. 6.2, 6.153, 6.26, 6.30 ,

8. 0.94, 0.947, 0.09, 0.97 ,

9. 1.58, 1.85, 1.50 ,

Vocabulary Greater than - a sign used to compare number values (>) Less than - a sign used to compare number values (<) 160

Level F

Chapter 9

Lesson 2

Lighthouse Math

Exercise 9-2 Name Write >, <, or = to compare. 1. 4.6

4.06

4. 7.054 7. 3.4

7.540

3.400

2. 3.29

3.290

3. 4.515

4.525

5. 6.832

6.831

6. 0.893

0.891

8. 2.567

20.567

9. 7.034

7.043

10. 0.506

0.516

11. 8.90

8.090

12. 9.05

9.050

13. 6.299

6.3

14. 0.001

0.100

15. 22.3

22.039

16. 62.06

62.060

17. 3.7

18. 4.15

4.156

3.700

Order the numbers from least to greatest.

20. 4.567, 4.756, 4.657

22. 3.25, 3.165, 3.325 ,

23. 5.55, 5.66, 5.565

21. 0.08, 0.8, 0.008

19. 6.35, 6.57, 6.4

24. 9.012, 9.12, 9.020

Challenge 26. Three boys timed each other running a lap around the track. Their times are below. John: 55.005 seconds Gabriel: 55.050 seconds Chris: 55.500 seconds List the boys from fastest to slowest.

25. Rick swam across the pool in 45.235 seconds. Stan swam across the pool in 45.532 seconds. Carl swam across the pool in 45.325 seconds. Who swam the fastest?

Lighthouse Math

Level F

Chapter 9

Exercise 2

161

Chapter 9-3 Rounding Decimals Daily Review 1. 5,203

Round each number to the underlined digit. 2. 369

3. 25,637

4. 984,091

Learn and Connect In Mr. Larson’s 5th grade class, students were put into groups to create a model parachute. Students were given time to work on and test the dropping speed of their parachute. The table shows the final results of each group’s parachute drop speed from the top of the school to the ground.

PARACHUTE DROP IN SECONDS

Group 1

4.206

Group 2

5.37

Group 3

5.314

Group 4

4.275

Round each group’s time to the nearest tenths place. 4.206 5.37 5.314 4.275

Group # had the parachute that fell the slowest.

Apply Round to the nearest whole number.

Round to the nearest tenth.

1. 7.548

2. 15.67

3. 127.96

4. 6,209.365

5. 58.11

6. 724.94

Round to the nearest hundredth.

Round to the nearest thousandth.

7. 8.367

8. 3.9999

9. 11.009

10. 57.4018

11. 7.548

12. 596.7914

Vocabulary Rounding - replacing a number with a simpler approximate value that is less or more 162

Level F

Chapter 9

Lesson 3

Lighthouse Math

Exercise 9-3 Name Round to the nearest whole number. 1. 65.089

2. 5.890

3. 0.7

4. 25.012

5. 2.369

6. 42.3

7. 30.65

8. 0.219

Round to the nearest tenth. 9. 8.096

10. 6.24

11. 23.789

12. 2.012

13. 3.97

14. 4.39

15. 6.509

16. 0.934

Round to the nearest hundredth. 17. 5.087

18. 8.921

19. 0.275

20. 4.053

21. 3.069

22. 2.999

23. 0.099

24. 6.367

25. 4.2444

26. 9.0001

27. 7.0058

28. 2.5125

29. 6.3292

30. 3.5678

31. 5.5262

32. 0.0099

Round to the nearest thousandth.

Challenge 33. Marc swam 50 meters in 25.675 seconds. What was his time rounded to the nearest tenth?

Lighthouse Math

34. Max swam 50 meters in 24.909 seconds. What was his time rounded to the nearest hundredth?

Level F

Chapter 9

Exercise 3

163

Chapter 9-4 Estimate Decimal Sums and Differences Daily Review

Round each decimal to the underlined digit.

1. 23.061

2. 507.25

3. 9.5714

4. 2,014.67

Learn and Connect Christopher and Brian are trying to decide what to order at Sam's Pizza Parlor. Their mom gave them $25 to spend. They each want to get a cookie, a drink and to share a pizza. Do they have enough money? The easiest way to answer our question is to estimate the cost to the nearest dollar, add up the items, and see if they have enough money. 2 drinks 2 cookies 1 pizza About how much will they be spending?

Do they have enough money?

Apply Round to the nearest whole number and estimate the sum or difference. 1. 23.56 + 15.81

2. 246.9 + 134.2

3. $17.14 � $ 9.56

4. 892.49 � 629.72

5. 48.90 � 36.27

6. $7.64 + $1.50

7. 92.54 + 12.71

8. $199.27 � $67.57

Rewrite, round to the nearest whole number and estimate. 9.

10. 507.347 � 423.109 =

65.78 + 12.90 =

Vocabulary Estimate - to find a value that is close enough to the correct answer 164

Level F

Chapter 9

Lesson 4

Lighthouse Math

Exercise 9-4 Name Round to the nearest whole number and estimate the sum or difference. 1.

394.7 + 326.2

$14.34 � $7.51

37.109 5. � 16.700

6. $4.74 + $2.25

86.145 + 13.420

8. $249.86 � $51.27

15.36 + 9.61

10.

469.6 � 142.3

11. $22.41 � $ 8.65

12.

13.

67.78 + 52.33

14.

$6.99 � $2.50

15.

16. $368.23 � $154.75

51.92 + 28.10

54.025 6.800

567.85 � 357.43

423.83 + 273.15

17. 27.58 + 16.30 =

18.

$7.43 - $3.10 =

19. 345.107 - 213.892 =

20.

6.734 + 18.203 =

21. $25.35 + $14.89 =

22.

473.7 - 352.008 =

23. $455.25 - $62.62 =

24.

784.309 + 225.9 =

Rewrite, round to the nearest whole number and estimate.

Challenge 25. A coat costs $245.99 and a hat costs $27.09. About how much will it cost to buy both?

Lighthouse Math

26. Shiloh weighs 29.484 kg and Seth weighs 26.725 kg. About how much more does Shiloh weigh?

Level F

Chapter 9

Exercise 4

165

Chapter 9-5 Adding Decimals Daily Review

Rewrite and solve.

893 + 932 =

7,685 � 1,572 =

8,305 � 6,894 =

57,752 + 14,028 =

Learn and Connect A space shuttle measures 122.2 feet long for just the shuttle. The addition fuel tank increases the length by 62 feet. How long are the space shuttle and fuel tank together? To add decimals we align the place values making sure the decimals are lined up. Then add zeros to show decimal places if necessary. Finally, add each column remembering to regroup when necessary. 122.2 + 62.0 The space shuttle is

feet long.

Apply Add. 1. 0.3 + 0.59

2. 1.25 + 0.368

3. 54.607 + 0.894

4. 67.8 + 9.875

5. 88.906 + 7.8

Rewrite and add vertically. 6. 1.3 + 0.9 =

7. 2.45 + 0.56 =

9. 17.598 + 5.764 =

10. 8.7 + 21.603 =

8. 11.5 + 0.976 =

11. 15.0073 + 132.9 = +

Vocabulary Addend - the numbers that are being added together Sum - the answer to an addition problem 166

Level F

Chapter 9

Lesson 5

Lighthouse Math

Exercise 9-5 Name Add. 1.

0.7 + 0.4

6. 35.98 + 7.858

2. 1.5 + 0.67

1.93 + 3.8

4. 4.09 + 0.345

5. 65.003 + 8.9

8. 65.932 + 9.749

9. 87.954 + 65.873

10. 19.9869 + 43.77

74.96 + 38.847

Rewrite and add. 11. 0.5 + 0.8 =

12. 0.56 + 0.7 =

13. 0.32 + 0.349 =

14. 1.56 + 0.6 =

15. 3.67 + 4.983 =

16. 6.709 + 23.8 =

Use the chart below to solve the problems. LENGTH

USA Falcon

70.1 meters

Russian Yenisei

79.843 meters

China Long

93 meters

USA Saturn Long

102.68 meters

17. W hat is the length of the USA Falcon and the USA Saturn Long space vehicles combined?

SPACE VEHICLES

18. What is the largest space vehicle? 19. W hat is the combined length of the China Long and the Russian Yenisei? 20. What is the smallest space vehicle?

Challenge Fill in the missing digits to complete this addition equation.

21.

+ 2 4. 8

5 1 0

3 2. 5 2 1

Lighthouse Math

22.

900

+ 5 8. 8

23. +

. 3 3 8

Level F

Chapter 9

. 3 9 2. 1 3 4. 5

Exercise 5

167

Chapter 9-6 Subtracting Decimals Daily Review

Rewrite and add.

25.16 + 8.6 =

316.2 + 57.4 =

716.98 + 32.6 =

15.77 + 42.36 =

Learn and Connect Jake used to drive 4.36 miles to school. He moved and is now 2.5 miles closer to school. How far does Jake have to drive to school now? 1) Be sure the decimals are lined up. 2) Place zeros in any missing decimal places. 3) Subtract, borrow when necessary. 4.36 � 2.5

4.36 � 2.50 miles

Apply

Subtract. 1. 3.64 � 0.25

2. 48.7 � 2.6

92 � 1.64

139.70 � 25.04

5. 17.18 � 11.5

Rewrite and subtract vertically. 6. 3.3 � 0.7 =

7. 21.9 � 1.7 =

�

8. 12.8 � 0.865 =

�

Subtract and compare the differences using <, >, =. 9. 61.07 � 48.39

10. 58.34 � 45.643

Vocabulary Difference - the answer to a subtraction problem 168

Level F

Chapter 9

Lesson 6

Lighthouse Math

Exercise 9-6 Name Subtract. 1.

2.46 � 0.35

27.8 � 3.9

3. 44 � 2.35

4. 173.4 � 52.01

5. 17.18 � 13.30

6. 132.58 � 121.64

47.4 � 12.68

8. 676.91 � 24.387

9. 62 � 8.678

10. 33.76 � 21.18

11.

64.2 � 9.1

12.

8.75 � 0.62

13. 174 � 27.381

14. 392.4 � 56.17

15. 15.83 � 12.42

16.

4.75 � 0.36

17.

37.6 � 1.5

18.

19. 249.8 � 36.15

20.

81 � 2.75

24.50 � 16.29

Rewrite and subtract vertically.

� 24. 628.38 � 63.21 = � 27. 28.9 � 13.234 = �

22. 56.3 � 8.45 =

23. 2.4 � 0.473 =

�

25. 217.24 � 73.702 = �

26. 418.7 � 24.31 = © Lighthouse Curriculum. Copying strictly prohibited.

21. 23.3 � 5.27 =

�

28. 3 � 2.146 =

29. 367.2 � 54.899 =

�

Challenge 31. The store’s banner announcing the grand opening was too long to fit in the space provided. The banner measured 6.5 meters. The store owner cut 0.575 meters off the banner. How long is the banner now?

30. Tony’s long jump measured 7.8 meters. Andrew’s jump was 1.673 meters shorter than Tony’s. How long was Andrew’s jump?

Lighthouse Math

Level F

Chapter 9

Exercise 6

169

Chapter 9-7 Subtracting Decimals - Add to Check Answers Rewrite and add.

Daily Review 1.

0.8 + 0.6 =

1.5 + 0.45 =

3.4 + 0.78 =

15.78 + 1.985 =

Learn and Connect Thousands of satellites circle the Earth allowing for many forms of communication. One of the smallest satellites is the Dove weighing 4.98 kilograms. The slightly larger Skysat satellite is still considered a mini satellite, but it weighs in at 99.7 kilograms. What is the difference in weight between these two satellites? To subtract, align the place values vertically. Then subtract while borrowing when necessary. 8 16 10

9 9. 7 0 � 4. 9 8 9 4. 7 2

The Skysat is kilograms larger than the Dove.

Apply Subtract. 1.

1.9 � 0.5

3.78 � 0.8

3. 5.89 � 4.97

24.78 � 16.9

Check

6.9 � 0.0987

Check

5. 5.692 � 0.9854

14.07 � 8.983

Subtract and check with addition. 6.

3.48 � 1.9

Check

8. 67.098 � 13.895

Check

+ 1.90 3.48

+ 16.90 24.78

Vocabulary Inverse - the opposite operation (addition and subtraction) (multiplication and division) 170

Level F

Chapter 9

Lesson 7

Lighthouse Math

Exercise 9-7 Name Subtract and check with addition. 1.

1.6 � 0.8

4.567 Check � 1.868

Check

2.67 Check � 0.85 +

5. 25 � 0.894

Check

34.9 � 7.08

26.70 Check � 5.944 +

Check

Rewrite and subtract. 7. 1.9 � 0.8 =

9. 16.85 � 1.43 =

10. 8.45 � 0.67 =

11. 13.09 � 8.56 =

12. 6.8 � 1.78 =

13. 24 � 0.78 =

14. 34.6 � 0.894 =

Solve each problem. 15. The Digital Globe Worldview-3 Satellite is 2,800 kilograms. The NASA satellite LandSat 8 is 2,071.8 kilograms. How much larger is the Worldview- 3 than the LandSat 8?

16. The LandSat 8 is orbiting at 10.9 kilometers per second, while the Worldview-3 is orbiting 16.89 kilometers per second. What is the difference between these two speeds?

Challenge 18. Your teacher asks you to weigh two textbooks and determine the difference in their weight. The first one weighs 5.68 pounds. The second one weighs 7.2 pounds. What is the difference in their weight?

17. You had $25.00 in your pocket. If you buy a drink for $3.19, a sandwich for $8.67, and a cookie for $1.59. How much money do you still have left?

Lighthouse Math

Level F

Chapter 9

Exercise 7

171

2.3 � 1.7 =

Chapter 9-8 Review Estimate each sum or difference to the nearest whole number.

Daily Review 1. 23.64 + 10.93

19.1 2. + 6.7

3. 203.29 � 96.8

4. 158.6 + 163.1

49.3 5. � 8.4

Learn and Connect Using the information to the right, answer the questions below to review all the knowledge you’ve gained in this chapter.

AVERAGE TEMPERATURE FOR THE MONTH OF JULY

Order the temperatures from least to greatest. ,

What is the difference in temperature between Denver and Albuquerque? What is the temperature of Phoenix rounded to the nearest tenth?

Denver

82.5°F

Phoenix

96.37°F

Albuquerque

89.49°F

Salt Lake City

84.6°F

Apply What is the place value of the 5 in each number? 1. 240.576

2. 96.045

Complete the table. Round to the hundredths.

3. 8.15 Write >, < or = to compare.

Round to the thousandths.

7. 47.08

47.18

4. 23.1576

8. 154.39

154.039

5. 18.0093

9. 62.78

62.780

Number

6. 408.9715

10. 581.415

581.416

Rewrite. Find each sum or difference. 12. 513.573 � 78.04

11. 59.01 + 17.24

172

Level F

Chapter 9

Lesson 8

Lighthouse Math

Exercise 9-8 Name Write the value of the 3 in each number. 1. 24.003

2. 67.312

3. 45.239

Complete the table. Round to whole number

Number

Round to tenths

Round to hundredths

Round to thousandths

4. 2.8736 5. 47.1839 6. 5.8274 7. 6.0099 8. 8.9937

Write >, <, or = to compare. 9. 5.625

5.256

10. 3.04

3.400

11. 2.5

2.50

12. 9.51 + 2.47 =

13. 731.735 � 48.74 =

14. 233.5 � 97.004 =

15. 672.54 + 84.003 =

16. 6.6 � 3.905 =

17. 4.328 + 0.847 =

18. 456.2 + 43.103 =

19. 134.75 � 87.749 =

Rewrite. Find each sum or difference.

Challenge 21. Moses drove 4.276 miles from home to the coffee shop. Then he drove 5.125 miles from the coffee shop to work. What is the total distance Moses drove?

20. The family took a jet to Florida that was 47.25 meters long. Then they took a small plane that was 9.725 meters long to an island. How much longer was the jet?

Lighthouse Math

Level F

Chapter 9

Exercise 8

173

Chapter 10

NYS NG Standards NY-5.NBT.2 NY-5.NBT.7

NY-6.NS.3

CC Standards 5.NBT.A.2 5.NBT.B.7

174

6.NS.B.3

In Chapter 10 we will learn about

Multiplying and Dividing Decimals It will be important to pay close attention to how we place the decimal point as we complete each problem. • Multiplying decimals with whole numbers • Multiplying decimals by decimals • Multiplying decimals with zeros • Dividing decimals with whole numbers • Dividing decimals by decimals © Lighthouse Curriculum. Copying strictly prohibited.

• Dividing decimals with zeros We can apply our previous learning of long division of whole numbers to decimals. We can notice what steps to take when zeros are involved with long division. We can extend a division problem with extra zeros to continue the dividing process.

175

Chapter 10-1 Multiply Decimals by Whole Numbers Daily Review

Round each number to the highest place value to estimate the product.

1. 64 � 537 =

2. 97 � 52 =

3. 678 � 76 =

4. 862 � 903 =

Learn and Connect The Feinberg family is sitting at the snack stand at the local aquarium. They want to buy a large lemonade for each of the five people in their family. If each drink costs $3.75, how much money will they spend? Use the area model to multiply 3.75 � 5.

0.7

0.05

3.5

0.25

It will cost

Add 15 3.5 + 0.25

for lemonade.

Apply Solve each problem using the area model and then check your work using the standard algorithm. 1. 4.5 � 7 =

3. 34.92 � 4 =

2. 5.62 � 8 = 4

.02

Algorithm Check: 4.5 � 7

Algorithm Check: 5.62 � 8

Algorithm Check: 34.92 � 4

Vocabulary Area Model - a strategy that allows for each place value to be multiplied separately and the products added together at the end to reach the total product

176

Level F

Chapter 10

Lesson 1

Lighthouse Math

Exercise 10-1 Name Solve each problem using the area model and then check your work using the standard algorithm. 1. 2.7 � 9 =

2. 8.54 � 3 =

Algorithm Check:

3. 34.06 � 7 =

Algorithm Check:

�

Algorithm Check:

�

6.8 � 9

0.32 � 7

8.9 � 5

0.04 � 3

0.35 � 8

6.07 � 2

10.

34.6 � 5

11.

4.56 � 6

12.

9.04 � 4

13.

12.3 � 9

14.

67.34 � 5

15.

5.438 � 8

16.

382.1 � 4

17.

49.21 � 5

18.

80.03 � 7

Challenge 19. Create your own area model grid for 5.61 � 3. Can you make each box to scale with how large the numbers are compared to each other?

Lighthouse Math

Level F

Chapter 10

Exercise 1

177

Solve each problem using the strategy of your choice.

Chapter 10-2 Multiplying Decimals by Decimals Daily Review 1.

Multiply. 2.

7.05 � 2

8.2 � 5

27.3 � 9

6.209 � 4

58.64 � 7

Learn and Connect James is visiting the whale exhibit at the local aquarium. He is amazed at the life sized models of whales hanging from the ceiling. The blue whale is the largest. The finback whale is about 0.8 times the size of the blue whale. The killer whale is only 0.4 times the size of the finback whale. How large is the killer whale compared to the blue whale? 1) Model 0.8 � 0.4

2) Check your model by multiplying. 0.8 � 0.4

Hint: Remember your decimal place. The killer whale is

times the size of a blue whale.

Apply Place the decimal point in the product. 1.

64.25 � 12.6

80955

1.78 � 13.9

24742

Multiply. 19.36 � 5.04

65.2 � 3.7

3.88 � 1.06

975744

Rewrite and multiply. 6. 5.134 � 6.42 =

7. 0.28 � 0.82 =

8. 2.236 � 0.78 =

Vocabulary Product - the answer to a multiplication problem 178

Level F

Chapter 10

Lesson 2

Lighthouse Math

Exercise 10-2 Name Place the decimal point in the product. 1.

42.65 � 6.6

281490 5.

4.25 � 2.7

7.81 � 19.3 150733

11475

13.96 � 4.05 56538

2.64 � 16.3 43032

9.46 � 2.03 192038

16.39 � 2.03 332717

21.64 � 3.04 657856

Multiply. 9.

52.3 � 7.3

10.

8.38 � 6.01

11.

25.6 � 5.4

12.

7.27 � 5.02

13.

2.56 � 1.8

14.

4.3 � 0.6

15.

26.25 � 7.3

16.

4.96 � 3.75

17. 0.81 � 0.96 =

18. 2.24 � 2.24 =

19. 9.36 � 0.8 =

20. 2.56 � 1.8 =

21. 0.68 � 0.47 =

22. 24.3 � 2.65 =

Rewrite and multiply.

Challenge 23. Gasoline costs $3.24 a gallon. How much does 13.8 gallons cost? Round to the nearest hundredth.

Lighthouse Math

Level F

24. Jay worked 5.25 hours. If he earned $8.75 per hour, how much did he earn in total? Round to the nearest hundredth.

Chapter 10

Exercise 2

179

Chapter 10-3 Multiplying Decimals with Zeros Daily Review 1.

Multiply. 2.

62.8 � 0.3

149.6 � 2.1

8.64 � 0.5

21.17 � 0.4

26.25 � 0.76

Learn and Connect Lucas is at the local ice cream shop. He’s reading the nutrition facts for some of the items. Lucas realizes that a two scoop ice cream cone contains 25 times more iron than their small fruit smoothie. How much iron does their two scoop ice cream cone contain? 1) A fruit smoothie has

mg of iron.

An ice cream cone has 2) Multiply

times this amount.

0.006 � 25

3 decimal spots 0 decimal spots put the decimal 3 spots in from the right

An ice cream cone has

mg of iron.

Apply Multiply. 1.

2.15 � 0.03

0.004 � 17

0.06 � 0.08

3.13 � 0.009

0.05 � 0.03

8.32 � 0.002

0.007 � 0.005

8.02 � 0.006

Rewrite and multiply. 9.

0.28 � 0.004 =

10. 0.02 � 0.3 � 0.4 =

11. 0.05 � 0.08 � 4.7 =

12. 3.68 � 0.001 =

180

Level F

Chapter 10

Lesson 3

Lighthouse Math

Exercise 10-3 Name Multiply. 1.

5.12 � 0.04

0.007 � 14

0.04 � 0.09

1.12 � 0.008

0.06 � 0.04

3.28 � 0.005

0.008 � 0.006

2.08 � 0.003

4.24 � 0.005

10.

0.003 � 12

11.

0.03 � 0.06

12.

3.26 � 0.01

13. 0.482 � 0.005 =

14. 0.04 � 0.05 � 0.06 =

15. 0.06 � 0.09 � 7.3 =

16. 6.38 � 0.002 =

17. 0.375 � 0.005 =

18. 0.07 � 0.05 � 0.02 =

19. 4.04 � 0.00 =

20. 8.3 � 0.002 =

Rewrite and multiply.

Challenge 21. A tiny organism is 0.003 inches wide. How wide are 45 of the organisms lined beside each other?

Lighthouse Math

Level F

22. A wire is 0.04 inches thick. How thick is a wire that is 0.02 times as thick?

Chapter 10

Exercise 3

181

Chapter 10-4 Dividing Decimals by Whole Numbers Daily Review

Rewrite and divide.

1. 192 � 6 =

2. 80 � 5 =

3. 546 � 7 =

Learn and Connect Thomas is doing a science experiment on precipitation. He gathered data on the total amount of rain for the months of May, June, July and August. Thomas would like to find the average rainfall for these spring and summer months. To find the average, we add the amounts collected each month and then divide by the number of months.

1) Add: 4.17 + 3.31 + 4.11 + 3.25 =

2) Divide:

3.71 4)14.84 � 12 28 � 28 04

AMOUNT OF RAIN (inches) May

4.17

June

3.31

July

4.11

August

3.25

inches.

The average rainfall for the 4 months is

inches.

Apply Divide. 1.

9)121.23

2. 49)313.11

3. 6)140.4

4. 5)296.5

Rewrite and divide. 5. 351.5 � 5 =

6. 16.32 � 12 =

3,685.92 � 56 =

Vocabulary Quotient - the answer to a division problem Average - the sum of the values divided by the total number of values in the set

182

Level F

Chapter 10

Lesson 4

Lighthouse Math

Exercise 10-4 Name Solve each problem. Don’t forget to move the decimal point to the answer. 1.

9)1.89

2. 5)6.50

3. 7)4.76

4. 4)19.92

5. 6)42.24

6. 12)108.36

Solve each problem. 7.

Mr. Johnson collected eight dollars from each student in his class for a field trip. If he collected $184.00, how many students went on the trip?

Michael, Jack and James bought a pizza together. If the pizza cost $12.75, how much does each boy need to contribute to share the cost equally?

10. If you buy eight identical candy bars for $9.20, what is the cost of a single candy bar? © Lighthouse Curriculum. Copying strictly prohibited.

11. Four friends all put their money together. They have $216.00 dollars. If they each put in the same amount of money, how much money did they contribute?

Jacob saves $9.00 each week from his allowance. If he has $126.00 saved, how many weeks has he been saving?

12. Peter bought a pack of 4 notebooks for $4.76. How much did each notebook cost?

Challenge How would you divide up the cost with a remainder of money? 13. Sam and Ben wanted to share the cost of an ice cream sundae. The sundae costs $2.17. How would you divide up the cost with a remainder of money? Explain your reasoning.

Lighthouse Math

Level F

Chapter 10

Exercise 4

183

Chapter 10-5 Dividing Decimals with Zeros in the Quotient Daily Review 1. 24 � 3 =

2. 54 � 9 =

3. 49 � 7 =

4. 32 � 4 =

Divide.

6. 48 � 6 =

7. 27 � 3 =

8. 64 � 8 =

5. 35 � 7 =

Learn and Connect Hector and his two sons are spending the day at the amusement park. They paid a total of $32.04 for admission to get into the park. If each ticket costs the same amount, how much did each admission cost? 1) We will divide the total cost of

people.

2) Divide:

$10.68 3)32.04 �3 02 � 00 20 � 18 24 � 24 0

3) Each admission into the amusement park cost .

Apply Divide. 1.

6)3.024

2. 5)30.35

3. 8)0.184

4. 9)0.054

5. 4)2.508

Rewrite and divide. 6. 3.549 � 7 =

184

Level F

8.024 � 4 =

Chapter 10

Lesson 5

8. 2.106 � 3 =

Lighthouse Math

Exercise 10-5 Name Divide. 1.

8)2.032

4)3.024

7)0.028

4. 8)0.064

5. 6)3.006

15)1.05

4)0.144

9)0.576

9. 16)0.608

10. 5)0.335

11. 0.888 � 12 =

12. 0.425 � 5 =

13. 0.354 � 6 =

14. 0.048 � 6 =

15. 2.814 � 7 =

16. 0.364 � 4 =

17. 3.216 � 8 =

18. 0.279 � 3 =

19. 0.042 � 6 =

20. 0.368 � 4 =

21. 5.463 � 9 =

22. 0.156 � 3 =

Rewrite and divide.

Challenge Solve each problem. 23. The scientist had 0.189 liters of a solution to split evenly between 3 beakers. How much solution will be in each beaker?

Lighthouse Math

Level F

24. Six small paper clips weigh 0.336 kilograms. If they all weigh the same amount, how much does each paper clip weigh?

Chapter 10

Exercise 5

185

Chapter 10-6 Dividing Decimals by Decimals Daily Review

Rewrite and divide.

1. 0.144 � 4 =

2. 0.335 � 5 =

3. 0.309 � 3 =

Learn and Connect Connor wants to complete a 3.1 mile race. He wants to finish the race in 27.9 minutes. What pace per mile does Connor need to keep to finish in that amount of time? 9 ) ) 3.1 27.9 31 279 � 279 0 Move the Make the decimal in the divisor a whole dividend the number by same number moving the of places. decimal point. Connor must keep a

minute pace per mile to finish in 27.9 minutes.

Apply Draw arrows to show the decimal movement and write in the new decimal spots.

2.8)23.45

2. 0.16)5.478

0.02)92.158

4. 35.2)49.31

6. 1.2)1.32

0.3)92.1

8. 1.8)5.76

Divide. 5.

0.8)0.208

Rewrite and divide. 9. 15.75 � 2.5 =

10. 33.4 � 0.08 =

11. 0.1485 � 16.5 =

Vocabulary Divisor - the number that is being divided by (15 ÷ 3) Dividend - the number that is being divided (15 ÷ 3)

186

Level F

Chapter 10

Lesson 6

Lighthouse Math

Exercise 10-6 Name Draw arrows to show the decimal movement and write in the new decimal spots. 1.

3.6)18.36

2. 0.18)3.672

0.05)40.155

4. 23.4)63.28

Divide. 0.9)7.2

6. 0.9).63

0.4)53.6

8. 2.4)8.16

10. 0.4)6.84

11. 1.6)11.52

12. 1.3)31.2

13. 0.08)4.8

14. 0.5)9.21

0.18)3.24

15.

1.52 � 0.4 =

16. 0.86 � 0.25 =

17.

12.35 � 1.9 =

18. 3.616 � 0.08 =

19.

0.54 � 2.7 =

20. 0.84 � 4.2 =

21. 0.042 � 2.1 =

Rewrite and divide.

22. 2.416 � 0.04 =

Challenge Solve each problem. 23. If a large flag pole is 16.4 feet tall and is made of 4 separate smaller poles, how long is each pole?

Lighthouse Math

Level F

24. If Sam has a ribbon that is 9.36 meters and he needs to cut pieces that are 0.03 meters long, how many smaller ribbons will he have?

Chapter 10

Exercise 6

187

Chapter 10-7 Extending Dividing Decimals Round each decimal to the underlined digit.

Daily Review 1. 23.0145 =

2. 97.193 =

3. 913.87 =

4. 4.603 =

Learn and Connect The 6th grade math teachers are excited for the new school year! They have gone shopping to buy all the school supplies for their students. Each teacher will have 25 students in their class. How much did Mr. Anderson spend per student? 1) Mr. Anderson has spent

2) Divide:

TOTAL COST OF SCHOOL SUPPLIES

students and

Mr. Smith

$225

Mr. Anderson

$281

Mr. Loyal

$212

. $11.24 25)$281.00 � 25 31 � 25 60 � 50 100 � 100 0

We continue to add 0 until our division problem reaches an end.

3) Mr. Anderson spent

per student.

Apply Divide. 1.

8)82

2. 5)41.2

12)85.8

4. 35)163.8

Rewrite and divide. 5. 497.4 � 8 =

188

6. 19.6 � 5 =

Level F

Chapter 10

Lesson 7

9.48 � 15 =

Lighthouse Math

Exercise 10-7 Name Divide. 1.

6)363

2. 4.2)12.81

4)12.5

4. 8)53

8)820

6. 4)3.49

14)7.7

8. 25)1.2

9. 68.4 � 8 =

10. 48.78 � 9 =

11. 24.66 � 12 =

12. 63 � 4 =

13. 100.4 � 25 =

14. 4.3 � 2 =

15. 57.9 � 0.6 =

16. 2.7 � 12 =

17. 23.67 � 6 =

Rewrite and divide.

Challenge Solve each problem. 18. In science class, Mr. Jones has 30.6 milliliters of a solution. He needs to divide the solution equally among 8 groups of students. How much solution will each group get?

Lighthouse Math

Level F

19. James paid $25.60 for gas. Gas was on sale for $3.20 per gallon. How many gallons of gas did he buy?

Chapter 10

Exercise 7

189

Chapter 10-8 Review Daily Review

Find each product or quotient.

1. 25 � 5 =

2. 48 � 6 =

3. 42 � 7 =

4. 28 � 4 =

5. 64 � 8 =

6. 36 � 9 =

7. 18 � 6 =

8. 72 � 8 =

Learn and Connect At a deep ocean exhibit, James read the following sign in front of the deep water fish tank. James wonders how much is five tenths of one tenth or 0.5 of 0.1? When you are taking a decimal part of another decimal, you must multiply the decimals. Use decimal models to show this multiplication.

0.1

�

0.5

0.05

The answer to 0.5 � 0.1 = 0.05

Approximately, 0.05 of the fish in the ocean live in deep water.

Apply Divide. 1.

4)37.6

2. 8)61

3.3)2.64

9.24 � 12

4. 0.27)0.324

Multiply. 5.

190

26.1 � 0.04

19.45 � 6

Level F

Chapter 10

Lesson 8

0.007 � 0.08

158.7 � 13.9

Lighthouse Math

Exercise 10-8 Name Multiply. 1.

25.6 � 5.4

9.04 � 4

0.06 � 0.08

6.9 � 9

26.25 � 7.3

8.32 � 0.002

0.04 � 3

4.96 � 3.75

6.07 � 2

10.

8.38 � 6.01

11. 9)1.89

12. 4)3.024

13. 0.08)4.8

14. 8)53

15. 6)42.24

16. 7)2.814

17. 12)2.7

18. 0.06)0.234

Divide.

Challenge Solve each problem. 19. A piece of wood is 0.75 inches tall. How tall are 4.5 identical pieces of wood stacked together?

Lighthouse Math

Level F

20. If 20 sheets of paper stacked on top of each other are 0.855 centimeters thick, how thick is one sheet of paper?

Chapter 10

Exercise 8

191

Chapter 11 NYS NG Standards NY-4.MD.1 NY-4.MD.3 NY-5.MD.5b

NY-6.G.1 NY-6.G.2 NY-7.G.4

CC Standards 4.MD.A.1 4.MD.A.3 5.MD.A.1 5.MD.C.5.B

192

6.G.A.1 6.G.A.2 7.G.B.4

In Chapter 11 we will explore the concepts of

Geometry Geometry helps us understand the measurements and relationships of lines, angles, surfaces and solids found in the everyday world. • Find the perimeter and area of a rectangle and triangle. • Determine the circumference and area of a circle. • Apply measurements of length, weight and capacity.

diameter

circumference

radius

We can use a formula to find the area and perimeter of rectangles and triangles. We can use radius and diameter to calculate circumference and area of circles. We can convert between measurements of feet, inches and yards. We can convert between measurements of pounds, ounces, cups, gallons and pints.

193

Chapter 11-1 Converting Units of Length Find each sum, difference, quotient or product.

Daily Review 1. 32.14 – 18.39

6)119.34

3. 56.49 � 3

42.1 + 32.06 =

Learn and Connect Mr. Ackerman is measuring two bookshelves to fit into a space next to his desk. One bookshelf measures 3 feet, 4 inches. The other one measures 4 feet, 1 inch. What is the difference between the widths of the bookshelves? UNITS OF LENGTH

4 feet01 inch10 – 3 feet 4 inches

3 feet 13 inches – 3 feet 4 inches

12 inches = 1 foot 3 feet = 1 yard

To subtract, we need to regroup 1 foot into 12 inches. Now we have a total of 13 inches.

36 inches = 1 yard 5,280 feet = 1 mile 1,760 yards = 1 mile inches = in. foot = ft

The difference between the bookshelves is

yard = yd mile = mi

Hint: Multiply to convert larger units to small ones. Divide to convert smaller units to larger ones.

Apply Convert each length. 1.

5 1 yd =

1 mi 12 in. =

ft in.

4 ft 3 in. =

in.

144 in. =

3,520 yd =

104 in. =

6 ft 7 in. + 9 ft 11 in.

10.

in.

Convert each length. 7.

5 ft 6 in. – 3 ft 10 in.

6 yd 1 ft – 2 yd 3 ft

8 yd 6 in. + 4 yd 10 in.

Vocabulary Customary System - measurement defined as weights, lengths, capacity and temperature Convert - to change something from one form to another form (for example: feet to inches) 194

Level F

Chapter 11

Lesson 1

Lighthouse Math

Exercise 11-1 Name Convert each length. 1.

7 yd 2 ft =

3 mi =

62 ft =

10.

18 yd 1 ft =

13.

4 1 ft =

16.

2 yd 6 in. =

5 ft 6 in. =

in.

180 in. =

10,560 ft =

96 in. =

in.

6 yd 8 in. =

in.

5 mi =

11.

2 mi =

12.

87 in. =

14.

3 ft 2 in. =

in.

15.

108 in. =

17.

7,040 yd =

18.

17 ft =

in.

19.

5 ft 5 in. – 2 ft 9 in.

20.

8 yd 1 ft – 4 yd 2 ft

21.

6 ft 3 in. + 2 ft 7 in.

22.

6 yd 14 in. + 9 yd 21 in.

23.

17 ft 1 in. – 9 ft 6 in.

24.

13 yd 3 ft – 6 yd 2 ft

25.

6 ft 7 in. + 15 ft 9 in.

26.

7 mi 860 yd + 3 mi 925 yd

27.

4 ft + 3 ft

28.

3 yd 2 ft + 2 yd 2 ft

29.

9 ft 3 in. – 4 ft 5 in.

30.

7 yd 5 in. – 3 yd 9 in.

8 in. 6 in.

Challenge Solve each problem. 31. John’s grandfather bought 4 yd 16 inches of fabric. How many inches of fabric did he buy?

Lighthouse Math

32. Bob long jumped 13 ft 10 inches. Isaac long jumped 15 ft 3 inches. How many more feet and inches did Isaac jump than Bob?

Level F

Chapter 11

Exercise 1

195

Add or subtract.

Chapter 11-2 Customary Units - Weight and Capacity Daily Review

Solve each expression.

1. 4² =

2. 3³ =

3. 5 � 10² =

4. 10³ � 4 =

5. 8² =

Learn and Connect Leo is making punch for the 6th grade graduation party. He has 32 glasses to fill. Each glass holds 6 fluid ounces. How many pints of punch should Leo make? 1) We know there are

glasses and each can hold

CAPACITY 8 ounces = 1 cup 2 cups = 1 pint

ounces.

2 pints = 1 quart

2) L et’s multiply our glasses by ounces for each glass. � = total ounces needed.

4 quarts = 1 gallon ounce = oz cup = c pint = pt quart = qt gallon = gal

3) T he problem asks us to show this as pints. We divide the total ounces by number of ounces in a pint. (1 pint = 2 cups 1 cups = 8 oz 2 cups = 16 oz) 4) ÷ = total oz oz in a pt 5) Leo needs to make

WEIGHT 16 ounces = 1 pound

pints of punch.

2,000 pounds = 1 ton pound = lb

ton = T

6,000 lb =

3 gal 4 qt =

15 lb 5 oz + 9 lb 12 oz

pints of punch.

Apply Convert each weight or capacity. 1.

32 qt =

gal

10 c =

80 oz =

76 oz =

9 c 4 oz – 4 c 8 oz

Add or subtract. 7.

3 gal 2 qt + 1 gal 2 qt

Vocabulary Capacity - the maximum amount something can contain 196

Level F

Chapter 11

Lesson 2

Lighthouse Math

Exercise 11-2 Name Convert each weight or capacity. 1.

12 qt =

gal

12 c =

64 oz =

52 oz =

14 pt =

10 qt =

10.

100 oz =

11.

4 gal 6 pt =

8,000 lb =

2 gal 2 qt =

2,500 lb =

12.

5 qt =

gal

13.

4 gal 3 qt + 2 gal 1 qt

14.

8 c 3 oz – 5 c 7 oz

15.

12 lb 4 oz – 4 lb 10 oz

16.

13 lb 7 oz + 4 lb 10 oz

17.

5 qt 1 pt – 3 qt 1 pt

18.

7 c 5 oz + 3 c 5 oz

19.

5 gal 2 qt + 2 gal 3 qt

20.

16 lb 4 oz – 8 lb 11 oz

Challenge Solve each problem. 21. Matthew bought 14 quarts of milk. How many gallons and quarts did he buy?

22. Twin babies weighed 12 lb 7 oz together. The first twin weighed 6 lb 14 oz. How much did the second twin weigh?

23. The car took 2 quarts and 1 pint of oil. The truck needed 4 quarts and 1 pint of oil. How much oil is needed for the car and the truck? If you have 2 gallons of oil, is there enough for both the car and the truck? Why or why not?

24. A baby blue whale is born 25 feet long and can weigh 6 tons at birth. How many pounds is a baby blue whale at birth?

Lighthouse Math

Level F

Chapter 11

Exercise 2

197

Add or subtract.

Chapter 11-3 Using a Formula Daily Review

Find each sum or difference.

1. 2,031 – 347

2. $56.98 + $8.99

3. 5,006 – 517

4. 43,018 – 9,207

5. 3,467 + 6,701

Learn and Connect In science class, Thomas is learning about Fahrenheit and Celsius. He learned that Fahrenheit is a temperature unit used in the U.S. Celsius is used to measure temperature in other countries. His teacher has asked him to convert 86°F to its equivalent in °C. 1) We will use the conversion information: °C to °F: Divide by 5, then multiply by 9, then add 32 °F to °C: Subtract 32, then multiply by 5, then divide by 9 2) Let’s change 86°F by subtracting multiplying by

, then

, and dividing by

3) Following the order of operations we can calculate: (86 – 32) � 5 ÷ 9 = °C.

Use the formula to find the perimeter.

Use the formula to find the area.

1. P = 2l + 2w

2. A = b · h 2

4 yd

l = length w = width b = base h = height r = radius

7 in.

in2

8 yd

6 in.

Use the formula to find the volume of each shape.

cm3

5. V = b · l · h 2

10 yd

yd3

6 cm

ft3

11 ft

4. V = π · r2 · h

4 cm

15 yd

3. V = l · w · h

Apply

f 15

13 ft

Vocabulary Volume - the amount of space taken up by a 3-dimensional object Pi symbol - 3.14 198

Level F

Chapter 11

Lesson 3

Lighthouse Math

Exercise 11-3 Name Use the conversion formulas on the previous page to convert the temperatures. 1.

104 °F =

°C

25 °C =

°F

15 °C =

°F

45 °C =

°F

68 °F =

°C

50 °F =

°C

Use the formula to find the perimeter. 8. P = 2l + 2w

7. P = 2l + 2w 5 ft

6 cm

9 ft

10 cm

Use the formula to find the area. 9. A = b·h 2

10. A = b · h 2

5 cm

cm2

5 yd

cm2

4 cm

8 yd

Use the formula to find the volume of each shape. 13. V = b · l · h 2

12. V = π · r2 · h

4 in.

11. V =l·w·h

10 in.

3 cm

15 cm 3 in. 6 cm

8 cm

cm3

Challenge 14. Jim used a formula to find the area of one of these shapes. He said one of the shapes below is 48 square inches. Which shape’s area did he find? What was the formula he used?

9 in.

15 in.

10 in.

10 in. 8 in.

12 in.

Lighthouse Math

4.5 in. 12 in.

12 in.

Level F

Chapter 11

Exercise 3

199

Chapter 11-4 Rectangles - Perimeter and Area Daily Review

Find each product.

1. 56 � 3

2. 104 � 5

3. 98 � 4

4. 1,567 � 2

5. 460 � 8

6. 35 � 9

Learn and Connect Ethan bought wallpaper to decorate one of his bedroom walls. The wall is 11 feet wide and 15 feet long. He also wants to put a white border around the wall. Find the area for the wallpaper and the perimeter for the border. 1) To find the area we need to determine the square feet that covers Ethan’s wall. Area = length x width. Area =

�

ft2

2) To find the perimeter we need to determine the distance around Ethan’s wall. Perimeter = 2(length) + 2(width).

Perimeter = 2(

) + 2(

Apply Find the perimeter and area. 1.

3 cm

5 ft

7 ft

2m 9m

8 cm

Find the perimeter and area of the following rectangles. 4. l = 3.5 m, w = 7.2 m A=

5. l = 19.6 ft, w = 13.4 ft A=

Vocabulary Perimeter - the distance around a 2-dimensional shape Area - the amount of space occupied by a 2-dimensional shape 200

Level F

Chapter 11

Lesson 4

Lighthouse Math

Exercise 11-4 Name Find the perimeter and area. 1.

5 cm

2. 4 cm

3. 3 in.

8 cm

9 cm

7 in.

4 ft

5.5 in.

7 ft

2.3 in. 4.1 in.

20.45 in.

Find the perimeter and area of a rectangle with the following dimensions. Draw a rectangle to help you.

l = 2.3 m, w = 8.1 m

l = 32 in, w = 21 in

10. l = 0.34 yd, w = 12 yd

12. l = 193 ft, w = 138 ft

11. l = 0.525 m, w = 2.5 m

8. l = 18.5 ft, w = 14.3 ft

A= P=

Challenge Solve each problem. 13. V ictor is getting new carpet in his bedroom. His room is a rectangle that measures 10.5 ft by 13.2 ft. How many square feet of carpet does he need?

Lighthouse Math

14. Victor wants to put a wallpaper border around the perimeter of his room. How many feet of border does he need?

Level F

Chapter 11

Exercise 4

201

Chapter 11-5 Triangles - Perimeter and Area Daily Review

Find each quotient.

8)376

3)3,612

2)408

4)12,036

Learn and Connect Each triangular face of the Pyramid of Peace in Kazakhstan is made up of 25 smaller equilateral triangles. These triangles have measurements of 10.4 meters high and a 12 meter base. What is the area and perimeter of one of the smaller equilateral triangles? 1) T o find the area we will take the base times the height and divide by 2. Area = (

�

)÷2=

2) To find the perimeter we will add the measurements of all 3 side lengths. Perimeter = side + side + side. Perimeter =

Apply Find the perimeter and area. 1.

2. 4 ft

6 ft

8 ft

3. 10 m

12 ft

10 m

16 m

18 m

12 m

Find the perimeter and area of the following triangle dimensions. 4. h = 5 cm, b = 8 cm l = 6 cm, l = 12 cm A=

202

5. h = 2.5 in., b = 1.5 in. l = 3.3 in., l = 2.2 in. A=

Level F

Chapter 11

Lesson 5

6. h = 6.2 ft, b = 3.8 ft l = 6.4 ft, l = 6.4 ft A=

Lighthouse Math

Exercise 11-5 Name Find the area and perimeter. 1.

2. 4 ft

7 ft

5 ft

3. 6.2 cm

9 in.

9.3 cm

7 in.

13 in.

5.4 cm 9 ft

18 in.

8.7 cm

5. 9m

6. 31 ft

26 ft

42 ft

4 cm

4 cm 3.5 cm

15 in

4 cm

45 ft

h = 10 cm, b = 10 cm

l = 10 cm, l = 12 cm

8. h = 5 in.,

b = 4 in.

l = 5.8 in., l = 4.7 in.

h = 5.25 ft, b = 12 ft

10. h = 12.8 m, b = 16.5 m

l = 9 ft,

l = 15.1 m, l = 15.3 m

l = 7 ft

11. h = 10.3 cm, b = 15.6 cm A = l = 10.3 cm, l = 18.7 cm

Lighthouse Math

12. h = 6 in.,

Level F

b = 4.2 in.

l = 10.2 in., l = 7.3 in.

Chapter 11

Exercise 5

Find the area and perimeter of a triangle with the dimensions listed. Draw a triangle with these dimensions to help you.

203

Chapter 11-6 Circumference of a Circle Daily Review

Find each product.

1. 38 � 33

52 � 12

4. 106 � 45

19 � 26

5. 824 � 61

Learn and Connect A flowerpot has a circular base with a diameter of 27 centimeters. Find the circumference of the base of the flowerpot. Round to the nearest tenth. The formula to find the circumference (distance around) a circle is: C = πd or 2πr • π (Pi) = 3.14 • diameter = the distance across a circle, through the center • radius = halfway across a circle

radius diameter

2) The circumference of the

1) To find the circumference of the flowerpot we will take 3.14 times the diameter of

flowerpot is

cm.

C = 3.14 �

Apply Find the circumference of each circle. 1.

14 in.

4 ft

8 yd

10 ft

Complete the table. 5.

DIAMETER

2.8 in.

15 yd

19.6 ft

124 m

CIRCUMFERENCE

Vocabulary Circumference - the distance around a circle Diameter - a straight line passing through the center of a circle (all the way across) Radius - a straight line from the center of a circle to the side (halfway across) 204

Level F

Chapter 11

Lesson 6

Lighthouse Math

Exercise 11-6 Name Find the circumference of each circle. Round to the nearest hundredth. 1.

36 ft

C= 5.

4.5 in.

7 in.

17 cm

4.5 yd

C= 8.

4.2 cm

12.44 m

Complete the table. Round to the nearest hundredth. 9.

DIAMETER

3.3 in.

9 yd

22.6 ft

234 m

CIRCUMFERENCE

10. d = 1.8 ft

11. d = 86 yd

14. d = 15 in.

15. d = 5.25 ft

12. d = 7.05 in. C=

Find the circumference using the diameter listed. Round to the nearest hundredth. 13. d = 17.2 cm C=

16. d = 16.1 cm C=

17. d = 125 in. C=

Challenge Solve each problem. Round your answer to the nearest hundredth. 18. A ball has a diameter of 13 inches. How far will the ball roll in one complete turn?

Lighthouse Math

19. Tim is running on a circular track that has a diameter of 78.25 yards. How far does Tim run in 1 lap around the track?

Level F

Chapter 11

Exercise 6

205

Chapter 11-7 Find the Area of a Circle Estimate each sum by rounding to the nearest hundred.

Daily Review 1. 628 + 476 =

2. 1,559 – 813 =

Learn and Connect Ezra needs to buy mulch for the garden with the dimensions shown. For how much area does Ezra need to buy mulch? Round to the nearest tenth. The formula to find the area (space covering) of a circle is: A = πr² • π (Pi) = 3.14 • diameter = the distance across a circle, through the center • radius = halfway across a circle 1) To find the area of the garden we will take 3.14 times the radius squared. A = 3.14 �

�

2) The area of the garden is about

yds2.

Apply Find the area of each circle. 1.

6 yd

9 ft

2 in.

Complete the table. Round to the nearest hundredth. 5.

DIAMETER

3.9 in.

46 yd

15 ft

16.4 m

AREA

Solve. 6. What is the area of a round pizza that had a diameter of 16 inches?

206

Level F

Chapter 11

Lesson 7

in²

Lighthouse Math

Exercise 11-7 Name Find the area of each circle. Round to the nearest hundredth. 1.

5 mm

A= 5.

16 km

4.2 cm

26 km

12 cm

A= 7.

3.5 cm

A= 8.

18 in.

4.5 in.

Complete the table. Round to the nearest hundredth. 9.

DIAMETER

2.7 in.

32 yd

11 ft

17.4 m

CIRCUMFERENCE

10. r = 4 ft

11. r = 0.1 yd

12. r = 9.5 in.

13. r = 7.1 cm

14. r = 2.5 ft

15. r = 1.8 yd

16. r = 10 in.

17. r = 36 cm

Find the area using the radius listed. Round to the nearest hundredth.

Challenge 18. M r. Smith wants to know the area of his circular garden. The diameter of his garden is 8 ft. What is the area?

Lighthouse Math

19. T here is a large circle on the gym floor with a diameter of 24 feet. What is the area of the circle?

Level F

Chapter 11

Exercise 7

207

Chapter 11-8 Review Daily Review Find the average of each data set. 2. 4.2, 3.5, 2.8 =

1. 0.03, 0.17, 0.4 =

3. 26.1, 21.5, 23.8 =

Learn and Connect The Woodlawn Elementary School cafeteria staff is making homemade soup for Thursday’s lunch. They need 11 pounds of canned tomatoes, and the tomatoes come in 12 oz cans. How many cans will the cafeteria staff need to make their soup? 1) We know that 1 pound =

oz.

2) The cafeteria staff needs: 11 lbs x 16 oz a pound. 11 lbs x 16 oz = 3) Now we take

oz of total tomatoes

oz and divide it by 12 oz cans. 176 oz ÷ 12 oz =

cans

4) T he cafeteria staff will need

cans to make the soup.

Apply Convert each measurement. 1.

13 c =

87 in. =

10 yd =

4. 8 lb =

in.

11 qt =

19 yd 2 ft =

pt ft

Find the perimeter and area of each shape. 7.

8. 4 in.

9. 6m

5 in.

208

6 cm

14 m 8m

Level F

Chapter 11

Lesson 8

Lighthouse Math

Exercise 11-8 Name Convert each measurement. 1.

3 yd =

26 c =

4. 5 lb =

40 in. =

38 qt =

gal

11. 4 mi =

2 mi =

10. 57 pt =

gal

15 qt =

in.

14 yd 1 ft =

3T=

12. 180 in. =

pt ft lb ft

Add or subtract. 13.

4 ft – 2 ft

14.

5 in. 9 in.

15.

7 yd 1 ft – 5 yd 2 ft

16.

10 ft 9 in. + 8 ft 7 in.

7 yd 7 in. + 5 yd 11 in.

Find the perimeter or circumference and the area of each shape. Round to the nearest hundredth. 17.

18. 8 ft

19.

9 in.

21. A circle with: r = 2.4 yd

22. A rectangle with: l = 15.8 cm, w = 2.7 cm A=

Challenge 23. D raw and label the diameter of a circle with an area of 64π. What is the circumference of this circle?

Lighthouse Math

Level F

Chapter 11

Exercise 8

209

20. A triangle with: h = 6.2 ft, b = 3.8 ft l = 6.4 ft, l = 6.4 ft A=

7 ft 3.5 ft

13 in.

18 in.

12 ft

7 in.

Chapter 12 NYS NG Standards NY-5.G.4 NY-7.G.4 NY-8.G.2

NY-4.G.1 NY-4.G.2 NY-5.G.1 NY-5.G.2

CC Standards 0

210

5.G.B.4 7.G.B.4 8.G.A.2

4.G.A.1 4.G.A.2 5.G.A.1 5.G.A.2

In Chapter 12 we will explore

Types of Shapes, Lines and Angles Knowing these concepts helps us understand the relationships between different geometric figures.

• Identify lines, line segments and rays • Classify triangles by side length and angle measure • Name types of quadrilaterals • Determine congruent parts of polygons • List ordered pairs on a coordinate plane • State whether a shape has performed a translation, rotation or reflection • Classify polygons based on their number of sides

We can classify different types of triangles and quadrilaterals. We can identify the characteristics of congruent shapes. We can name lines, line segments and rays. We can determine if a shape is a polygon or not a polygon. We can recall all the parts of a circle. We can draw a translation, reflection or rotation from an original shape.

211

Chapter 12-1 Basic Geometric Vocabulary Name the shape shown.

Daily Review

Learn and Connect Types of lines plane - a flat surface that extends to infinity

Points E, F, and G are in plane T.

point - a geometric element that has zero dimensions X

intersecting - lines that cross, but don’t make a right angle

perpendicular - lines that intersect and create a 900 angle

endpoints - points that end a line segment

parallel - lines that continue on indefinitely, are equidistant and never touch

Y XY

Types of angles right - measures exactly 900

line - a collection of points along a straight path with no endpoints

line segment - part of a line that contains every point on the line between its endpoints

ray - a line with a single endpoint that goes on and on in one direction

Line relationships

acute - measures less than 900

B AB

obtuse - measures more than 900 Q

straight - measures exactly 1800

Apply Name each figure. 1.

2. xo

Draw and label each line. 5.

212

AB CD

Level F

Chapter 12

Lesson 1

ST intersecting UV

Lighthouse Math

Exercise 12-1 Name Name the figure. 2.

E F

8. B

1800

Draw and label each figure. AB intersecting CD

12. Acute angle

Lighthouse Math

10. Ray RN

11.

13. Obtuse angle

14. Right angle

Level F

Chapter 12

Exercise 1

Points A, B, and C in a plane

213

Chapter 12-2 Classifying Polygons Daily Review

Identify as line, segment, ray or point.

Learn and Connect Polygons are closed figures made up of line segments or sides. The corner points of a polygon are the vertices or a vertex. Regular polygons - all angles are equal in measure and all sides are equal in length Irregular polygons - angles are not equal in measure and sides are not equal in length Name the two irregular polygons in the chart on the right. and

Triangle 3 sides Quadrilateral 4 sides Pentagon 5 sides Hexagon 6 sides Heptagon 7 sides Octagon 8 sides

Types of polygons

Nonagon 9 sides Decagon 10 sides

Apply Name each polygon. Write regular or irregular. 1.

214

Level F

Chapter 12

Lesson 2

Lighthouse Math

Exercise 12-2 Name Name each polygon. Write regular or irregular. 1.

Complete the chart. 10. Polygon

triangle

quadrilateral

pentagon

hexagon

Number of sides Number of vertices

Drawing

Lighthouse Math

Level F

Chapter 12

Exercise 2

215

Chapter 12-3 Classifying Triangles Daily Review

Find the circumference or area for the circle dimension given. Use 3.14 for π.

C = 2(π)r

1. radius = 5 cm

2. diameter = 12 in

3. radius = 3.6 m

A = (π)r2

Learn and Connect In geometry, we name triangles by the letters or numbers assigned to their vertices.

Classify by sides

equilateral - 3 sides congruent

ΔABC B

isosceles - 2 sides congruent

1) Classify ΔABC.

scalene - 0 sides congruent

Sides = Angles = The sum of the angles of a triangle equals 180°.

Classify by angles

2) Find the missing angle measure. Z

acute - all 3 angles less than 900

1180

obtuse - 1 angle more than 900

ΔXYZ

330

right - 1 angle equals 900

180 �

�

Apply Classify each triangle by side and angle. 1.

side =

angle =

angle = T

Find the missing measure. 4.

V W

420

6. 350

640 S

216

Level F

370

Chapter 12

630

350 T

Lesson 3

Lighthouse Math

Exercise 12-3 Name Classify each triangle by sides. 3.

Classify each triangle by angle. 4.

1090

230

800

300

480

450

700

900

450

Find the missing angle measures. 9.

370

510 360

460

630

11.

10.

12.

1180

860

330

640

470

15.

14.

13.

530 600

Lighthouse Math

350

770

600

Level F

Chapter 12

Exercise 3

350

217

Chapter 12-4 Classifying Quadrilaterals Find the perimeter or area for the rectangle dimensions given.

Daily Review

1. l = 2 in, w = 6 in

2. l = 5 ft, w = 9 ft

3. l = 2.2 cm, w = 4 cm

4. l = 18 m, w = 3 m

Learn and Connect Types of quadrilaterals * shapes with 4 sides and 4 angles *

Parallelogram - opposite sides are parallel, 2 sets of sides are different in length

Rectangle - a parallelogram with 4 right angles

Rhombus - opposite sides are parallel, 4 sides are equal in length

Square - a rectangle with all sides equal length

Trapezoid - a quadrilateral with exactly one pair of parallel sides

The sum of the angles in a quadrilateral equal 360°.

Apply Classify each quadrilateral by name and identify the number of pairs of parallel sides. 1.

X D

name

parallel sides

Find the missing measure. 4.

218

E = 29°

G = 102°

F = 87°

Level F

Chapter 12

Lesson 4

M = 90°

O = 90°

N = 115°

Lighthouse Math

Exercise 12-4 Name Classify each quadrilateral by name and identify the number of pairs of parallel sides. 1.

name

parallel sides

Find the missing angle in each quadrilateral. 5.

840

520

230 430

500 1460

2340

1280

750

1460

1280

340

860

470

10.

11.

12. 720 690 890

650

670 980

490

Lighthouse Math

Level F

Chapter 12

Exercise 4

219

Chapter 12-5 Congruent Polygons Draw the line, line segment, or ray indicated.

Daily Review 1. LM

2. QR

3. WX

Learn and Connect B

Congruent - shapes that are equal in size and shape. This symbol means congruent . Corresponding parts - matching sides and angles between congruent shapes.

Q P

Use the congruent triangles to find the missing corresponding side or angle for each example listed below. Corresponding Sides

Corresponding Angles

ΔABC

ΔPQR

* Triangle ABC is congruent to triangle PQR.

Apply Are the figures shown congruent? Circle yes or no. 1.

2. yes

yes

Name the congruent sides.

Name the congruent angles.

T X

220

Level F

Chapter 12

Lesson 5

Lighthouse Math

Exercise 12-5 Name Are the figures shown congruent? Circle yes or no. 1.

2. yes

yes

6. yes

4. no

yes

Name the congruent sides. V

10.

500

600 C

Name the congruent angles. 11.

12.

600

B C

Lighthouse Math

Level F

Chapter 12

Exercise 5

221

Chapter 12-6 Parts of a Circle Daily Review 1.

Classify each triangle by side and angle. 2.

side =

angle =

Learn and Connect Parts of a Circle circle - a closed figure made up of points in a plane that are the same distance from a center

center - the middle point

circumference - the perimeter of a circle

central angle - an angle with a vertex at the center

diameter - cuts the circle in half through the center

radius - half of the diameter from the center

chord - a straight line that does not touch the center

arc - part of the circumference of a circle

P C

840 B

The measure of a circle is 360°.

Apply Use the image to answer the questions. 1. Name the letter that represents the center.

2. What line segment makes up the diameter? 3. True or False: A central angle is shown.

4. Name the line segment that shows the chord.

5. Name a line segment that makes up a radius. 6. If the radius = 4 cm, what is the circumference?

7. Name two letters that form an arc.

222

Level F

Chapter 12

Lesson 6

Lighthouse Math

Exercise 12-6 Name Use the image to answer these questions. 1.

Which line segment is a chord?

Which line segment is the diameter?

Which line segment is a radius?

Name the central angle.

Name an arc.

3 in

How long is the radius?

How long is the diameter?

What is the circumference of the circle?

central angle AOB

10.

arc AX

11.

chord XB

12.

diameter AC

13.

radius OC

Complete the table. Round the answer to the nearest hundredth. 14. radius

diameter

3 in

4.5 in

12 in

4 in

5.05 in

7.32 in

10.4 in

circumference

Lighthouse Math

Level F

Chapter 12

Exercise 6

223

Draw and label the following parts on the circle.

Chapter 12-7 Transformations Daily Review

y-axis 5 A 4 3 2 B 1

Name the ordered pair (x,y) for each point.

1. A

2. C

3. B

4. E

1 2 3 4 5

x-axis

Learn and Connect Shapes transform when they move in position while staying the same size and shape. The original point will be marked as a letter and the new point, after the movement, is indicated with a mark called “prime” A'. The three main transformations are show here. Reflection (flip) - a mirror image across a line or point

Translation (slide) - a move to a new location, points stay within the same plane

Rotation (turn) - a turn clockwise or counter-clockwise Y

line of reflection

Y 6 5 4 3 2 1

A' B 1 2 3 4 5 6

1 B'

center of rotation

7 6 5 4 3 2 1

(3, 3)

1 2 3 4 5 6 7

Apply Name the transformation shown. 1.

Write the ordered pair for each vertex.

3 2

A B

B -3 -2 -1 -1 -2

-3

224

Level F

Chapter 12

Lesson 7

Lighthouse Math

Exercise 12-7 Name Write which type of transformation is shown - translation, reflection or rotation. Then write the ordered pair for each vertex. 1.

8 6

B' -5

-2

4. C

A -6

-4

-2

B' C'

-6

-4

B' 2

-2

-4

Lighthouse Math

Level F

Chapter 12

Exercise 7

225

Chapter 12-8 Review Daily Review

Classify each angle.

Learn and Connect A ferris wheel rotates 60° and then stops so a group at the bottom can get off. How many more degrees does it need to rotate to make a full rotation? We learned that a circle measures 360°. So, we can subtract the distance the ferris wheel has already gone. 360° �

Apply Is the polygon regular?

Classify each shape by its sides.

yes no

Draw a line matching each figure and name. 3.

What is the measure of the missing angle? 4.

ray

200

perpendicular lines

Complete the congruent statements.

line

U Q

line segment

226

Q ΔQSR

parallel lines

Level F

Chapter 12

Δ S

Lesson 8

W V

Lighthouse Math

Exercise 12-8 Name Name the figure or type of angle. 1.

E F

Name the type of triangle or quadrilateral. Classify the triangles by sides and angles. 7.

10.

Name the parts of the circle. 11. Chord

12. Central angle

13. Radius

14. Diameter

15. Arc

, and

Find the missing angle. 16.

1180

17.

18. 840

330

19.

860 560 1460

20.

470

21.

750

340

1460

340

460

Lighthouse Math

Level F

Chapter 12

Exercise 8

227

Chapter 13 NYS NG Standards NY-6.RP.1 NY-6.RP.2 NY-6.RP.3 NY-6.RP.3a

NY-6.RP.3c NY-6.RP.3d NY-6.NS.6c NY-7.G.1

CC Standards 6.RP.A.1 6.RP.A.2 6.RP.A.3 6.RP.A.3.A

228

6.RP.A.3.C 6.RP.A.3.D 6.NS.C.6.C 7.G.A.1

In Chapter 13 we will explore

Fractions, Decimals and Percents • Write ratios for real world situations • Determine equivalent ratios • Use ratios in similar shapes to find missing side lengths • Solve proportions for unknown values

Fraction

Decimal

Percentage

3 10

0.3

30%

• Compare and order: fractions, percents, decimals

We can write ratios for real world situations and find an unknown value. We can solve proportions for an unknown value. We can find a missing side length in similar shapes. We can convert between percents, decimals and fractions. We can compare and order the values of percents, decimals and fractions.

229

Chapter 13-1 Writing Ratios Daily Review

Reduce each fraction.

1. 68

5 2. 20

2 3. 18

16 4. 40

9 21

Learn and Connect Jake is going through his school supplies. He is separating his pencils and markers into two groups. He has 14 pencils and 25 markers. How can we write this as a ratio of pencils to markers. 1) We know that there are markers.

pencils and

2) The ratio of pencils to markers is

Let’s write this scenario as pencils to total items. 1) We know that there are total items.

pencils and

2) T he ratio of pencils to total items is

Apply Write each ratio as a fraction. Do not simplify. 1. red crayons to blue crayons

2. red crayons to total crayons

3. blue crayons to red crayons

4. blue crayons to total crayons

Write each ratio as a fraction. Do not simplify. 5.

apples to chilli peppers

plus sign to circles

stars to smiles

Vocabulary Ratio - comparing two quantities 230

Level F

Chapter 13

Lesson 1

Lighthouse Math

Exercise 13-1 Name Write each ratio as a fraction. Do not simplify. 1. Mugs to cups.

2. Tomatoes to onions.

3. Carrots to vegetables.

4. Books to pens.

5. Pumpkins to lettuces.

6. Length to width.

3 cm

8 cm

Challenge Solve each problem. 7. I n a class, there are 11 boys wearing neckties and 12 boys without. What is the ratio of boys wearing neckties to boys in the class?

8. R ob was throwing rocks into the water. Six of the ten rocks that he threw skipped across the water, but the others sank. What is the ratio of rocks that skipped to the total rocks thrown?

9. J ohn’s cat had 9 kittens. If 7 kittens were gray and 2 were white, what is the ratio of white to gray kittens?

10. There are 12 trumpet players in the band. If 6 of them wear red and 6 wear black, what is the ratio of the players wearing red to the total players?

Lighthouse Math

Level F

Chapter 13

Exercise 1

231

Chapter 13-2 Equal Ratios Compare using >, <, or =.

Daily Review 2 1. 15

6 15

3 2. 31

1 31

7 3. 19

9 19

8 4. 43

2 43

Learn and Connect At Abbott’s Bakery, they make 6 pies for every 10 cakes. At Dale’s Bakery they makes 8 pies for every 15 cakes. Are these ratios equivalent? 1) We know that Abbott’s Bakery makes pies for every cakes. Dale’s Bakery makes pies and cakes.

2) Abbott’s ratio can be written in fraction form as . Dale’s ratio can be written in fraction form as .

3) We can compare by finding a common denominator.

4) We can compare by cross multiplying.

6 = 8 10 15 � 3 � 2

18 = 16 30 30

6 = 8 10 15

6 � 15 = 90 8 x 10 = 80 90 ≠ 80

The ratios of pies to cakes between the 2 bakeries are not equivalent. We compared the ratios and they are not the same.

Apply Use equivalent fractions. State = or ≠. 1.

1 4

4 8

12 21

5 6

3 7

7 11

20 24

5 6

10 12

3 4

4 6

2 3

12 18

4 5

12 16

Use cross multiplying. State = or �. 2 5

5 12

10.

1 2

7 14

11. 87

2 3

12. 31

1 4

9 13. 15

7 13

14.

3 8

6 16

15. 65

25 30

16. 25

4 12

Vocabulary equivalent - equal 232

Level F

Chapter 13

Lesson 2

Lighthouse Math

Exercise 13-2 Name Use equivalent fractions. State = or ≠. 1.

9 24

12 32

3 7

15 35

5 6

40 54

30 36

5 6

8 3

40 15

5 8

15 24

5 6

9 21

3 9

4 15

6 24

4 16

10.

16 40

18 45

11. 92

50 12

18 12. 27

5 45

13. 21

2 4

14.

6 36

1 5

15. 35

9 15

16. 62

1 4

17. 93

1 3

18.

5 20

1 4

19. 4 8

2 4

7 20. 21

1 8

21. 43

5 6

22.

5 6

7 9

25 23. 35

6 14

24. 81

5 40

7 25. 24

5 9

26.

7 14

14 30

27. 32

7 8

28. 14 3

42 9

29. 25

21 9

30.

6 9

8 12

31. 87

12 15

7 32. 12

1 2

33. 12 15

2 3

34.

12 36

8 24

35. 43

5 8

36. 87

8 9

12 37. 30

2 5

38.

3 10

2 5

39. 32

1 5

8 40. 10

20 25

Use cross multiplying. State = or ≠.

Challenge Solve each problem. 41. Jacob drew a rectangle 4 inches wide and 7 inches long. Mark drew a rectangle 12 inches wide and 21 inches long. Is the ratio of width to length the same?

Lighthouse Math

42. Dad makes syrup with 3 cups of water and 2 cups of sugar. Grandpa makes syrup with 4 cups of water and 3 cups of sugar. Is the ratio of water to sugar the same?

Level F

Chapter 13

Exercise 2

233

Chapter 13-3 Proportions Daily Review

Solve for the variable.

1. 3x = 21

2. 64 = 8a

3. 2.5y = 10

4. 32r = 96

5. 18 = 9c

Learn and Connect Sam raked 3 bags of leaves in 16 minutes. If he continues to work at the same rate, how long will it take him to fill 6 bags of leaves? 1) We know that he can do

bags in

This can be written as a fraction

minutes. .

2) Using proportions we can set the fraction we know of equal to 6 . The variable x represents the unknown x amount of time we are trying to find. 4) S am will get 6 bags of leaves done in about minutes.

3) Let’s cross multiply! 3 6 16 = x

3x = 96

(To solve for x we divide 96 by 3.)

Hint: 3x means "3 times x"; remember a variable can be any letter that represents an unknown value

Apply Cross multiply to solve. 15 1. 6x = 18

16 y 2. 24 =3

4 8 3. m = 11

r 4. 10 = 21 7

5. Damon earned $35 for raking leaves in 3 hours. If he always charged the same rate, about how much will he make if he rakes leaves for 7 hours?

6. Thomas drove 10 miles and his car used up 5 gallons of gas. How many miles can he drive with 16 gallons of gas?

Vocabulary Proportion - two equivalent fractions or ratios Variable - a letter used to represent an unknown quantity 234

Level F

Chapter 13

Lesson 3

Lighthouse Math

Exercise 13-3 Name Cross multiply to solve. 6 9 2. y = 12

4 n 3. 6 = 12

3 15 4. z = 40

10 n 5. 7 = 70

1 5 6. x = 25

y 12 7. 9 = 27

5 15 8. 6= t

x 21 9. 8 = 14

3 v 10. 4 = 16

1.5 1.2 11. n = 7

y 4 12. 3.7 = 29.6

18 z 13. 25 = 7

2.8 t 14. 7 =4

3.6 1.2 15. 15 = v

n 1 16. 3.5 = 7

5.6 x 17. 2 =4

12 8 18. y =3

1.5 z 19. 6 = 12

t 3 20. 2.5 = 5

Challenge Solve each problem. 21. Bob ran 2 miles in 14 minutes. At the same rate, how far can he run in 35 minutes?

22. Andy walked 2.5 miles in 50 minutes. At the same rate, how far will he walk in 200 minutes?

23. A baby grows 2 inches every 3 months. How many inches does the baby grow in 12 months?

24. To make lemonade, Joe uses 2 cups of sugar for every 16 cups of water. How much water does he need if he only has 1.5 cups of sugar?

Lighthouse Math

Level F

Chapter 13

Exercise 3

235

4 5 1. 16 = x

Chapter 13-4 Similar Polygons Daily Review

Name the number of sides for each polygon.

1. Hexagon

2. Octagon

3. Quadrilateral

4. Pentagon

5. Decagon

6. Heptagon

Learn and Connect We can use proportions to determine a missing measurement in similar polygons. Similar polygons are the same shape but different size. Because of the relationship between the 2 polygons, we can use the corresponding sides to create proportions. 1) Let’s find the value of x. This variable is on the side labeled The corresponding side is labeled .

115o

18 = 30 x 25

25 T

. M

450 = 30x

2) To find the length of NP, we write and solve a proportion. MN = RS NP ST

x 15

(To solve for x we divide 450 by 30.) 3) The length of NP is

Apply These shapes are similar. Name the corresponding sides. 1.

W A

These shapes are similar. Find the missing side length. 15

10 ?

8 ? 14

4 7

Vocabulary Polygon - a closed figure consisting of a set of line segments connected such that no two segments cross Corresponding - the angles and side that are in the same relative position in similar polygons 236

Level F

Chapter 13

Lesson 4

Lighthouse Math

Exercise 13-4 Name Name the corresponding sides. P

L A

15 F

25 30

P C

18 D

G N

20 N

These shapes are similar. Find the missing side length. 12

5. 10

8. 10

?= D

B 13 D

A E x

m Z

12 10

10.

F 6

12.

11.

3 cm

6 mm

4.5 cm

4 mm n

Lighthouse Math

2.5 mm

9 cm

Level F

Chapter 13

Exercise 4

237

Chapter 13-5 Percents Daily Review

Add or subtract.

1. 2.53 + 1.7 =

2. 8.01 – 4.94 =

3. 25.4 + 9.6 =

4. 17.2 – 15.3 =

5. 63.4 - 42.8 =

6. 78.32 + 6.4 =

Learn and Connect Jonah was interested to see how many pieces of mail he received each day. For a week he recorded his data in the table shown. He noticed Wednesday was a big day. Jonah wants to calculate what percent of his overall mail came on Wednesday.

PIECES OF MAIL Monday

Tuesday

Wednesday

Thursday

Friday

1) We know that on Wednesday Jonah received The total pieces he received for the week was 2) To determine the percent we take 9 divided by 25.

9 ÷ 25 = 0.36

pieces of mail. .

3) We can write a decimal as a percent by multiplying by 100, or moving the decimal point 2 spots right. 0.36 =

4) We can write a percent as a decimal by dividing by 100, or moving the decimal point 2 spots left. 18% =

The percent of his overall mail that came on Wednesday was 36%.

Apply Write as a percent. 1.

0.12

0.08

0.35

0.9

16%

46.2%

10. 3%

1.62

Write as a decimal. 6.

32%

Vocabulary Percent - the amount per 100 and is shown using the percent sign (%) 238

Level F

Chapter 13

Lesson 5

Lighthouse Math

Exercise 13-5 Name Write as a percent. 1. 0.39

2. 0.17

3. 0.02

4. 0.98

5. 0.37

6. 0.16

7. 0.05

8. 0.40

9. 0.51

10. 0.65

11. 0.38

12. 0.87

13. 1.87

14. 0.01

15. 0.99

16. 50%

17. 36%

18. 12%

19. 200%

20. 19%

21. 85%

22. 10%

23. 71%

24. 16%

25. 1%

26. 75%

27. 20%

28. 4%

29. 107%

30. 54%

Write as a decimal.

Challenge Solve each problem. 31. Tyler bought carnival tickets for $100. He paid $6 in tax. What percent was the tax?

32. Charlie set a goal to ride his bike 100 miles in a week. By Thursday he had ridden 73 miles. What percent of his goal had he ridden by Thursday?

Lighthouse Math

Level F

Chapter 13

Exercise 5

239

Chapter 13-6 Percents, Fractions, Decimals Daily Review

Turn each percent into a decimal.

1. 25%

2. 18%

3. 36.5%

4. 48%

Learn and Connect Mr. Lindahl has 24 students in his 3rd grade class. He just gave a math test and the table shows the fraction of students that received each grade. Let’s use our knowledge of percents, decimals and fractions to look at this data in the different forms.

FRACTION OF STUDENTS

1) Write the fraction of students that received an A as a: 5 Decimal - 12 = 5 ÷ 12 = 0.417

5 12

1 4

1 6

1 12

Percent - 0.417 � 100 = 41.7% 2) Write the fraction of students that received a D as a: Decimal -

Percent -

� 100 =

0.083 12)1.0000 – 96 40 – 36 40 – 36

3) Take the percent of 36% and write it as a: Decimal -

÷ 100 =

Fraction -

9 or reduced to 25

This will continue to repeat so we will round to 0.083. You can show a repeating decimal by 'capping' it with a line over the repeated numbers. Example 0.083

Apply Write as a percent. 1. 25

6 25

1 4

4 9

1 8

Write as a fraction in simplest form. 6.

82%

27%

10. 43%

Solve. 11. Mr. Jones noticed that 25 of 65 students in his band classes were wearing blue. Write this ratio as a percent, decimal and fraction. percent

240

Level F

Chapter 13

Lesson 6

decimal

fraction

Lighthouse Math

Exercise 13-6 Name Write as a percent. 1.

3 5

1 8

1 6

1 9

5. 17 20

3 11

3 7

5 8

3 4

10. 5 9

14. 16 25

15. 17 50

11. 1 3

12. 7 8

9 13. 20

16. 35%

17. 8%

18. 40%

19. 75%

20. 79%

21. 16%

22. 6%

23. 90%

24. 88%

25. 10%

26. 70%

27. 65%

28. 21%

29. 58%

30. 43%

Write as a fraction in the simplest form.

Challenge Solve each problem. 31. G reg scored 90% on the math test. Abe got 8 out of 9 problems correct. Who scored the higher percentage?

Lighthouse Math

3 32. Jason did 25 of his homework during study hall, 1 7 of his homework as soon as he got home, and 20 10 of his homework after dinner. What percent of his homework does he still have to do?

Level F

Chapter 13

Exercise 6

241

Chapter 13-7 Compare and Order - Percents, Fractions, Decimals Indicate <, >, or =.

Daily Review 1. 0.65

2. 1.8

0.68

3. 19.23

1.80

19.32

4. 0.07

0.007

Learn and Connect A supermarket found that the 35 of customers bought

vegetables, 0.09 bought herbs, and 8% bought fruit.

Which purchase was made by a greater percentage of customers?

We can answer this question using the knowledge we’ve gained in this chapter about converting fractions, decimals and percents. You can use the conversion you find easiest. For this example, let’s turn our three numbers into decimals. fruit

vegetables

herbs

3 5

0.09

or 8 ÷ 100

0.6

0.08

5)3.0 – 30 0

When we order our numbers it’s always important to use their original form. In this case we have 0.08, 0.6, and 0.09. From least to greatest we could list them as: fruit, herbs, vegetables. The greatest percentage of items purchased by customer are:

Apply Circle the greatest number. 3 1. 20 , 0.1, 3%

2. 0.67, 32 , 60.9%

7 3. 15 , 0.45, 40%

7 , 0.08, 77% 4. 10

11 5. 0.1, 100 , 1.1%

6. 0.35, 31 , 30.9%

Order from least to greatest. List your answers in original form. 9 1 , 3 7. 35.5%, 0.3, 25

242

8. 0.24, 25%, 51 , 0.251

Level F

Chapter 13

Lesson 7

4 9. 10 , 32%, 82 , 0.01

Lighthouse Math

Exercise 13-7 Name Circle the greatest number. 1.

5 20, 0.2, 2%

9 0.85, 10 , 80.9%

3 12 , 0.35, 30%

6 10 , 0.06, 67%

6 0.65, 100 , 6.5%

0.4, 41 , 49%

3 5 , 0.3, 35%

0.7, 37, 70.3%

10 15 , 0.5, 55%

7 , 0.07, 70% 10. 25

1 11. 0.11, 10 , 1.2%,

12. 0.25, 51 , 20.5%

2 1 13. 22.2%, 0.2, 22 , 2

14. 0.45, 4.5%, 45, 0.455

8 15. 10 , 82%, 82, 2.08

16. 64%, 6.4, 4 6, 0.65

17. 0.73, 75%, 45, 0.751

1 1 18. 10 , 1%, 50 , 0.05

Challenge Solve each problem. 19. A aron scored 85% on the math test.

20. O n a survey, 25% of kids said their favorite

Ivan got 0.9 of the problems correct.

their favorite was strawberry, and 0.3 said

Put their scores in order from least to

their favorite was vanilla. Which is the

greatest.