Issuu

G Level

Lighthouse

Math

Basic Edition

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LEVEL G

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©Copyright 2021 Lighthouse Curriculum Inc. All rights reserved. Lighthouse Math Level G • ISBN 978-1-972340-00-4 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 P lace Value and Whole Number Addition and Subtraction Place Value Through Trillions...........................................................14 Compare and Order Numbers.......................................................... 16 Addition of Large Numbers............................................................. 18 Subtraction of Large Numbers.........................................................20 Addition and Subtraction Word Problems.........................................22 Expressions with Missing Addends................................................. 24 Order of Operations........................................................................26 Review..........................................................................................28

CHAPTER 2 Multiplication and Expand on that Learning Basic Fact Practice..........................................................................32 Multi-Digit Multiplication.............................................................. 34 Multiplying Large Numbers.............................................................36 Multiplication Word Problems.........................................................38 Exponents.................................................................................... 40 Missing Factors............................................................................. 42 Order of Operations....................................................................... 44 Review......................................................................................... 46 Lighthouse Math

Table of Contents

CHAPTER 3 Division Operations of All Whole Numbers Basic Fact Practice..........................................................................50 2-Digit Divisors..............................................................................52 3-Digit Divisors............................................................................. 54 Division Word Problems..................................................................56 Divide by Power of Ten...................................................................58 Missing Divisors and Dividends........................................................60 Order of Operations........................................................................62 Review......................................................................................... 64

CHAPTER 4 Operations with Fractions Rewriting Fractions.........................................................................68 Order and Compare Fractions..........................................................70 Add Fractions................................................................................ 72 Subtract Fractions...........................................................................74 Multiply Fractions........................................................................... 76 Divide Fractions............................................................................. 78 Order of Operations........................................................................80 Review..........................................................................................82

CHAPTER 5 Decimals through the Ten Thousandths Place Place Value With Decimals..............................................................86 Order and Compare........................................................................88 Add Decimals................................................................................90 Subtract Decimals...........................................................................92 Multiply Decimals.......................................................................... 94 Divide Decimals..............................................................................96 Order of Operations........................................................................98 Review........................................................................................100 7

Table of Contents

Lighthouse Math

CHAPTER 6 Number System to Include Negative Numbers Absolute Value.............................................................................104 Comparing & Ordering Numbers................................................... 106 Coordinate Plane.......................................................................... 108 Multiplying Integers ..................................................................... 110 Dividing Integers...........................................................................112 Multiplying & Dividing Rational Numbers........................................ 114 Order of Operations with Negative Numbers.................................. 116 Review........................................................................................ 118

CHAPTER 7 Negative Numbers and Solving Expressions with Negative Rational Numbers Adding Integers with Number Lines............................................... 122 Adding Negative Numbers with Zero Pairs..................................... 124 Adding Integers Word Problems.................................................... 126 Subtracting Integers with Number Lines......................................... 128 Rewriting Subtraction Statements as Addition................................. 130 Word Problems with Negative Numbers........................................ 132 Order of Operations with Integers.................................................. 134 Review........................................................................................ 136

CHAPTER 8 Negative Numbers and Simplifying Expressions to Learning How to Solve Equations Expressions..................................................................................140 Combining Like Terms.................................................................. 142 Distributive Property.....................................................................144 Solving One-Step Equations.......................................................... 146 Two-Step Equations..................................................................... 148 Multi-Step Equations.................................................................... 150 Equation Word Problems.............................................................. 152 Review........................................................................................ 154 Lighthouse Math

Table of Contents

CHAPTER 9 Skills with Ratios Introduction to Ratios.................................................................... 158 Equivalent Ratios.......................................................................... 160 Unit Rate & Unit Ratio................................................................... 162 Introduction to Proportions............................................................ 164 Proportion Word Problems............................................................ 166 Scale Figures................................................................................ 168 Scale Factor & Scale Word Problems.............................................. 170 Review........................................................................................ 172

CHAPTER 10 Review and Build Skills with Ratios Introduction to Percentages........................................................... 176 Fractions, Decimals and Percents................................................... 178 Percent of a Number..................................................................... 180 Part, Whole and Percent Word Problems....................................... 182 Tax and Tip.................................................................................. 184 Discount & Markdown.................................................................. 186 Simple Interest............................................................................. 188 Review........................................................................................ 190

CHAPTER 11 Geometry Concepts Classifying Angles........................................................................ 194 Supplementary, Complementary and Adjacent Angles..................... 196 Find Missing Angles..................................................................... 198 Identify Missing Angles in Triangles...............................................200 Equations for Missing Angles........................................................202 Transversal Vocabulary................................................................. 204 Transversal Angles........................................................................206 Review........................................................................................208 9

Table of Contents

Lighthouse Math

CHAPTER 12 Area and Perimeter Perimeter.................................................................................... 212 Area of Rectangles and Parallelograms........................................... 214 Area of Triangles.......................................................................... 216 Circles......................................................................................... 218 Composite Area...........................................................................220 Surface Area of Rectangular Prisms................................................ 222 Volume of Rectangular Prisms.......................................................224 Review........................................................................................ 226

CHAPTER 13 Review Data in Many Different Contexts Introduction to Probability.............................................................230 Finding Probability of a Single Event............................................... 232 Probability of Multi-Step Events....................................................234 Mean, Median, Mode, Range........................................................ 236 Data............................................................................................ 238 Input/Output Tables................................................................... 240 Graphing Functions.......................................................................242 Review....................................................................................... 244

CHAPTER 14 Review all Concepts Order of Operations Review..........................................................248 Integer Operations Review............................................................250 Equations Review......................................................................... 252 Ratio, Scales, Proportions Review...................................................254 Percent, Tax, Interest Review......................................................... 256 Geometry Review......................................................................... 258 Probability Review........................................................................260 Functions and Graphs Review........................................................ 262 Lighthouse Math

Table of Contents

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

NY-4.NBT.4 NY-5.OA.1 NY-4.OA.3

CC Standards 3.NBT.A.1 3.NBT.A.2 4.NBT.A.2

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

In Chapter 1 we will review previous learning of

Place Value and Whole Number Addition and Subtraction We will also practice finding missing addends and review the order of operations involving addition and subtraction.

• Place value • Order & compare numbers • Addition • Subtraction • Addition and subtraction word problems • Missing addends and evaluating expressions • Order of operations • Review Real world application of the skills covered in this chapter will be explored through word problems and evaluating expressions. Students will further develop their understanding of the order of operations.

Chapter 1-1 Place Value Through Trillions Daily Review

Write the place value of each number in blue.

1. 894,693

3. 576,399,512

712,689,295

4. 59,902,321,763,832

Learn and Connect The sun is the closest star to Earth. It is a medium-sized yellow star that is 2,713,406 miles around. We can represent this amount in standard form, expanded form and written form. Standard Form: 2,713,406 Written Form: two million, seven hundred thirteen thousand, four hundred six Expanded form: (2 � 1,000,000) + (7 � 100,000) + (1 � 10,000) + (3 � 1,000) + (4 � 100) + (6 � 1)

Apply

Fill in the standard form for each number given. 1. F ifty five thousand, six hundred twenty-three

2. (6 � 100,000) + (5 � 10,000) + (4 � 1,000) + (9 � 10) + (6 � 1)

3. U ranus has a circumference of ninety-nine thousand, seven hundred eighty-six miles. What is the number in standard form?

4. The circumference of the largest planet, Jupiter, is eighty-eight thousand, eight hundred forty-six miles around. What is the number in standard form?

5. T wenty-three million, five hundred three thousand, six hundred ninety-nine

6. The circumference of the smallest planet, Mercury, is 9,525 miles around. What is the number in written form?

Fill in the missing values to write the number in expanded form. 7.

63,904,283

(

� 10,000,000) + (

� 1,000,000) + (

� 100,000) + (

� 1,000) + (

� 100) + (

� 10) + (

� 1)

Vocabulary Expanded Form - a number form that writes each digit multiplied by the place value of that digit Written Form (Word Form) - a number form that writes each number using words 14

Level G

Chapter 1

Lesson 1

Lighthouse Math

Exercise 1-1 Name Write each in standard form. 1. Four hundred sixty-three million, three hundred eighty-two thousand, two hundred twenty-two.

2. 6,000,000,000 + 400,000,000 + 50,000,000 + 2,000,000 +300,000 + 40,000 + 1,000 + 700 + 60 + 5

3. ( 2 � 10,000,000) + (3 � 1,000,000) + (4 x 100,000) + (8 � 10,000) + (9 � 1,000) + (2 � 100) + (3 � 10) + (8 � 1)

4. Eight trillion, nine hundred thirty-two million, four hundred fifty-five thousand, seven hundred twelve.

5. 6 00,000 + 40,000 + 3,000 + 200 + 5

6. (4 � 1,000,000,000) + (7 � 10,000,000) + (2 � 1,000,000) + (8 � 100,000) + (9 � 10,000) + (1 � 1,000) + (5 � 10) + (2 � 1)

Write each number in word form. 7. 3 42,512,643,780

8. 2 ,652, 341,057,382

9. 65,436,317,252,892

Find each missing value to write the number in expanded form. 10.

4,562,789

(4 � 11. (

) + (5 � 100,000) + (

�

) + (2 � 1,000) + (

� 100) + (8 � 10) + (9 � 1)

70,605,562,117 � 10,000,000,000) + (6 � 100,000,000) + (5 �

(2 � 1,000) + (

Lighthouse Math

�

)+(

�

) + (6 � 10,000) +

) + ( 1 � 10) + (7 � 1)

Level G

Chapter 1

Exercise 1

Chapter 1-2 Compare and Order Numbers Write the expanded form of each value.

Daily Review

1. 382,389,293 = 2. 70,293,281 =

Learn and Connect Troy is a realtor. He has four houses listed for sale. He wants to list them in order by price. Help Troy by writing the orders of each house from greatest to least. To solve, stack the numbers on top of each other. Make sure to line up each place value. Then, begin comparing from the largest digit on the left. Price of Red House:

Price of Green House:

Price of Blue House:

Price of Yellow House:

Therefore, the order of the houses from greatest to least is:

Apply Compare the numbers using the symbols: <, >, =. 1.

3,483,271,823

5,382,182

1,283,382

17,283

5,382,182

27,382,123

9,198,289

999,887

82,293,321

3,483,295,3238

17,285

Write the numbers in order. 7. Greatest to least: 8,823,271; 37,281,283; 989,189; 12,390,210

Level G

Chapter 1

8. Least to greatest: 2,289,182; 9,923,100; 10,283,281; 78,892

Lesson 2

Lighthouse Math

Exercise 1-2 Name Compare the numbers using the symbols: <, >, =. 1. 4,324,565,178

56,467,453

432,454,687,345

3. 564,578,432

564,213,454

5,678,432,345

7,458,382,598

78,573,291,673

78,573,292

5. 84,586,675,324,432

84,586,675,324,645

7. 65,489,523

65,489,523,342

9. 114,578,902

114,568,902

10. 418,562,307,002

432,454,875,432

418,562,343,423

Write the numbers in order. 11. Least to greatest: 5,685,483,425; 342,463,412; 5,685,654,589

12. G reatest to least: 78,873,456,231,983; 78,873,456,318,435; 78,873,456,089,574

13. L east to greatest: 54,382,453,131; 783,482,584; 574,390,352,394

14. G reatest to least: 9,845,423,123; 6,432,123; 8,435,457,632,593

Challenge Solve. 15. An accountant was reviewing the expenses for a company. He wanted to put the following expense categories in order from least amount spent to greatest amount: advertising $5,342,143; payroll - $35,432,312,278; office supplies - $74,341; utilities - $500,321,231

Expense Category

Amount

Complete the table to the right by ordering the expenses from least to greatest.

Lighthouse Math

Level G

Chapter 1

Exercise 2

Chapter 1-3 Addition of Large Numbers Daily Review 1.

2,340,382

Compare the numbers using the symbols: <, >, =. 2. 123,289

940,389

123,378

3. 2,729,920

2,619,422

Learn and Connect Mr. Applebaum is buying a new car. The car costs $102,345. To have the car painted red, he will have to pay an additional $12,456. What will be the total amount Mr. Applebaum pays for his car after it is painted red? To solve, we have to add the price of the car and the price to paint the car red. Start by lining up the large numbers by their place value. Then, add. Price of the car Price to paint car

Therefore, Mr. Applebaum will pay $

for his car after it is painted red.

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Add. 1. 6,289,271 + 289,192

2. 289,298,192 + 128,392,190

3. 892,819,290 + 892,291

4. 8,290,201 + 389

28,902 + 18,292

Set up the problem and add. 6. 78,984 + 675 =

7. 8,976,453 + 362 =

+ 9. 895,987 + 89,975 =

10. 378,283 + 1,348 =

Chapter 1

11. 1,283,489 + 124 =

Level G

8. 893,986 + 28,974 =

Lesson 3

Lighthouse Math

Exercise 1-3 Name

14,568 + 5,456

53,467 + 484

84,572 + 6,436

145,623 + 531

673,462 + 611

6. 54,623 + 351

67,463 + 684

543,682 + 5,426

684,592 + 543

10.

984,523 + 54,673

11. 783,421 + 78,423

12.

843,420 + 84,327

13.

236,401 + 84,509

14. 5,456,298 + 671

15. 8,549,321 + 903

16. 4,382,412 + 6,382

17. 5,048,392 + 3,094

18. 7,354,233 + 32,584

19. 87,594,582 + 584,523

20. 4,570,342 + 542,341

21. 12,436,543 + 351

22. 6,498,012 + 51,643

23. 54,623 + 23,548

24.

25. 5,483,432 + 6,089,435

26.

27. 45,612,809 + 37,421

28. 30,452,582 + 25,483,402

29. 530,425,648 + 561

8,452,321 + 3,421,258

843,531 + 405,862

30. 7,547,234,138 + 543,256

Challenge Solve each problem. 31. The population of Denver, Colorado is 2,932,415 and the population of Kansas City, Missouri is 2,170,823. What is the total population of these two cities?

Lighthouse Math

32. A real estate investor bought a commercial office building for $865,342. The title company charged him $6,782 in fees to handle the transaction. What was the total amount the investor paid for the property?

Level G

Chapter 1

Exercise 3

Add.

Chapter 1-4 Subtraction of Large Numbers Daily Review

Set up and add.

1. 786,278 + 521 =

2. 178,378 + 1,278 =

3. 892,128,213 + 28,289 =

Learn and Connect Edward is visiting a local zoo. He saw an Asian elephant that weighed 2,438 pounds. Then, he walked over to the African elephant. What is the difference between the weight of the Asian elephant and the African elephant? To solve, we have to subtract the weight of Asian elephant from the weight of the African elephant. Start by lining up the large numbers by their place value. Then, subtract. Weight of the African elephant: Weight of the Asian elephant:

–

Therefore, the difference in weight between the

African and Asian elephant is

pounds.

Apply Subtract. 1. 2,283,271 – 123,289

182,372,882 – 123,289,923

3. 289,382,372 – 372,382

4. 3,281,234 – 721,271

5. 281,289 – 208,280

Set up the problem and subtract. 6. 23,489 – 293 =

7. 12,780,952 – 362 =

–

Level G

Chapter 1

8. 324,786 – 23,876 =

–

Lesson 4

Lighthouse Math

Exercise 1-4 Name

1. 34,268 – 4,416

52,467 – 514

44,532 – 5,431

381,623 – 815

462,673 – 423

6. 32,873 – 351

17,963 – 684

545,612 – 542

284,602 – 543

10.

572,433 – 34,273

11. 832,421 – 38,413

12.

624,420 – 92,325

13.

471,671 – 74,039

14. 3,529,298 – 391

15. 6,372,321 – 483

16. 2,439,312 – 2,352

17. 5,108,372 – 3,390

18. 4,328,233 – 32,482

19. 43,204,582 – 724,503

20. 6,400,342 – 732,321

21. 43,127,543 – 4,251

22. 8,052,012 – 34,513

23. 72,633 – 33,508

24. 593,531 – 475,802

25. 8,342,435 – 3,740,432

26.

27. 43,981,609 – 37,421

28. 30,412,162 – 25,424,731

29. 634,478,388 – 561

30. 2,527,634,118 – 783,214

6,593,321 – 3,442,358

Challenge Solve each problem. 31. The population of Boston is 684,379 while the population of the greater Boston metro area is 4,628,910. What is the difference in population between the metro area and the city of Boston?

Lighthouse Math

Level G

32. A couple purchased a house in 1990 for $145,692. They sold the house recently for $1,232,600. How much more did the house sell for than what they paid?

Chapter 1

Exercise 4

Subtract.

Chapter 1-5 Addition and Subtraction Word Problems Daily Review

Rewrite and subtract.

1. 345,214 – 452 =

2. 137,382 – 4,378 =

3. 1,238,489 – 28,092 =

Learn and Connect Mannie and his family are going to an arcade. His whole family was able to play 122 different games while they were there. How many games did they not get to try? To solve, we need to subtract the number of games played by the family from the number of games in the arcade. Number of games in the arcade: – Number of games played: Therefore, Mannie and his family did not get to try

games.

Apply Read each word problem and solve. 1. A company donated 12,347 backpacks to a local school district. One school asked for 678 of the backpacks. How many backpacks does the school district still have to give out? 2. T he population of Bennington in 2019 was 1,456,321 people. In 2020, 345,214 people moved out of the town. What was the population after the people left? 3. T he first week a hotel opened, it sold out all of their rooms for the week and made $12,348. The next week, they weren’t able to fill all of their rooms and only made $10,328. How much money did they make during their first two weeks?

Level G

Chapter 1

Lesson 5

Lighthouse Math

Exercise 1-5 Name Solve. Show your work. The hardware store was making an order for new tools. Use the list of prices below to solve the following problems: Type

Cost

Hand tools

$26,435

Power saws

$35,742

Table saws

$23,421

Air compressors

$18,352

Cordless drills

$21,280

1. How much more do the power saws cost than the table saws? 2. What is the combined cost of the hand tools and the cordless drills? 3. How much more did the hardware store spend on hand tools than air compressors? Solve. Show your work. A popular theme park made $7,377,967,100 in 2020. In 2021, they grossed $8,837,713,363.

4. How much more did they make in 2021 than in 2020? 5. What was the combined earnings for the two years? 6. It cost $115,000,000 to take care of the park in 2020. What was the net earnings of the first year after the cost of maintaining the park? 7. It cost $113,000,000 to take care of the park in 2021. What was the net earnings of the second year after the cost of maintaining the park? 8. Using your answer to questions 6 and 7, determine the combined net earnings of the park for the past two years.

Lighthouse Math

Level G

Chapter 1

Exercise 5

Chapter 1-6 Expressions with Missing Addends Daily Review

Set up and solve.

1. 382,182 + 123 =

2. 823,489 – 2,348 =

3. 183,421 + 12,345 =

Learn and Connect Raymond and his mother and father went strawberry picking. Raymond picked 18 strawberries and placed them in a basket. His mother added 23 strawberries to the basket as well. Later, Raymond’s father added some strawberries. Raymond didn’t see how many his father added, but he counted how many strawberries were left in the basket. How many strawberries did his father add? The expression below can be used to explain how many strawberries Raymond has. 18 + 23 +

= 45

To solve, find the total of strawberries Raymond already knows about. Then, subtract the amount from the total strawberries in the basket. 18 + 23 =

; 45 –

Therefore, Raymond’s dad added

strawberries.

Apply Find the missing addend. 2.

85 = 38 +

345 = 123 + 40 +

1,234 = 456 + 325 +

= 1,036

– 2,538 = 620

+ 5,271 = 10,404

10.

+ 198 = 398

11.

- 9,892 = 286

12.

57 = 29 +

123 = 50 + 3 +

+ 21 + 53 = 138

+ 24

Find the missing number. 7.

1,289 –

Level G

Chapter 1

Lesson 6

5,271 +

= 7,624

Lighthouse Math

Exercise 1-6 Name Find the missing addend. 1.

= 56, 341

14, 562 +

= 35,690

+ 34,356 = 43,685

67,508 +

= 114,452

+ 4,521

34,520 = 18,795 +

45,321 +

3. 5.

9,575 =

11,254 +

= 45,378

78,490 +

= 234,671

10.

145,382 +

= 342,358

11.

542,306 =

+ 23,431

12.

365,782 +

= 783,291

13.

28,453 = 16,432 +

14.

15.

420,582 = 341,608 +

16.

+ 31,497 = 67,083

+ 67,342 = 238,560 515,887 +

= 730,900

17.

2,562 –

= 1,085

18.

– 3,421 = 3,107

19.

14,580 –

= 12,423

20.

– 43,256 = 12,456

21.

76,435 –

= 34,221

22.

– 143,321 = 98,450

23.

187,345 –

= 157,342

24.

457,325 –

– 789,321 = 154,289

26.

3,295,463 –

25.

= 251,089 = 1,568,304

27.

4,560,023 –

= 78,412

28.

– 6,342,390 = 2,791,423

29.

567,342 –

= 512,598

30.

– 34,781 = 4,352,800

31.

435,689 –

= 321,321

32.

756,888 –

Find the missing number.

= 145,511

Challenge Solve. 33. T he combined weight of two truckloads of gravel was 79,223 lbs. The first truckload weighed 36,475 lbs. How much did the second truckload weigh?

Lighthouse Math

Level G

Chapter 1

Exercise 6

Chapter 1-7 Order of Operations Daily Review 1.

Find the missing addend. 2. 150 + 200 +

+ 38 + 13 = 87

3. 15 + 22+

=382

= 61

Learn and Connect The order of operations is a rule in math that tells us how and in what order to work out an expression. Read the story below and think of an expression that can explain how to find the amount of money Kenneth has left. On Kenneth’s birthday, he received $105 at his birthday party. His grandparents sent him an additional $56 and a birthday card. Kenneth decided to buy a new backpack with his money. The backpack cost $32. On his way home, he found $5 on the ground. How much money does Kenneth have now? To solve, we need to consider the order of operations. We use parentheses to tell us what to do first. It doesn’t matter if the parentheses come at the beginning, middle or end in the expression. They are always done first. Then, we follow the operations from left to right.

Fill in the information from the story and then solve. (

)–

Therefore, Kenneth has

+ left.

Apply Solve using the order of operations. 1.

(15 + 22) – 25 =

(372 + 85) – 12 =

572 + (258 – 172) =

(32 + 84) – (21 + 45) =

780 – (234 + 6) =

92 – 15 + (6 – 3) =

3 + 9 + (10 – 5) =

(270 – 4) + 5 =

(5 + 20 + 19) – 21 =

Level G

Chapter 1

Lesson 7

Lighthouse Math

Exercise 1-7 Name

(4 + 5 ) – (9 – 3) =

16 – (8 + 2) =

(24 + 55) – 32 =

189 – (34 + 62) =

342 + (876 – 432) =

(92 – 63) + 12 =

6,243 + (1,989 – 300) =

(8,741 – 8,042) + 3,459 =

(15,542 – 87) + 43,426 =

10. 56,781 – (86,534 – 42,314) =

11. 13,425 + (8,245 – 3,325) =

12. (76,231 – 34,257) + 45,682 =

13. (23,418 + 80,346) – 65,326 =

14. 12,361 + (74,520 – 45,023) =

15. (8,235 – 3,241) + 15,687 =

16. 341,237 – (24,538 + 43,265) =

17. (756,430 – 542,381) + 42,314 =

18. 7,342 + (2,341 – 1,253) =

19. (342,582 + 452,679) – 653,215 =

20. 1,542,387 – (34,251 + 32,000) =

Solve using the order of operations. Show your work.

21. 5,325,086 + (4,325,618 – 1,324,859) = 22. (53,425,436 – 2,342,563) + 51,264 = 23. 14,508,690 – (53,425 + 43,256) =

24. (83,412 + 34,265) – 26,534 =

Write an equation and solve. 25. O n Monday, a worker earned $255 for 8 hours of labor. The same worker spent $15 for gas and $12 for lunch. How much money did the worker have left at the end of the day?

Lighthouse Math

Level G

Chapter 1

Exercise 7

Chapter 1-8 Review Daily Review Use the order of operations to solve. Show your work. 1. (6 - 3) + (10 – 5) =

2. 5 + (30 – 29) + 4 =

3. 22 + (32 – 15) – 4 =

Learn and Connect Complete the chart by filling in the place value names.

thousands

ten thousands

hundred thousands

THOUSANDS

bilions

ten billions

hundred billions

BILLIONS

Use the place value chart to answer the question below.

Theo read the number 4,566,778,287,000 as “four trillion, five hundred sixty-six billion, seven hundred seventy-eight million, two hundred eighty-seven thousand.” Write the number in word form correctly below. Then, write the expanded form of the number.

Apply Compare the numbers using the symbols: <, >, =. 1.

82,378,182

3,279,298,234

278,289

3,279,998,241

24,839,298

7. 137,289 – 984

109,238,271

278,289 18,389,398

Solve. 5. 782,134 + 18,278

26,389 – 14,289

Level G

Chapter 1

Lesson 8

432, 278 + 782

Lighthouse Math

Exercise 1-8 Name Complete the table. Word Form: Two hundred eighty-seven million, three hundred forty-six thousand, five hundred twenty-one

Standard Form:

Expanded Form:

Compare the numbers using the symbols: <, >, =. 1.

85,235,671

67,856,435

234,534,673,864

574,783,245

574,783,205

7,678,432,564

234,534,749,536 7,678,432,564

Order the numbers. 5.

Least to greatest: 7,342,543,654; 743,453,456; 6,765,482,353

Greatest to least: 34,564,543,436; 34,564,543,134; 34,564,543,782

7. 23,453 + 6,578

–

54,325 567

146,735 + 65,467

10.

–

556,412 5,426

11. 547,482 + 645,327

Solve using the order of operations. 12. (674 – 243) + 892 =

13. 7,892 + (5,678 - 2,341) =

14. (5,436 + 14,356) – (2,342 – 1,231) =

Challenge Solve. 15. D A school district had 82,341 enrolled students. Last year, the district had 78,349 enrolled students. How many more students were enrolled this year than last year?

Lighthouse Math

Level G

Chapter 1

Exercise 8

Add or subtract.

Chapter 2 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.7

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

In Chapter 2 we will review previous learning of

Multiplication and Expand on that Learning We will practice finding missing factors, evaluating expressions and applying the order of operations to problems that include multiplication. • Review: Whole numbers • Basic fact practice • Multiply multi-digit numbers • Multiply large numbers • Multiplication word problems • Exponents © Lighthouse Curriculum. Copying strictly prohibited.

• Missing factors and evaluating expressions • Order of operations • Review Students will gain real world understanding through word problems and evaluating expressions. Students will continue to expand their understanding of the order of operations as they apply to more complex mathematical processes including exponents.

Chapter 2-1 Basic Fact Practice Solve.

Daily Review

1. 5 + 5 + 5 + 5 =

2. 12 + 12 + 12 + 12 + 12 =

3. 11 + 11 + 11 =

Learn and Connect Rick and Bob each have the same number of stickers. Rick puts all of his stickers in equal rows of 6 across his notebook and Bob puts all his stickers in equal rows of 8 across his notebook. What is the least number of stickers that Rick and Bob can have? To solve, we have to find the multiples of both 6 and 8. The multiples of a number are a set of numbers made by combining the number repeatedly. When you divide a multiple by its factor, it will divide evenly with no remainder. Write the multiples of 6 and 8. Then, find the first multiple they have in common. 6:

Therefore, Rick and Bob have

stickers.

Apply Write the first six multiples of each factor. 1.

11:

10:

12:

Multiply. 7.

3 � 4

5 � 3

12 � 4

10.

8 � 6

11.

9 � 2

12.

11 � 7

13.

8 � 2

14.

12 � 9

15.

9 � 3

16.

5 � 7

17.

6 � 2

18.

4 � 4

19.

3 � 0

20.

1 � 9

Level G

Chapter 2

Lesson 1

Lighthouse Math

Exercise 2-1 Name Write the first six multiples of each factor. 1.

3 � 4

8 � 5

12 � 3

6 � 6

8 � 2

10.

7 � 9

11.

5 � 4

12.

3 � 2

13.

6 � 8

14.

6 � 9

15.

5 � 9

16.

8 � 2

17.

10 � 6

18.

4 � 7

19.

8 � 3

20.

7 � 6

21.

4 � 4

22.

9 � 4

23.

6 � 4

24.

3 � 5

25.

2 � 9

26.

11 � 6

27.

5 � 6

28.

8 � 7

29.

12 � 7

30.

9 � 9

31.

3 � 7

32.

8 � 8

33.

4 � 8

34.

7 � 4

Challenge 35. A box of cookies contained 3 rows of 12 cookies. How many cookies were in the box?

Lighthouse Math

Level G

36. There are 8 pillows on each sofa in the furniture store. If they have a total of 12 sofas on display, how many pillows are there in total?

Chapter 2

Exercise 1

Multiply.

Chapter 2-2 Multi-Digit Multiplication Write the first six multiples of the factors.

Daily Review 1.

Learn and Connect Henry is a subway train operator. By the end of the day, he picked up and dropped off 12 full trains of people at the next station. How many total people did Henry pick up and drop off? To solve, we have to multiply the number of people on the full train by the number of times Henry dropped off all of the people. Number of people on a full train: Times he dropped off people: � = Total amount of people dropped off Therefore, Henry picked up and dropped off

people that day.

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Solve. 1.

782 � 2

704 � 4

7,279 � 8

3,782 � 5

72 � 35

58 � 26

199 � 2

283 � 45

387 � 212

10.

673 � 352

11.

4,987 � 267

12.

1,902 � 8

Level G

Chapter 2

Lesson 2

Lighthouse Math

Exercise 2-2 Name

472 � 3

836 � 6

410 � 5

362 � 8

2,893 � 2

437 � 32

835 � 58

197 � 60

218 � 73

10.

632 � 45

11.

1,253 � 14

12.

3,572 � 38

13.

2,352 � 35

14.

8,304 � 12

15.

7,314 � 58

16.

4,320 � 342

17.

6,480 � 375

18.

4,526 � 302

19.

8,435 � 523

20.

6,432 � 421

Challenge Solve. 21. The county fair draws a crowd of 2,580 people each day. How many people attend the fair over 14 days?

Lighthouse Math

Level G

22. A tour bus can hold 65 passengers. The bus does two tours per day. How many passengers would ride the bus after 21 days?

Chapter 2

Exercise 2

Solve.

Chapter 2-3 Multiplying Large Numbers Daily Review

Solve.

1. 452 � 34 =

2. 456 � 224 =

3. 2,134 � 321 =

Learn and Connect Nathan bought a new car last year. At the end of the year, the car indicated how many miles he drove the entire year. If Nathan drove the same amount of miles each year for 12 years, how many total miles will he have driven since buying the car? To solve, we have to multiply the number of miles traveled in one year by 12 years. Number of miles traveled in one year: Number of years: � = Total of miles on the car after 12 years Therefore, Nathan will have traveled

miles in his car after 12 years.

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Solve. 1.

83,231 � 2

73,281 � 5

718,128 � 7

123,289 � 4

12,126 � 35

23,478 � 12

234,558 � 11

172,283 � 32

37,128 � 248

10.

237,289 � 178

11.

126,389 � 234

12.

212,389 � 8

Level G

Chapter 2

Lesson 3

Lighthouse Math

Exercise 2-3 Name

12,742 � 53

53,782 � 47

23,613 � 62

30,482 � 41

87,320 � 34

38,489 � 315

83,415 � 837

14,273 � 503

41,325 � 232

10.

34,552 � 572

11.

432,381 � 4

12.

212,415 � 6

13.

432,571 � 3

14.

37,420 � 7

15.

356,023 � 8

16.

401,506 � 12

17.

382,378 � 11

18.

443,521 � 76

19.

397,241 � 48

20.

340,299 � 23

Challenge Solve. 21. A school district provides pencils for their entire student population. If they have 36,413 students in the district and they provide each student with 24 pencils per year, how many pencils will they need to buy?

Lighthouse Math

Level G

22. The city allocates 2,325 gallons of water per customer in their monthly billing amount. If there are 7,326 customers, how many gallons of water are allocated per month?

Chapter 2

Exercise 3

Solve.

Chapter 2-4 Multiplication Word Problems Daily Review

Solve.

1. 43,456 � 24 =

2. 133,456 � 4 =

3. 23,123 � 342 =

Learn and Connect Steven is building some bookshelves for his brother. He needs 8 boxes of long nails that have 115 nails in each box and 7 boxes of short nails that have 207 nails in each box. How many total nails will he have if he buys everything he needs from the store? To solve word problems, you should use the following strategy: » Read and Understand Read the problem and consider what is being asked. In this problem, we need to find how many total nails are in all of the boxes Steven bought. »» Plan Make a plan to solve the problem.

We know that we need to multiply the number of boxes by the number of nails inside the boxes. Then, to find the total, we need to add the nails in each set of boxes. Number of long nails in 1 box × Number of boxes = total number of long nails + Number of short nails in 1 box × Number of boxes = total number of short nails = Total amount of nails »»» Solve Work out the problem. Number of long nails in 1 box: Number of boxes:

Number of short nails in 1 box: Number of boxes:

�

Total number of short nails: Total number of long nails:

Therefore, Steven will have a total of

Level G

Chapter 2

nails.

Lesson 4

Lighthouse Math

Exercise 2-4 Name Solve using the problem solving strategy. 1.

» Read and Understand Read the problem and consider what is being asked. »» Plan Make a plan to solve the problem. »» Solve Work out the problem and check that your answer is reasonable by estimating the answer.

An appraiser is a person who determines the market value of a house. For every property appraised, the appraiser charges a fee of $1,650. If the appraiser conducts 275 appraisals per year, what is the total amount of fees charged?

A loan payment on a new house is $2,768 per month. If the loan is for 30 years, how much will be paid over the life of the loan?

A loan payment on a new house is $3,486 per month. If the loan is for 15 years, how much will be paid over the life of the loan?

4. The city plans to spend $578,000 per year over the next 6 years to improve the local streets. How much will they spend on street improvements?

The average price for four new car tires is $459. If 12,345 people buy 4 new car tires in a year, how much would the car dealership make?

There are 7,342 residences in a city. If the average home has 5 people living there, what is the general population of the city?

A restaurant sells 125 pies per day. How many pies would they sell over 30 days?

The library checks out 323 books per day. If they are open 312 days per year, how many books does the library check out per year?

Lighthouse Math

Level G

Chapter 2

Exercise 4

A couple is planning to purchase a home. They are trying to decide which loan to take. Use this information to answer problems 2 and 3 below:

Chapter 2-5 Exponents Solve.

Daily Review 1. 5 � 5 =

2. 8 × 8 =

3. 9 × 9 =

4. 6 × 6 =

Learn and Connect Robert has a bubble machine that produces twice as many bubbles every minute. If the machine starts with 2 bubbles in the first minute, how many bubbles will be coming out of the machine after 6 minutes? To solve, we can use exponents. An exponent tells us how many times to multiply the same number by itself. Base

Exponent

The exponent 6 means we are multiplying the number 2 by itself 6 times. 2×2×2×2×2×2 = Therefore, in 6 minutes the bubble machine will produce

bubbles.

Apply Solve. 2.

4×4×4×4=

4. 6 × 6 =

7×7×7×7=

6. 25 × 25 × 25 =

8. 13 × 13 × 13 × 13 × 13 × 13 =

3×3×3×3=

11 × 11 × 11 =

5×5×5×5×5=

Determine the solution to the exponent. 9.

10. 52 =

24 =

11. 33 =

12. 035 =

13. 123 =

Solve. 14. 53 + 23 =

15. 42 � 22 =

�

16. 63 + 54 =

17. 73 � 43 =

�

18. 82 � 62 =

�

19. 122 + 04 =

Level G

Chapter 2

Lesson 5

Lighthouse Math

Exercise 2-5 Name Write in exponent form. 1. 5 × 5 × 5 =

2. 4 × 4 =

3. 10 × 10 × 10 × 10 × 10 =

4. 7 × 7 × 7 × 7 =

5. 8 × 8 =

6. 3 × 3 × 3 × 3 × 3 =

8. (5 × 5) × (4 × 4) =

9. (3 × 3 × 3) × (2 × 2) =

11. 10 × (4 × 4 × 4) =

12. 10 × (3 × 3) =

13. 32 =

14. 73 =

15. 55 =

16. 84 =

17. 26 =

18. 92 =

19. 123 =

20. 154 =

21. 23 × 32 =

22. 44 × 53 =

23. 10 × 72 =

24. 10 × 63 =

9×9×9=

10. (5 × 5) × (10 × 10) =

Write in factor form.

Find the value. 25. 43 =

26. 25 =

27. 82 =

28. 124 =

29. 73 × 22 =

30. 32 × 62 =

31. 10 × 43 =

32. 10 × 52 =

33. 33 + 72 =

34. 82 � 62 =

35. 93 + 24 =

36. 44 � 25 =

Lighthouse Math

Level G

Chapter 2

Exercise 5

Chapter 2-6 Missing Factors Compare the exponents using the symbols: >, <, =.

Daily Review 1. 32

2. 23

3. 53

4. 63

Learn and Connect Josiah has some boxes of cupcakes. He bought 8 of the exact same boxes with the same amount of cupcakes in each. He now has a total of 56 cupcakes. Which expression can be used to explain C, the number of cupcakes in each box? A. 56 × 8 = C B. 56 × 7 = C

C. 8 + 56 = C D. 8 × C = 56

To solve, consider the missing information from the word problem. We know the total cupcakes and the amount of boxes, however we are missing the number of cupcakes in each box. the amount of cupcakes in each box × the number of boxes = the total amount of cupcakes Which equation matches this information?

Apply

Fill in the missing factor. 1.

5�

= 15

9�

= 54

� 9 = 81

3�

� 4 = 12

2�

= 18

= 15

5�

= 35

� 12 = 48

� 3 = 24

10. 10 �

= 50

11. 11 �

= 77

12. 4 �

= 40

13. 8 �

= 16

14. 9 �

= 99

15. 11 �

= 77

16. 2 �

= 20

17.

� 10 = 30

18. 10 �

= 90

� 12 = 36

20. 5 �

= 60

21. 12 �

= 12

22. 11 �

= 44

23. 8 �

= 56

24. 12 �

= 144

25. 3 �

26. 11 �

= 88

27. 1 �

= 19

28. 24 �

= 24

29. 2 �

30. 5 �

= 25

19.

Level G

Chapter 2

Lesson 6

Lighthouse Math

Exercise 2-6 Name Fill in the missing factor.

4. 7.

= 12

� 5 = 40

= 60

� 10 = 100

11.

2�

12 �

10. 13. 6 � 16.

= 36 � 5 = 15

= 21

� 6 = 18

= 22

� 5 = 45

12.

7�

2�

14. 4 �

= 36 � 8 = 72

14 �

= 28 � 7 = 35

15. 12 �

= 32

17.

4�

18.

� 24 = 48

= 144 � 7 = 84

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

Solve for the variable. 19. 5 ∙ x = 35

20. 3 ∙ a = 24

21. 9 ∙ b = 63

22. a ∙ 8 = 64

23. b ∙ 6 = 48

24. c ∙ 12 = 48

25. 7 ∙ x = 28

26. 8 ∙ v = 32

27. b ∙ 9 = 27

28. a ∙ 6 = 18

29. d ∙ 3 = 36

30. x ∙ 7 = 49

Challenge Write an expression and solve. 31.

Each morning the donut shop prepares boxes with 6 donuts in each box. This morning there were 72 donuts. How many boxes were there?

Lighthouse Math

Level G

32.

Each morning the donut shop also prepares bags with 13 donut holes (a baker’s dozen) in each bag. This morning there were 117 donut holes. How many bags of donut holes were there?

Chapter 2

Exercise 6

Chapter 2-7 Order of Operations Find the missing factor.

Daily Review 1. 8 �

2. 9 �

= 64

3. 3 �

= 108

= 33

4. 12 �

= 24

Learn and Connect When working with the order of operations, parentheses come first followed by exponents. Then, it is multiplication followed by addition and subtraction. Consider the following equation: First, work out the exponents: Next, complete the other operations in the parentheses:

(53 + 2) � 6 · 5 (

+ 2) � 6 ∙ 5 �6∙5

Then, solve any multiplication:

�

Last, solve all addition and subtraction from left to right:

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

Therefore, (53 + 2) � 6 � 5 =

Apply Use the order of operations to solve. Show your work. 1.

(5 ∙ 3) + 7 � 8 =

(6 + 7) ∙ 4 � 3 =

(3 ∙ 4) + (8 ∙ 9) =

42 + 3 ∙ 2 =

73 ∙ 5 + 6 =

(32 ∙ 2 + 5) � 17 =

(4 + 8 ∙ 4) � (2 ∙ 3) =

80 + (23 ∙ 9) =

52 + 22 - 12 =

10. 6 ∙ 5 + 7 · 2 =

Level G

Chapter 2

Lesson 7

Lighthouse Math

Exercise 2-7 Name Put parentheses around the numbers and operations you should use first. Solve. 1.

6+7∙5=

4. 8 � 6 + 33 =

2. 8 ∙ 4 � 12 =

3. 6 + 62 ∙ 3 =

6. 29 � 6 + 4 ∙ 9 =

8 ∙ 6 ∙ 2 � 26 =

(9 + 7) � (8 ∙ 2) =

8. 23 + 54 � 9 ∙ 5 =

9. 8 ∙ 7 � 15 =

10. (6 ∙ 7) + (5 � 2) =

11. 56 � 4 ∙ (8 + 3) =

12. (34 + 6) � 12 ∙ 3 =

13. 178 - 9 ∙ 42 =

14. (5 ∙ 6) + 82 � (3 ∙ 4) =

15. 82 + 4 ∙ (12 ∙ 4) =

16. (15 + 25) ∙ (8 ∙ 7) � 3 =

17. (15 ∙ 2) � (6 ∙ 5 ) + 36 =

18. 288 � 122 ∙ 2 =

19. 63 ∙ (4 + 48) =

20. 8 ∙ 7 + 23 � 32 =

21. (42 ∙ 23) + (52 � 15) =

Lighthouse Math

Level G

Chapter 2

Exercise 7

Use the order of operations to solve. Show your work.

Chapter 2-8 Review Daily Review

Solve using the order of operations.

1. 32 ∙ 5 + 6 =

2. ( 3 + 4) ∙ 12 + 7 =

3. (12 ∙5 + 20) � (20 + 2) =

Learn and Connect Fred is making a recipe for cookies. He wants to make 13 batches of the recipe. Fill in the chart to help Fred determine how many grams of each item he will use for 13 batches. Item

Grams per batch

Butter

55 g

Sugar

110 g

Flour

143 g

Chocolate chips

75 g

Grams for 13 batches

Apply

Solve. 1.

282 � 2

28,172 � 5

3,278 � 9

3,190 � 24

226 � 35

2,168 � 26

12,078 � 12

827 � 278

Find the missing factor. 9. 13. 9 �

� 5 = 20 = 27

10.

� 7 = 14

14. 12 �

= 72

Level G

Chapter 2

11. 4 � 15. 144 �

Lesson 8

= 40 = 144

12. 6 �

= 36

16. 9 �

= 54

Lighthouse Math

Exercise 2-8 Name Write the first six multiples of each factor. 1.

12:

, ,

Multiply. 5.

8 � 6

6 � 7

15 � 39

710 � 50

9 � 3

10.

480 � 4

11.

2,178 � 16

12.

362 � 35

13.

4,672 � 3

14.

23,476 � 6

15.

16,427 � 83

16.

675,420 � 2

17.

536 � 312

18.

4,527 � 608

19.

38,426 � 231

20. If 35,698 people attended the circus and the tickets cost $85 each, how much were the total ticket sales for the circus? Write in exponent form. 21. 6 × 6 × 6 =

22. 10 × (4 × 4) =

23. (7 × 7) × (3 × 3 × 3) =

Write in factor form and then find the value. 24. 23 =

25. 82 =

26. 134 =

Solve for the variable. 27. a ∙ 7 = 63

28. b ∙ 3 = 36

29. 8 ∙ c = 48

30. 4 ∙ x = 28

Solve using the order of operations. Show your work. 31. 152 � 7 ∙ 32 =

Lighthouse Math

32. (7 ∙ 86) + 52 � (5 ∙ 4) =

Level G

Chapter 2

Exercise 8

Solve.

Chapter 3 NYS NG Standards NY-3.OA.4 NY-3.OA.5 NY-3.OA.6 NY-3.OA.7 NY-3.OA.8

NY-4.NBT.6 NY-5.OA.1 NY-5.NBT.6 NY-6.NS.2

CC Standards 3.OA.A.4 3.OA.B.5 3.OA.B.6 3.OA.C.7 3.OA.D.8

4.NBT.B.6 5.OA.A.1 5.NBT.B.6 6.NS.B.2

In Chapter 3 we will review

Division Operations of All Whole Numbers We will practice our facts and use long division to divide by 2 and 3-digit divisors. We will also explore division's role in the order of operations. • Basic fact practice • We will use our multiplication facts to do simple division. • Divide by 2 and 3 digit divisors • We will divide large numbers up to 5 digits by divisors with 2 and 3 digits.

• Explore division word problems • We will determine if a word problem includes the remainder or just the quotient. • Divide by powers of 10 • We will find the pattern used to quickly divide numbers by multiples of ten. • Find missing divisors and evaluate expressions • We will use our understanding of fact families to find missing pieces of equations. • Review division in the order of operations • We will recognize that multiplication and division are on the same level in the order of operations and come before addition and subtraction.

Chapter 3-1 Basic Fact Practice Daily Review 1. 5 ×

Find the missing factor. 2. 8 ×

= 20

= 64

× 12 = 48

× 3 = 15

Learn and Connect A store clerk is putting potatoes into bags of 12. He has a total of 132 potatoes. How many bags of potatoes can he make? To solve, we can use the following equation: 132 ÷ 12 = Multiplication is the inverse, or the opposite of division, so we can also use this equation to solve: 12 ×

= 132

We know that 12 × 11 = 132, therefore 132 ÷ 12 = 11. This means that the store clerk can make 11 bags.

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Write the inverse operation to solve for the missing answer. Example: 44 ÷ 11 = 4 ; 4 × 11 = 44 1.

90 ÷ 10 =

;

2. 42 ÷ 7 =

;

3. 144 ÷ 12 =

;

4. 81 ÷ 9 =

;

6. 27 ÷ 3 =

;

9)36

99 ÷ 11 =

Solve. 7.

5)55

12.

2)10

13. 8)48

Level G

6)36

14. 7)56

Chapter 3

Lesson 1

10. 1)2

11. 7)21

15. 12)48

16. 5)30

Lighthouse Math

Exercise 3-1 Name Solve. 1)2

1)7

6)36

4)12

8)32

5)40

8)64

9)18

7)63

10. 9)45

11. 8)72

12. 3)27

13. 5)30

14. 9)9

15. 8)16

16. 9)63

17. 2)4

18. 4)28

19. 7)14

20. 3)27

21. 5)55

22. 9)36

23. 6)30

24. 1)5

25. 3)27

26. 2)10

27. 8)48

28. 7)56

29. 12)48

30. 5)35

31. 12)24

32. 8)16

33. 7)49

34. 3)36

35. 5)25

36. 6)60

37. 8)88

38. 7)14

39. 12)48

40. 5)45

41. 5)15

42. 8)24

43. 11)77

44. 10)60

45. 8)96

Lighthouse Math

Level G

Chapter 3

Exercise 1

Chapter 3-2 2-Digit Divisors Daily Review

Solve.

1. 25 � 5 =

2. 66 � 11 =

3. 36 � 12 =

4. 18 � 3 =

Learn and Connect Jeff works at a fabric store. He has a large roll of flower printed fabric. A customer wants the entire roll split into bundles of 13 yards each. How many bundles will Jeff make with all of the fabric? To solve, we have to divide the total amount of fabric by 13 yards. = Total number of bundles Yards for one bundle

Total amount of fabric

Therefore, Jeff can make

bundles.

Apply Solve.

21)234

15)278

18)288

12)468

20)2,320

24)1,824

32)8,064

21)9,387

10. 16)3,280

Level G

Chapter 3

Lesson 2

22)264

Lighthouse Math

Exercise 3-2 Name Solve.

2. 22)792

3. 18)300

4. 13)170

6. 12)2,808

32)4,896

8. 33)4,080

40)6,579

10. 25)3,280

11. 16)2,515

12. 13)1,602

13. 11)7,159

14. 12)2,556

15. 15)3,510

16. 50)4,280

17. 91)9,282

18. 18)5,672

19. 85)7,575

20. 24)2,407

21. 45)3,568

22. 71)7,313

23. 31)1,937

24. 62)8,924

25. 73)6,781

23)428

Challenge 26. There are 2,460 buses in the bus station terminal. If 15 buses leave per hour, how many hours will it take for all the buses to be out of the terminal?

Lighthouse Math

Level G

27. Over a month, Mike collected 325 shells. He wants to create decorative vases with the shells. If he uses 25 shells for each vase, how many vases can he make?

Chapter 3

Exercise 2

1. 15)315

Chapter 3-3 3-Digit Divisors Daily Review

Solve.

1. 242 � 15 =

2. 248 � 21 =

3. 1,224 � 12 =

Learn and Connect There are 2,356 fish in the aquarium. Each exhibit has the same amount of fish. How many total fish exhibits are in the aquarium? To solve, we have to divide the total number of fish by the amount of fish in each exhibit. First, when dividing by three digit numbers, we start at the third digit from the left. This is because a three digit number will be too large to divide into a two digit number. Now, let's look to our long division example to the right. Consider how many groups of 124 you can make with 235. 124 × 1 = 124

Next, subtract and bring down the next digit. Then, decide how many groups of 124 you can make with 1,116. 124 × 9 = 1,116

001

0019

124)2,356 124 111

124)2,356 124 1116 � 1116 0

Therefore, there are 19 fish exhibits.

Apply Solve. 1.

234)1,284

374)3,928

236)7,208

234)4,479

253)23,479

374)23,849

236)72,389

512)38,382

Level G

Chapter 3

Lesson 3

Lighthouse Math

Exercise 3-3 Name

1. 234)712

134)805

3. 206)824

5. 561)6,662

6. 234)6,436

9. 715)8,014

10. 512)8,263

11. 574)4,305

12. 276)4,832

13. 274)34,204

14. 148)61,304

15. 144)26,846

16. 851)63,885

17. 351)57,062

18. 567)77,127

19. 646)81,126

20. 635)83,762

366)7,835

152)912

512)2,484

Solve.

Challenge 21. A grocery store is packing potatoes into packages. Each package holds 125 ounces of potatoes. If they have 23,384 ounces of potatoes, how many full packages can they make?

Lighthouse Math

Level G

22. A factory produces 325 paper towel roll packs an hour. How many hours will it take them to produce 5,200 packs of paper towel rolls?

Chapter 3

Exercise 3

Chapter 3-4 Division Word Problems Daily Review

Solve.

1. 2,379 � 108 =

2. 2,389 � 214 =

3. 32,308 � 305 =

Learn and Connect A delivery truck is loaded with 135 refrigerators. The refrigerators weighed 34,425 pounds in total. If each refrigerator weighed the same amount, how much do five refrigerators weigh? To solve word problems, you should use the following strategy: » Read and Understand Read the problem and consider what is being asked. In this problem, we already know the total weight of the refrigerators, but we need to find the weight of a single refrigerator. Then, we need to find the total of five refrigerators. »» Plan Make a plan to solve the problem. We know that we need to divide the total weight of the refrigerators by the number of refrigerators. Then, we need to multiply the weight of a single refrigerator by five.

total weight of the refrigerators ÷ number of refrigerators = weight of one refrigerator weight of one refrigerator × five refrigerators = weight of five refrigerators »»» Solve Work out the problem. Weight of a single refrigerator:

Weight of a single refrigerator: Total number of refrigerators:

Five refrigerators:

135)34,425

Total weight of refrigerators

Therefore, five refrigerators weigh

Total weight of five refrigerators:

pounds.

Apply Solve using the problem solving strategy. 1.

A farmer needs to put 12,389 pounds of carrots into crates. Each crate holds 328 pounds. How many crates will he need to hold all of the carrots?

Level G

Chapter 3

Lesson 4

Lighthouse Math

Exercise 3-4 Name Solve using the problem solving strategy. A group of 27 students needs to pay a total of $486 to attend the school field trip. If each student paid the same amount, how much did each student pay?

A store sold 123 stoves that cost the same amount. If they made a total of $83,025 from the sales, how much is the cost of one stove?

A grocery store is stocking items on shelves. They have 20,358 different types of cereal boxes to place on shelves. If each shelf holds 234 cereal boxes, how many shelves will they need to stock all the boxes?

A school is passing out 3,487 pencils. If each student gets 12 pencils, how many students can receive all 12 pencils?

An apple farmer collected 5,772 apples. He shipped the apples out to grocery stores in equal containers holding 123 apples each and kept the rest. How many apples did he keep?

At an aquarium, they feed the fish a total of 20,370 oz. of food a month. If there are 30 days in the month and they feed an equal amount of food each day, how many ounces of food do they use in one day?

It costs $12 to buy a ticket to the circus. If the circus made $34,488 on tickets, how many did they sell?

Lighthouse Math

Level G

Chapter 3

Exercise 4

Chapter 3-5 Divide by Power of Ten Solve.

Daily Review 1. 256 � 5 =

2. 158 � 104 =

3. 264 � 2 =

Learn and Connect A furniture company is allowing people to pay the cost of the recliner over the course of 3, 10, 20 or 100 days. A customer is trying to decide which option to choose. Determine the price the customer would have to pay each day based on each option. To solve, we have to divide the cost of the sofa by the number of days they will be paying off the sofa. Tips for Dividing with Zeros: When dividing with zeros ONLY 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. For example: 160 ÷ 4 = 16 ÷ 4 = 40 dividend

divisor

When dividing with zeros in BOTH the divisor and dividend, 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. For example: 160 ÷ 40 = 16 ÷ 4 = 4 Type of plan

3 days

10 days

20 days

100 days

Cost per day

Apply Solve using the division with zeros trick. 1. 9)270

2. 4)280

3. 5,000)300,000 4. 90)90,000

5. 9)81,000

Find the missing divisor or dividend. 6. 9.

7,200 ÷

= 800

÷ 80 = 7

Level G

2,700 ÷

= 900

10. 9,000 ÷

= 450

11. 9,000 ÷

Chapter 3

Lesson 5

÷ 800 = 6 = 300

Lighthouse Math

Exercise 3-5 Name Solve using the division with zeros trick. 1.

11)44,000

200)1,200

5,000)300,000

80)80,000

4)16,000

3)15,000

70)4,200

600)360,000

80)720,000

10. 30)24,000

11. 8)960,000

12. 700)49,000

Find the missing divisor or dividend.

16.

÷ 40 = 30

19. 560 ÷ 22.

=8 ÷ 3 = 800

25. 8,100 ÷ 28.

= 700

÷ 5 = 700

14. 2,400 ÷ 17.

= 800

23.

= 80

÷ 80 = 50

26. 490 ÷ 29.

18.

÷ 6 = 90

20. 48,000 ÷

15. 3,600 ÷

= 70 ÷ 8 = 700

÷ 4 = 90

21. 2,100 ÷ 24.

= 40

= 30

÷ 600 = 5

27. 12,000 ÷ 30.

13. 4,200 ÷

= 30

÷ 800 = 6

Challenge Solve. 31. There are 2,200 trees in a local park. During an event, an equal number of ribbons were tied to each tree. If they had a total of 48,400 ribbons, how many ribbons were on each tree?

Lighthouse Math

Level G

32. A chocolate factory can produce 35,000 chocolates every 5 hours. How many chocolates do they produce in an hour?

Chapter 3

Exercise 5

Chapter 3-6 Missing Divisors and Dividends Daily Review

Divide.

1. 2,600 � 2 =

2. 25,000 � 2 =

3. 810,000 � 900 =

Learn and Connect Eli put an an equal amount of pants into his 5 dresser drawers. If he placed 11 pairs of pants into each drawer, how many pants did he start with? Choose the expression that best explains P, the number of pants Eli started with. A. 11 ÷ 5 = P B. P ÷ 5 = 11

C. 11 ÷ P = 5 D. 5 ÷ P = 11

To solve, consider the missing information from the word problem. We know how many dresser drawers we have and how many are in each drawer. In a division problem, we need to take the total and divide it into pieces. In this case, the total is unknown. total number of pants ÷ the number of drawers = pants in each drawer Which equation matches this information?

Apply

Fill in the missing divisor or dividend. 1.

16 ÷

81 ÷

÷5=9

25 ÷

÷ 4 = 10

÷ 12 = 7

÷4=3 18 ÷

=6 ÷ 10 = 4

10. 60 ÷

= 10

11. 77 ÷

12. 24 ÷

13. 18 ÷

14. 99 ÷

= 11

15. 40 ÷

16. 27 ÷

17.

÷3=6

18.

÷ 10 = 3

÷4=8

20. 30 ÷

21. 48÷

22. 55 ÷

23. 28 ÷

24. 49 ÷

25. 14 ÷

26. 18 ÷

27. 42 ÷

28. 16 ÷

= 16

29. 8 ÷

30. 10 ÷

19.

Level G

Chapter 3

Lesson 6

Lighthouse Math

Exercise 3-6 Name

55 ÷

= 11

45 ÷

÷6=5

45 ÷

28 ÷

÷ 12 = 11

÷ 7 = 70

÷ 3 = 12

20 ÷

11. 48 ÷

12. 35 ÷

13.

÷4=8

14. 30 ÷

= 10

15. 27 ÷

16.

÷3=9

17.

9÷

18. 3 ÷

20. 21 ÷

21.

÷7=6 ÷9 = 6

10. 72 ÷

19. 90 ÷

= 10

22.

÷ 12 = 5

23.

÷8=8

24.

25.

÷7=9

26.

÷6=7

27. 49 ÷

28.

÷ 12 = 4

29.

÷9=4

30. 144 ÷

= 12

32.

÷9=9

33.

÷9=7

36.

÷4=4

÷ 8 = 12

39.

÷ 4 = 11

41. 36 ÷

42.

÷ 6 = 12

Fill in the missing divisor or dividend.

Solve.

43. 16 ÷

44. 81 ÷

48. Arnold has 320 pictures. He has a red photo album that can hold 6 pictures on each page and a blue photo album that can hold 8 pictures on each page. Which photo album will he need to use if he wants all of his pictures in the album and each page full? Explain your answer.

31. 18 ÷ 34.

÷4=6

35. 72 ÷

37.

÷9=8

38.

40. 40 ÷

Challenge

45.

÷5=9

46. 60 ÷

= 10

47. 18 ÷

Lighthouse Math

Level G

Chapter 3

Exercise 6

Fill in the missing divisor or dividend.

Chapter 3-7 Order of Operations Find the missing divisor.

Daily Review 1. 25 ÷

2. 18 ÷

3. 33 ÷

= 11

4. 36 ÷

= 12

Learn and Connect When working with the order of operations, parentheses come first followed by exponents. Then, it is multiplication and division from left to right, followed by addition and subtraction from left to right. You might remember using PEMDAS to help you remember this process! Let's practice with the following equation: First, work out the exponents.

Then, solve any multiplication and division from left to right.

(63 + 2 · 3) � 6 ÷ 2

(

+ 2 · 3) � 6 ÷ 2

(

Next, complete the other operations in the parentheses. Starting with multiplication and then addition.

)�6÷2 �6÷2

Last, solve all addition and subtraction from left to right.

�

Therefore, (63 + 2 · 3) � 6 ÷ 2 =

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

Apply Use the order of operations to solve. Show your work. 1.

(62 ÷ 9) · 7 � 8 =

3 · 2 + (14 + 4) ÷ 2 =

(10 + 10) · 4 ÷ 8 =

(68 � 62) ÷ (3 + 5) =

(37 � 5) ÷ 2 + 72 =

7 · (10 + 6) + 52 =

(7 · 7 + 92) + 3 =

(62 + 72) ÷ 5 =

Level G

Chapter 3

Lesson 7

Lighthouse Math

Exercise 3-7 Name

25 ÷ 5 · 3 + 42 =

72 � 88 ÷ (11 · 2) ÷ 4=

(44 � 62) ÷ 4 · 8 =

(5 + 42) · (15 ÷ 5) =

(12 + 6) · 2 ÷ 32 =

12 ÷ (68 � 82) · 9 =

82 � (4 + 7) · 4 =

35 � 5 · 22 =

(62 · 2) � 70 ÷ 7 =

10.

(6 · 32) + (33 � 15) =

11.

63 ÷ 9 + 52 · 8 =

12.

6 · (2 · 52) ÷ 5 =

13.

12 � 88 ÷ 8 + 5 =

14.

92 + 4 � (42 ÷ 6) · 3=

15.

28 ÷ 4 � (2 + 3) =

16.

900 ÷ 32 � 5 · 9 =

17.

7 · 8 + 48 ÷ 22 =

18.

8 · 9 � (62 + 8) =

Lighthouse Math

Level G

Chapter 3

Exercise 7

Use the order of operations to solve. Show your work.

Chapter 3-8 Review Daily Review

Solve using the order of operations.

1. (11 · 8 � 72) + 2 =

2. 7 · (13 + 6) � 22 =

3. (11 · 8 - 82) � 6 =

Learn and Connect Bonnet Elementary School is putting on a school play. The administrators are setting up the chairs for the audience. They have 240 chairs to set up. They are trying to decide if they should set up the chairs in rows of 6, 8 or 12. Complete the chart to determine how many chairs will need to be in each row for each arrangement. Rows

Chairs in each row 6 8 12

Apply Solve. 2. 18)1,825

3. 325)125,368

4. 121)152,460

5. 16)23,568

1. 20)1,856

Find the missing divisor or dividend. 6.

÷5=4

10. 9 ÷

11. 12 ÷

14. 12 ÷

15.

Level G

÷ 7 = 12 =2

27 ÷

12. 144 ÷

÷5=3

16.

Chapter 3

Lesson 8

48 ÷

= 12

13. 54 ÷

17.

÷ 10 = 9

45 ÷

Lighthouse Math

Exercise 3-8 Name

1. 4)36

6)24

8)40

3)21

5. 40)2,920

21)2,247

16)6,571

55)9,626

9. 124)2,580

10. 252)4,298

11. 385)9,775

12. 41)5,292

13. 70)560,000

14. 50)5,500

15. 400)360,000

16. 6)18,000

19. 64 ÷

20. 42 ÷

Find the missing divisor or dividend. 17.

÷6=4

18.

÷ 9 = 11

Solve. 21. A worker made $30,000 in one year. If the worker worked a total of 2,500 hours, how much money does the worker get paid each hour?

Lighthouse Math

Level G

22. There were 879 bottles of water were distributed at an event. Each person got 3 bottles and no bottles were left over. How many people were at the event?

Chapter 3

Exercise 8

Solve.

Chapter 4 NYS NG Standards NY-3.NF.3 NY-4.NF.2 NY-4.NF.4 NY-5.NF.1 NY-5.NF.2

NY-5.NF.3 NY-5.NF.6 NY-5.NF.7 NY-6.NS.1 NY-7.NS.2

CC Standards 3.NF.A.3 4.NF.A.2 4.NF.B.4 4.MD.B.4 5.NF.A.1 5.NF.A.2

5.NF.B.3 5.NF.B.4 5.NF.B.6 5.NF.B.7 6.NS.A.1 7.NS.A.2

In Chapter 4 we will review

Operations with Fractions We will practice adding, subtracting, multiplying and dividing fractions including the use of mixed numbers. We will also use the order of operations to solve equations with fractions. Rewriting fractions • We will practice simplifying and rewriting proper fractions and improper fractions. Order & compare • We will use comparison symbols to determine which fractions are larger using GCF. Addition • We will add fractions with other fractions and mixed numbers with mixed numbers.

Subtraction • We will subtract fractions with other fractions and mixed numbers with mixed numbers. Multiplication • We will multiply fractions with whole numbers, fractions with other fractions and mixed numbers with mixed numbers. Division • We will multiply fractions with whole numbers, fractions with other fractions and mixed numbers with mixed numbers. Order of operations • We will use what we have learned about the order of operations to solve equations with fractions.

Chapter 4-1 Rewriting Fractions Daily Review

Solve.

1. 25 ÷ 5 =

2. 6 ÷ 2 =

3. 60 ÷ 12 =

4. 30 ÷ 3 =

5. 18 ÷ 9 =

Learn and Connect Sam entered a bike race that is 25 miles long. Each day, he practices on a track near his home that is 25 miles long. Each mile is marked with a sign that says how many miles he has ridden his bike. Sam stops and rests at the same mile marker everyday. What fraction of the race would he have completed by the time he needs to stop? To solve, we need to create a fraction by making the numerator the number of miles Sam rides before stopping and the denominator being the total miles he needs to ride. Miles before he stopped Total miles in race

5 5

To write this number in simplest form, we need to find the 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, Sam biked

15 25

� �

= =

of the race before needing to rest.

Apply Simplify each fraction. 1.

5 � 10 �

= =

12 � 20 �

= =

3. 14 � 35 �

= =

8 � 20 �

75 2 =

= =

Turn the improper fractions into proper fractions and simplify. 5.

3 2 =

52 10 =

39 4 =

Vocabulary Greatest Common Factor (GCF) - the greatest factor that both numbers have in common 68

Level G

Chapter 4

Lesson 1

Lighthouse Math

Exercise 4-1 Name Simplify each fraction. 1.

4 8

16 20 =

10 35

4 6

21 35

24 28 =

3 9

30 36 =

21 49 =

10.

9 12

11.

5 30

12.

18 48 =

13.

4 10

14.

8 14

15.

20 32 =

16.

25 30 =

Turn the improper fractions into proper fractions and simplify. =

18.

12 5 =

19.

21. 26 = 7

22.

48 10 =

23. 30 = 9

24. 54 = 12

25.

26.

27 5 =

27.

28. 74 = 9

6 4

66 8 =

20. 14

34 6 =

68 8 =

17.

Challenge 29. Timothy sliced a loaf of bread into 26 evenly spaced slices. He and his family ate 18 slices of bread. What fraction of the loaf of bread is remaining?

Lighthouse Math

Level G

30. Ron is starting to read a short story for school that is 20 pages long. His mother wants him to finish three-fourths of the story before dinner. How many pages does Ron need to read before dinner?

Chapter 4

Exercise 1

Chapter 4-2 Order and Compare Fractions Daily Review

Turn each improper fraction into a mixed number.

1. 10 3 =

2. 19 4

3. 33 7 =

4. 67 9 =

Learn and Connect Paul and Josh are painting their rooms. Paul has painted 32 of his wall and Josh has painted 3 of 5 his wall. Who has painted more of their wall? To solve, we have to compare 2 and 3 to see which is the larger number. 3

First, we need to make equivalent fractions by changing the denominators using the least common multiple. List the multiples for each denominator and find the first one they have in common. Then, rewrite your fractions with a common denominator. Multiples of 3: 3 ,

Multiples of 5: 5 ,

� �

2 3

= =

� �

3 5

= =

Last, compare the fractions by finding the fraction with the larger numerator.

Therefore,

has painted more of his wall.

Apply Rewrite each fraction with a common denominator. Then, compare using the symbols >, <, =. 1.

5 9

1 2

5 6

2. 4

3. 7

1 3

4. 5

5 10

5. 6

1 2

Rewrite each fraction with a common denominator. Then, place them in order from least to greatest. 6.

3 2 1 5 , 3 , 6

3 4 1 10 , 15 , 6

Vocabulary Least Common Multiple (LCM) - the smallest multiple that each number has in common 70

Level G

Chapter 4

Lesson 2

Lighthouse Math

Exercise 4-2 Name Rewrite each fraction with a common denominator. Then, compare using the symbols >, <, =. 1. 2

1 3

2. 4

4 5

3. 10

5 8

4. 5

5 7

5. 8

12 16

6. 11

5 8

7. 7

5 8

8. 9

3 8

3 5

10. 9

9. 3

2 6

5 9

11. 7

4 5

12. 9

13.

3 5 7 4 , 6 , 9

14.

2 4 3 5 , 7 , 10

15.

5 4 1 12 , 6 , 4

16.

2 5 7 3 , 9 , 18

Challenge 17. John and Sam are both working on their math homework. John’s worksheet has 10 problems and he has finished 6 of them. Sam’s worksheet has 15 problems and he has finished 8 of them. Who has finished the larger fraction of problems on his worksheet?

Lighthouse Math

Level G

18. Caleb and Isaac are riding their bikes to school. Caleb lives 5 miles away and has already biked 3 miles. Isaac lives 7 miles away and has already biked 5 miles. Which boy has the smaller fraction left to bike to school?

Chapter 4

Exercise 2

Rewrite each fraction with a common denominator. Then, place the newly written fractions in order from least to greatest on the lines provided.

Chapter 4-3 Add Fractions Daily Review

Write the fractions in order from least to greatest.

2 7 5 5 , 15 , 10

1 7 3 2 , 8 , 4

Learn and Connect Anthony decided to figure out how tall he was. After taking his height, his friend Leo decided to take his height as well. Leo is 1 2 ft taller than Anthony. How tall is Leo? 6

To find Leo's height, we need to add 1 2 ft to Anthony's height. 6

First, create equivalent fractions by finding the least common multiple for each denominator. 9, 18, 27, 36 6, 12, 18,24

�2 2 = 4 18 �2 �3 6 = � 3 + 1 18

4 91

+1 62

8 5 18

8 5 18 54 ÷2= 9 ÷2

Then add the numerators and the whole numbers and keep the denominators the same. Last, simplify.

Therefore, Leo is 5 4 ft tall. 9

Apply Add and simplify. 1. +

2 7 1 2

3 87

+3 31

2 3 4 6

9 9 10

+2 35

Level G

6 11 + 93

2 63

+4 82

Chapter 4

Lesson 3

2 5 1 3

5 82

4 +2 10

Lighthouse Math

Exercise 4-3 Name Add and simplify. 2.

3 10 + 32

1 85

12.

2 32

17.

11.

+3 25

16.

+4 4 9

5 9 1 2

7 8 4 5

2 32

13.

5 37

18.

4 9 2 4

4 61

14.

3 1 10

19.

+5 41

+1 31

7 10 + 35

+1 83

2 7 2 5

10.

3 7 3 8

3 35

15.

3 95

20.

+4 65

+6 43

+2 65

2 6 3 4

5 6 4 9

6 62

7 +2 10

3 8 1 3

7 5 10

+3 81

Challenge 21. James and Kevin want to make a jump rope by combining two pieces of rope. They have one piece that is 5 3 feet long and one piece that is 4 5 feet long. What would the length be after 4 8 combining the two pieces?

Lighthouse Math

Level G

Chapter 4

Exercise 3

Chapter 4-4 Subtract Fractions Daily Review

Add and simplify.

6 3 7 + 14 =

1 2 8 + 5 =

2 1 3 + 6 =

Learn and Connect David’s water bottle had 28 1 fl oz of water inside. He 2 started drinking some of the water. When he was done, he had drank 10 3 fl oz of water. How much water is left 4 in the water bottle? To solve, we have to subtract the amount of water David drank from the amount of water in David’s water bottle when he started. First, create equivalent fractions by finding the least common multiple for each denominator.

28 21

� 10 43

�2 = 28 42 �2 �1 3 = � 1 10 4

2, 4, 6, 8 4, 8, 12, 16

Notice, you cannot subtract the numerators because 2 is smaller than 3. Therefore, you have to borrow a whole in fraction form.

28 21

� 10 43

�2 = 28 42 �2 �1 3 = � 1 10 4

+ 4 = 4 17 43

Therefore, David has 17 43 fl oz of water left.

Apply Subtract and simplify. 1.

3 5 3 � 10

6 21

�3 87

2 3 2 9

4 8 3 � 12

7 9 7 � 12

9 43

4 32

5 5 12

�

�5 32

Level G

�3 21

Chapter 4

Lesson 4

�3 31

Lighthouse Math

Exercise 4-4 Name Subtract and simplify. 2.

5 10 � 31

4 85

12.

7 32

17.

�

11.

�3 25

16.

�4 4 9

�

5 9 1 2

�

7 8 4 5

13.

�1 31

7 9 2 4

4 61

14.

3 8 10

19.

�

�5 41

5 37

7 10 � 35

�1 83

18.

�

6 7 2 5

10.

�

5 7 3 8

8 12 � 85

9 35

15.

6 62

3 95

20.

�

�4 65

�6 43

�2 65

5 6 3 4

7 �2 10

5 8 1 3

7 5 10

�3 81

Challenge 21. Nathan is trying to hang a picture on the wall. He can reach 5 85 feet up the wall on his own. What is the shortest step stool would need to be for him to hang the picture 8 2 feet off of the 5 ground?

Lighthouse Math

Level G

Chapter 4

Exercise 4

Chapter 4-5 Multiply Fractions Daily Review

Subtract and simplify.

3 1. 12 � 14 =

2. 2 31 � 81 =

2 32 � 65 =

Learn and Connect Students in Mr. Martell’s class were conducting an experiment. For their experiment, they had to stack books on top of each other to create a ramp. All of the books were the same thickness. If they used 6 books to hold up one end of the ramp, how tall was the ramp? To solve, we have to multiply the thickness of the book by the number of books stacked on top of each other. 6 � 3 35 First, turn the whole number into a fraction by placing the whole over 1. Then, turn the mixed number into an improper fraction.

6 � 61

3 35 � 18 5

Then, multiply the numerators and denominators. 6 18 108 1 � 5 � 5

�

Since the answer is an improper fraction, we must turn it into a mixed number. 108 3 5 � 21 5

Therefore, the ramp will be 21 35 inches tall.

Apply Multiply and simplify. 1.

6 � 82 =

2. 4 � 35 =

4 = 3. 12 � 10

4 8 1 7 � 12 =

6. 3 32 � 1 41 =

7. 3 91 � 4 32 =

8. 2 71 � 7 63 =

10. 2 31 � 45 =

11. 7 43 � 5 =

12.

9. 38 � 42 =

Level G

Chapter 4

Lesson 5

3 �2 4 9 =

3 1 4 � 8 =

Lighthouse Math

Exercise 4-5 Name Multiply and simplify. 1.

2 41 � 3 =

2. 6 32 � 2 41 =

3 3. 1 10 �4=

3 � 1 83 =

2 21 � 4 31 =

8. 3 83 � 4 =

9. 4 65 � 43 =

10. 1 83 � 4 43 =

11. 3 � 5 47 =

12. 2 97 � 2 35 =

4 13. 6 4 8 � 8 =

14. 2 45 � 4 25 =

15. 1 81 � 3 41 =

5 32 9 � 3 =

4 25 � 3 41 =

Challenge 16. The horses on a ranch eat 2 41 pounds of hay a day. How much hay will be needed to feed the horses for 5 days?

Lighthouse Math

Level G

17. Nathan reads 3 21 pages of his book every minute. If he reads for 5 2 minutes, how 3 many pages will he finish?

Chapter 4

Exercise 5

Chapter 4-6 Divide Fractions Multiply and simplify.

Daily Review 1.

6 � 21 =

1 3 � 4 =

1 1 3 � 8 =

4. 2 62 � 41 =

Learn and Connect Oren bought some chocolate at the store for his friends. He split the chocolate into 1 3 oz pieces and gave out all 4 of the pieces to his friends. How many friends received 1 3 oz of chocolate if Oren gave out every piece? 4

To solve, we have to divide the weight of the original chocolate by the 1 3 oz pieces. 4

7 � 1 3

First, turn the whole number into a fraction by placing the whole over 1. Then, turn the mixed number into an improper fraction. 7 � 71

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

1 43 � 47 �

Last, we change the improper fraction back to a mixed number and simplify if necessary. 44 7) 28 �28 00

7 7 1 � 4 �

7 4 28 1 � 7 � 7

Therefore, 4 friends received chocolate.

Apply Find the reciprocal 1. 43

2. 2 21

6. 25 � 4 =

7. 10 � 81 =

8 2 10. 10 � 1 10 =

2 4 11. 1 10 � 1 10 =

11 12. 1 12 � 1 10 12 =

4. 95

Divide and simplify. 5. 12 � 21 =

2 1 1 3 � 3 =

Level G

Chapter 4

Lesson 6

2 85 � 91 =

Lighthouse Math

Exercise 4-6 Name Find the reciprocal. 1

1. 3

2. 3 5

4. 8

Divide and simplify. 5.

1 41 � 2 41 =

7 1 10 � 25 =

2 2 �2 3 =

1 83 � 2 51 =

10. 2 27 � 1 81 =

11.

1 25 � 1 41 =

12.

5 9 9 � 11 =

13. 1 97 � 2 43 =

14.

2 37 � 3 =

15.

3 1 �22 = 2 3

16.

5 2 11 �4 =

17.

2 � 1 4 8 =

18.

1 43 � 4 =

19.

5 � 2 45 =

7 4 8 � 9 =

Challenge 20. The teacher brought 2 21 gallons of water to share with her 20 students. If each student gets an equal amount and all the water is used, what fraction of a gallon will each student get?

Lighthouse Math

Level G

21. Adam spreads his reading assignment of 20 32 pages evenly over 5 nights. How many pages did he read each night?

Chapter 4

Exercise 6

Chapter 4-7 Order of Operations Daily Review 1.

Divide and simplify.

4 � 31 =

1 5 � 7 =

2 3 7 � 4 =

5 1 7 � 5 =

Learn and Connect Mr. Monroe is giving out hot chocolate to his students from a pitcher that holds 54 31 fl oz of hot chocolate. He accidently spilled 1 fl oz of hot 6 chocolate while making it. Then, he poured 4 fl oz for himself. He split the remaining hot chocolate into 15 cups. Write an equation to show how many fl oz of hot chocolate each student received. To solve, we need to consider the order of operations. We use parentheses to tell us what to do first. It doesn’t matter if the parentheses come at the beginning, middle, or end in the equation, they are always done first. Then, we move left to right, solving multiplication and division first followed by addition and subtraction. Fill in the information from the story and then solve.

(

�

) ÷

Therefore, Mr. Monroe gave each student

fl oz of hot chocolate.

Apply Use the order of operations to solve. 1. 15 + ( 43 � 81 ) � 5 =

2. 21 + 21 · 5 � 3 =

3. 41 · 2 81 + 15 =

4. 2 � 91 + 8 · 6 =

5. 15 · ( 31 + 51 ) � 6 =

1 6. 7 + ( 32 + 18 )+5=

8. 22 � 31 · 4 6 =

9. 66 � 6 � 83 =

1 2 5 · 3 + 15 ÷ 5 =

Level G

Chapter 4

Lesson 7

Lighthouse Math

Exercise 4-7 Name

1. 4 + ( 41 � 51 ) =

2. 3 � (2 � 45 ) � 25 =

3. 32 � (4 � 25 ) � 2 =

4. 51 � 2 + (5 � 41 ) =

5. 3 � 41 � (2 � 32 ) =

2 6. 3 � 4 9 � (4 � 3 ) =

4 1 1 1 5 � 4 � 3 � 2 =

8. 1 37 � 37 � 43 =

3 1 9. 4 9 � 4 � 6 �3=

10. 43 + 21 � ( 65 � 32 ) =

7 11. 65 � (10 � 25 ) =

12. 2 32 � ( 45 � 83 ) =

9 13. 10 � ( 21 � 41 ) =

14. 32 � 31 � ( 85 � 21 ) =

15. ( 83 � 41 ) � 2 51 =

16. 97 � ( 65 � 31 ) � 32 =

17. 1 32 � 35 � 32 =

7 18. 83 � (10 � 21 ) � 25 =

Lighthouse Math

Level G

Chapter 4

Exercise 7

Use the order of operations to solve.

Chapter 4-8 Review Daily Review

Solve using the order of operations.

1. 41 · 25 + 4 ÷ 2 =

7 2. 15 � 1 31 · 25 =

3. 22 � 5 � 21 =

Learn and Connect A nearby park has four different trails. Some trails are longer than others. The chart below shows the distance of each trail moving in one direction. TRAIL NAME

Hawk Trail

Sparrow Trail

Eagle Trail

Hummingbird Trail

DISTANCE (MILES)

7 43

2 62

3 5 12

1 87

If Paul took the Hawk Trail five times last week and the Eagle Trail one time, what is the total distance Paul traveled on the trails? To solve, we have to multiply the number of times he walked the Hawk Trail by the distance of the trail and then add the distance of the Eagle Trail. 7 43 � 5

3 +5 12

31 5 4 � 1 =

Therefore, Paul traveled

miles on trails last week.

Apply Use the chart above to answer the questions. 1. Ben rode his bike up and down Sparrow Trail. Ben rode a total of 9 1 miles. 3 How many times did he ride up and down Sparrow Trail?

Level G

2. How much longer is Hawk Trail than Eagle Trail?

Chapter 4

Lesson 8

3. Yesterday, Sam walked Sparrow Trail and Eagle Trail. What was the total distance Sam walked?

Lighthouse Math

Exercise 4-8 Name Simplify each fraction. 12 1. 18 =

2. 30 42 =

3. 49 70 =

Turn the improper fractions into proper fractions and simplify. 4. 13 5 =

5. 31 9 =

6. 62 11 =

Rewrite each fraction with a common denominator. Then, compare using the symbols >, <, =. 7

7. 10

2 3

8. 9

6 11

9. 7

7 9

10. 10

9 15

11. 2 + ( 43 � 25 ) =

12. 32 � (1 � 35 ) � 25 =

13. 1 41 � ( 85 � 41 ) =

14. 65 � 21 � (1 31 � 41 ) =

15. 25 � 51 � ( 71 � 81 ) =

16. 83 � 41 � ( 81 � 32 ) =

Use the order of operations to solve.

Challenge 17. A baker sells 31 of a pie. He bakes another pie then sells 3 of the new pie. If he combines 8 the remaining pies, as a simplified mixed number, how many pies does he have left?

Lighthouse Math

Level G

18. A recipe calls for 2 43 cups of flour. If the chef wants to make 2 of a full recipe, how 3 many cups of flour should he use?

Chapter 4

Exercise 8

Chapter 5 NYS NG Standards NY-4.NF.7 NY-4.MD.2 NY-5.NBT.7

NY-5.NBT.3 NY-5.OA.2 NY-6.NS.3

CC Standards 4.NF.C.7 4.MD.A.2 5.NBT.A.3

5.NBT.B.7 5.OA.A.2 6.NS.B.3

In Chapter 5 we will review

Decimals Through the Ten Thousandths Place We will also use decimals to solve basic operations and use our knowledge of the order of operations to solve expressions with decimals. Decimal place value to ten thousandths place • We will write the word form, standard form, fraction form and expanded form of decimal numbers. Order & compare • We will use comparison symbols to show which decimal numbers are greater or less than others. Addition • We will add decimal numbers and mixed numbers using decimals. © Lighthouse Curriculum. Copying strictly prohibited.

Subtraction • We will subtract decimal numbers and mixed numbers using decimals. Multiplication • We will multiply decimals and discover how to place the decimal point in the product. Division • We will divide decimals and discover how to place the decimal point in the quotient. Order of operations with decimals • We will use the order of operations to solve expressions using decimal numbers.

Chapter 5-1 Place Value With Decimals Compare the numbers using: <, >, =.

Daily Review 1. 54,893

2. 89,328,543

54,983

3. 6,983

89,328,543

9,683

ten thousandths

thousandths

hundredths

tenths

ones

tens

hundreds

thousands

ten thousands

hundred thousands

One ten thousandth is a very small number. Imagine taking a 1 inch piece of paper and cutting it into 10,000 pieces! Each piece would be 0.0001 inches. A sheet of paper is 0.0039 inches thick. This means, it 39 of a whole inch. To read this is 10000 number correctly, start by writing the number in the place value chart.

milions

Learn and Connect

Therefore, 0.0039 is read as

Apply Write the place value of each number in red.

1. 3.87

2. 9.42

3. 345.883

4. 67.005

Write the standard form of each number. 5. 687 thousandths

6. 1 and 52 hundredths

7. 1 and 6 tenths

8. 2 and 83 ten thousandths

Write the word form for each standard from. 9.

0.3

10. 1 .05

11. 7.0098

12. 0.045

Write the expanded form of each number. 13. 2.05

14. 23.157

Level G

Chapter 5

15. 8.0125

Lesson 1

Lighthouse Math

Exercise 5-1 Name Write the place value of each number in blue. 1. 1453.8147

2. 3129.1042

3. 9138.8183

4. 6374.7591

5. 6316.87

6. 9975.1324

7. 3145.8083

8. 4677.7599

Write the standard form of each number. 9.

1 256 ten thousandths

10. 2 and 5 hundredths

11. 10 and 4 tenths

12. 1 and 121 thousandths

13. 5 and 27 hundredths

14. 7 and 62 thousandths

Write the word form for each standard from. 15. 2 .0023

16. 6 .0123

17.

18. 9 .4

19. 1 1.02

20. 3.15

7.034

Write the expanded form of each number. 21. 3 .45

22. 3 5.286

23. 1.1325

24. 265.105

25. 4 0.735

26. 18.1009

27. 2003.045

28. 2 50.209

29. 2.0305

Lighthouse Math

Level G

Chapter 5

Exercise 1

Chapter 5-2 Order and Compare Daily Review

Identify the place value of each bolded, blue digit.

1. 12.3849

2. 8.2657

3. 235.652

4. 5.3687

Learn and Connect Mr. Weinberg’s class conducted an experiment. They threw paper airplanes made of different materials and recorded how far they flew. Which paper airplane flew the shortest distance?

AIRPLANE TYPE

Aluminum Foil

Construction Paper

Wax Paper

DISTANCE (ft)

2.17

2.038

2.0372

To solve, we need to compare the decimals. Start by stacking the decimal numbers on top of each other, lining up each decimal and place value.

Include placeholder zeros for spaces that do not have a digit.

Then, start at the left and compare digits. The ones are all the same, but the tenths are different.

2.0 3 8 0 2.1 7 0 0 2.0 3 7 2

2.0 3 8 0 2.1 7 � 0 2.0 3 7 2

Next, compare the next place value that has a different digit.

2.0 3 8 0 2.0 3 7 2 2.0372 is the smallest number.

2.17 is the largest number.

Apply Compare the place values below using <, >, =. 1. 90 5. 6.02 9. 72 13. 5.08

0.09 6.002 7.02 5.009

2. 0.5

0.05

3. 0.004

6. 1.04

1.004

7. 0.05

10. 0.8

0.09

11. 0.002

0.02

12. 0.0022

0.18

14. 2.15

2.105

15. 0.007

0.007

16. 0.319

0.39

0.04 0.05

4. 0.0019

0.19

8. 0.159

0.259

Write the decimals in order from least to greatest. 17. 0.3 ; 3 ; 3.03 ; 0.003

18. 1.532 ; 1.2 ; 1.099 ; 1.34

Level G

Chapter 5

Lesson 2

19. 23.4891 ; 32.9023 ; 23.078 ; 23.2341

Lighthouse Math

Exercise 5-2 Name Compare the place values below using <, >, =. 1. 20 5. 3.102 9. 3.1 13. 6.12

0.20

3.002

3.11

6.13

2. 5.5

5.05

3. 1.002

2.02

4. 0.0025

0.25

0.130

8. 1.048

0.48

6. 2.102

2.12

7. 0.13

10. 15.5

1.55

11. 0.104

0.0104

12. 0.3002

14. 0.04

0.040

15. 4.115

4.1151

16. 7.16

0.302

7.159

17. 1.5 ; 1 ; 1.15 ; 1.105

18. 0.321 ; 0.123 ; 0.213 ; 0.231

19. 18.128 ; 12.818 ; 18.212 ; 12.181

20. 0.555 ; 0.55 ; 0.5 ; 0.05

21. 1.102 ; 1.01 ; 1.101 ; 1.002

22. 9.3542 ; 9.3687 ; 9.304 ; 9.3587

23. 1.3 ; 1.303 ; 1.03 ; 1.033

24. 3.119 ; 3.201 ; 3.02 ; 3.1

25. 11.2165 ; 11.2055 ; 11.0216 ; 11.0615

26. 10.316 ; 10.2658 ; 10.26 ; 10.3015

Write the decimals in order from least to greatest.

Challenge 28. A teacher averaged the scores on the last test for each of his classes. The averages were 85.479, 85.409, 85.503 and 85.099. Write the averages in order from least to greatest.

27. T hree friends timed each other while running a mile. Their times were 7.234 minutes, 7.25 minutes and 7.5 minutes. Which time was the fastest?

Lighthouse Math

Level G

Chapter 5

Exercise 2

Chapter 5-3 Add Decimals Daily Review 1. 3.2

2.3

Compare the decimals using the symbols <, >, or =. 2. 3.000

3. 2.3567

2.32

4. 1.92

0.99

Learn and Connect David is making spaghetti for his family. His mother told him to use one small can of tomato sauce that is 2.3 oz. and one large can that is 5.372 oz. If he combines both cans of tomato sauce into a pot, how many ounces of tomato sauce will he use in total? To solve, we need to add the weight of the tomato sauce in both cans. When adding decimal numbers, it is important to line up the place values. Include zeros to the right of the decimal as place holders for numbers that do not include those digits.

2.300 + 5.372

Then, add normally. Remember to include the decimal in the same location that it is in which is always in between the ones and tenths.

Therefore, David will use

ounces of tomato sauce.

Apply Add. 1.

71.4 + 2.482

15.4274 + 21.103

105.695 + 0.3

152.000 + 7.685

Add by stacking the numbers on top of each other and lining up the place values. 5. 56.1 + 0.586 = +

9. 78 + 9.652 = +

6. 7.95 + 3.254 = +

10. 41.56 + 0.365 = +

Level G

7. 22.756 + 5.9 =

11. 125 + 569.23 = +

Chapter 5

Lesson 3

8. 32.548 + 4.6 = +

12. 200.75 + 26.35 = +

Lighthouse Math

Exercise 5-3 Name Add by stacking the numbers on top of each other and lining up the place values.

4. 0.696 + 300.7 = +

7. 7.307 + 0.943 = +

10. 178.08 + 7.19 = +

13. 59.5391 + 3.002 = +

16. 53.339 + 2.405 = +

Lighthouse Math

2. 48.205 + 0.536 = +

3. 10.924 + 13.251 = +

5. 413.15 + 10.086 = +

6. 6.831 + 13.539 = +

8. 0.2657 + 0.9543 = +

9. 4.0203 + 7.78 = +

11. 10.023 + 246.234 = +

12. 74.4455 + 85.5566 = +

14. 9.0581 + 10.96 = +

1. 123.05 + 2.58 =

15. 0.7477 + 0.9292 = +

17. 8.194 + 538.01 = +

18. 0.698+0.3376 = +

Level G

Chapter 5

Exercise 3

Chapter 5-4 Subtract Decimals Daily Review 1. 2.34 + 7.8

Add by stacking the numbers on top of each other and lining up the place values. 2. 12 + 3.89 3. 11.98 + 2.3 4. 7.9521 + 0.9

Learn and Connect Paul is comparing the amount of soda in a can to the amount in a bottle. He wants to know how much more soda there is in the bottle than in the can. What is the difference in ounces between the soda can and the soda bottle? To solve, we need to subtract the fluid ounces of both containers. When subtracting decimal numbers, it is important to line up the place values. Include zeros to the right of the decimal as place holders for numbers that do not include those digits.

25.00 � 12.02

Then, subtract normally. Remember to include the decimal in the same location that it is in which is in between the ones and tenths.

Therefore, the soda bottle has

more fluid ounces of soda than the can.

Apply Subtract. 1.

47.9 � 6.347

22.235 � 19.651

17.4 � 0.2

320 � 1.469

Subtract by stacking the numbers on top of each other and lining up the place values. 5. 752 � 5.23 = �

6. 68.5 - 2.521 = �

Level G

7. 12.562 � 9.7 = �

Chapter 5

Lesson 4

8. 79 � 2.356 = �

Lighthouse Math

Exercise 5-4 Name Subtract by stacking the numbers on top of each other and lining up the place values.

�

4. 300.696 � 3.7 = �

7. 7.303 � 0.943 = �

10. 178.08 � 7.19 = �

13. 59.91 � 3.002 = �

16. 53.339 � 2.405 = �

Lighthouse Math

2. 48.205 � 0.536 = �

3. 18.924 � 13.251 = �

5. 413.15 � 10.086 = �

6. 6.831 � 3.539 = �

8. 4.2657 � 0.9553 = �

9. 9.0203 � 4.78 = �

11. 210.023 � 46.234 = �

12. 84.4455 � 75.5566 = �

14. 19.0581 � 8.96 = �

1. 123.05 � 2.58 =

15. 0.9 � 0.727 = �

17. 583.194 � 8.01 = �

18. 0.68 � 0.3376 = �

Level G

Chapter 5

Exercise 4

Chapter 5-5 Multiply Decimals Daily Review 1. 12 � 3.25

Subtract by stacking the numbers on top of each other and lining up the place values. 2. 9.65 � 1.2 3. 7.568 � 0.23 4. 2.56 � 1.78

Learn and Connect A local pizza place is hiring. Lance wants to work 20.5 hours a week. If he got the job at the pizza place, how much would he make in a week? To solve, we need to multiply the number of hours Lance wants to work by the pay he would receive. To multiply decimal numbers, follow these steps. • •

•

Set up the multiplication problem by putting the number with the most digits at the top. Solve the multiplication problem as you would do normally. Then, count the number of digits after the decimal in each factor. Put the same number of digits behind the decimal in the product.

Therefore, Lance would make

12.58 � 20.5

2 digits after decimal � 1 digit after decimal =

3 digits after decimal

Apply Multiply and place the decimal the same number of the digits after the decimal in the factors. 1.

32.1 � 2.7

2. 122.3 � 2.36

12.3 � 4.2

19.1 � 17.3

89.3 � 2.1

78.21 � 0.9

2.371 � 0.62

8. 12.56 � 1.9

9. 273.1 � 9.5

10.

85.6 � 5.36

11. 16.2 � 0.7

12.

0.235 � 3.72

Chapter 5

Lesson 5

Level G

Lighthouse Math

Exercise 5-5 Name Multiply and place the decimal the same number of the digits after the decimal in the factors. 1. 42.6 � 3.4

2. 105.4 � 4.27

18.5 � 2.9

18.4 � 13.5

92.6 � 1.8

6. 77.33 � 0.6

54.1 � 1.7

8. 212.3 � 2.47

27.6 � 11.3

10.

56.5 � 4.9

11. 37.4 � 6.3

12.

178.21 � 0.9

13.

32.4 � 21.7

14.

323.6 � 1.76

15.

35.4 � 3.32

16.

17.

67.1 � 2.01

18. 62.04 � 0.2

19.

75.06 0.3

20.

�

58.7 � 4.03

18.4 � 21.8

Challenge 21. Jack ran 3.75 miles each day for 5 days. How many miles did he run in total?

Lighthouse Math

22. Caleb is doing a woodworking project. Each board he is using is 7.78 feet long. He has 12.5 boards. What is the total length of boards that Caleb has?

Level G

Chapter 5

Exercise 5

Chapter 5-6 Divide Decimals Daily Review

Set up and multiply: Remember to move and include your decimal in your answer.

1. 24 × 1.2

2. 2.41 × 5.2

3. 0.71 × 8

4. 15.3 × 0.3

Learn and Connect Timothy decided to buy some T-shirts. He ended up buying 12 T-shirts. If each T-shirt cost the same amount, how much was each T- shirt? To solve, we need to divide the total he spent on shirts by the number of shirts that he bought. •

•

When dividing decimals, set up the division problem. Divide the same way you would divide whole numbers. Then, place a decimal in the quotient by moving your decimal point directly above the decimal in the dividend.

Therefore, each T-shirt was

12)62.52

Apply Divide and bring up your decimal. 1. 3)3.24

2. 8)21.56

3. 9)5.31

4. 14)52.78

5. 15)8.55

8. 1.3)0.364

9. 2.2)7.216

10. 5.5)12.98

Hint: Move the decimal point in the divisor and the dividend to help you divide

6. 2.0)23.60

7. 1.2)4.236

Level G

Chapter 5

Lesson 6

Lighthouse Math

Exercise 5-6 Name Divide and bring up your decimal.

4)4.24

6. 3)8.22

2. 6)22.53

5)4.85

4. 10)43.20

5. 12)3.24

8. 7)54.74

9. 9)7.65

10. 11)58.96

8)6.72

11. 1.1)0.858

12. 1.2)4.092

13. 1.3)2.899

14. 1.4)0.322

15. 1.5)6.765

16. 3.3)10.659

17. 2.1)0.924

18. 2.5)1.275

19. 4.5)9.81

20. 30)99.60

Hint: Move the decimal point in the divisor and the dividend to help you divide

Challenge 21. Samuel needs to earn $46.2 in order to buy a gift for his dad’s birthday. He makes $9.24 per hour. How many hours will he have to work?

Lighthouse Math

Level G

Chapter 5

Exercise 6

Chapter 5-7 Order of Operations Daily Review

Set up and divide: Remember to move and include your decimal.

1. 5.230 ÷ 5 =

2. 8.256 ÷ 2.0 =

3. 1.805 ÷ 0.5 =

Learn and Connect Dennis bought 8.95 ounces of turkey. When he got home, he added it to the 0.58 ounces of turkey that was left in his refrigerator. He used 0.78 ounces of turkey for breakfast. Then, he separated the remaining turkey equally into seven sandwiches. How many ounces of turkey did he put in each sandwich? To solve, we need to consider the order of operations. We use parentheses to tell us what to do first. It doesn’t matter if the parentheses come at the beginning, middle, or end in the equation, they are always done first. Then, we move left to right, solving multiplication and division first followed by addition and subtraction. Fill in the information from the story and then solve. ( Therefore, Dennis put

�

) ÷

oz. of turkey in each sandwich.

Apply Solve using the order of operations.

Hint: PEMDAS

1. 7.1 � 5.68 + 2.78 � 3 =

2. (25.1 + 32.05) ÷ 5 + 7.57 =

3. 12.5 ÷ 2 (5 + 6 � 4) =

4. 5.68 ÷ 2 + 8.3 � 5 =

5. 19 � 0.256 + 5 � 15 =

6. (12.56 + 98) � (5.67 + 0.365) =

7. (15 � 2.356 + 0.356) � 2 =

8. 2 � (1.75 ÷ 2.5 + 7) =

Level G

Chapter 5

Lesson 7

Lighthouse Math

Exercise 5-7 Name

1. 6.23 � 7.54 + 1.35 � 6 =

2. 4.16� 3 + 2.74 � 6.92 =

3. 10.5 ÷ 4 (4 + 8 � 2) =

4. 24.315 � 3 (8 ÷ 10 � 2) =

5. 21 � 1.397 + 7 � 12 =

6. 19 + 4 � 15 � 2.598 =

7. (17 � 1.652 + 2.814) � 3 =

8. 39 � (13 � 3.842 + 5.731) =

9. (23.7 + 34.04) ÷ 5 + 9.38 =

10. (33.5 + 24.14) ÷ 4 + 8.13 =

11. 7.74 ÷ 3 + 10.6 � 4 =

12. 12.3 � 5 + 6.54 ÷ 3 =

13. (14.31 + 74) � (7.95 + 4.276) =

14. (11.2 + 43.1) � (0.25 + 0.16) =

15. 3 � (4.75 ÷ 1.5 + 9) =

16. 4 � (5.25 ÷ 1.4 + 11.16) =

Solve using the order of operations.

Challenge 17. Adam makes $5.30 per hour and Daniel makes $6.20 per hour. Adam works 2.5 hours and Daniel works 3.1 hours. How much money did they make combined?

Lighthouse Math

Level G

18. The art teacher has 3 packages of clay to divide among his students. Each package weighs 2.25 pounds and there are 25 students in the class. How much clay should each student get?

Chapter 5

Exercise 7

Chapter 5-8 Review Daily Review

Solve using the order of operations.

1. (78.28 ÷ 2) � 4 + 2 =

2. 10 � (1.7 � 3.2) + 2.2 =

Learn and Connect A grocery store listed the prices of fruit by the ounce.

$0.34

$0.89

$0.40

Write an expression to show the total price of 4.5 ounces of cherries and 3.75 ounces of apples. Then, solve. (

�

)+(

�

Therefore, the total cost of the fruit would be

Apply Answer the following questions using the prices of the fruit above. 1. A customer bought some grapes. She spent a total of $8.01 on grapes. How many ounces of grapes did she buy?

2. A customer bought 5 ounces of strawberries and 6.2 ounces of apples. How much did he spend on fruit?

3. What is the difference between the cost of the apples per ounce and the cost of the grapes per ounce?

4. A customer bought 5 ounces of cherries and 2 ounces of grapes. Which fruit did she spend the most money on? Explain.

100

Level G

Chapter 5

Lesson 8

Lighthouse Math

Exercise 5-8 Name Write the expanded form of each number. 1. 3.45

2. 35.286

3. 1.1325

Write the decimals in order from least to greatest. 4. 1.5 ; 1 ; 1.15 ; 1.105

5. 0.321 ; 0.123 ; 0.213 ; 0.231

6. 18.128 ; 12.818 ; 18.212 ; 12.181

Add by stacking the numbers on top of each other and lining up the place values. 7. 123.05 + 2.58 = �

8. 48.205 + 0.536 =

9. 10.924 + 13.251 =

�

Subtract by stacking the numbers on top of each other and lining up the place values.

�

11. 4.2657 - 0.9553 =

12. 9.0203 - 4.78 =

�

10. 7.303 - 0.943 =

Solve using the order of operations. 13. 6.23 � 7.54 + 1.35 � 6 =

14. 4.16 � 3 + 2.74� 6.92 =

15. 10.5 ÷ 4(4 + 8 � 2) =

16. 24.315 � 3 (8 ÷ 10 � 2) =

Challenge 17. A student’s backpack has textbooks, pencils and notebooks in it. Each textbook weighs 0.9 pounds, each pencil weighs 0.01 pounds, and each notebook weighs 0.5 pounds. If the student has 3 textbooks, 12 pencils and 5 notebooks in his backpack, what is the weight of the items in his backpack?

Lighthouse Math

Level G

Chapter 5

Exercise 8

101

Chapter 6 NYS NG Standards NY-5.OA.3 NY-6.NS.5 NY-6.NS.6 NY-6.NS.7

NY-6.EE.3 NY-7.NS.2 NY-7.NS.3 NY-7.EE.3

CC Standards 5.OA.B.3 6.NS.C.5 6.NS.C.6 6.NS.C.7

102

6.EE.A.3 7.NS.A.2 7.NS.A.3 7.EE.B.3

Chapter 6 builds students' understanding of the

Number System to Include Negative Numbers Students will expand their understanding of rational numbers (decimals, fractions & whole numbers) to include integers. Students will be applying their foundational skills of multiplication and division to learn how to compute or solve for negative numbers. They will also expand the coordinate grid from just quadrant I with positive x and y values to all 4 quadrants that may have negative coordinate points.

They will learn: • How to order & compare sets of numbers that include negative numbers • How to multiply expressions with negative numbers • How to divide expressions with negative numbers • How negative numbers are represented in real life The skills students will gain through these lessons include • Finding absolute value • Solving simple expressions with negative numbers • Placing negative numbers on a number line • Plotting points & identify points in all 4 quadrants • Solving expressions with exponents and a negative base One strategy students will use to solve multiplication and division problems with negatives is the triangle.

+ �

�

103

Chapter 6-1 Absolute Value Daily Review Underline the negative numbers. Circle any numbers that are opposites. Underline the negative numbers. Circle any numbers that are opposites. 2. 5 3. - 12 4. 4 5. 21 6. -3 7. 0 8. -4 9. 56 10. 12 1. -18 5 1. � 18 5 � 21 4 21 �3 10 0 �4 12 6 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Learn and Connect You woke up early and checked the temperature, it read -10ºF. When you checked the thermometer at 1pm the temperature had risen to 5ºF. You want to know how much the temperature increased. We can use absolute value to help us solve this problem. Absolute value is the distance a number is from zero. So -10 is 10 units from zero, and we would write that as |-10| = 10. What is the |5|?

9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

What was the total change in temperature?

Apply Find the absolute value. Use the number line, if needed.

1. |-5|

2. |9|

-11 -10 -9 -8

3. |4|

-7 -6 -5 -4

4. |-3|

-3

-2

-1

5. |-1|

6. |8|

7. |-6|

8. |2|

10 11

Use �, �, or � to compare.

9. |-9|

|-12|

10. |-3|

11. |7|

|6|

|-7|

12. |-1|

|0|

What do answers to problems 1-8 all have in common? Hint: Are they positive or negative?

Vocabulary Absolute Value - the distance a value is from zero, the notation looks like |x| 104

Level G

Chapter 6

Lesson 1

Lighthouse Math

Exercise 6-1 Name Write the following sentences with the absolute value sign, then solve.

1. The absolute value of negative five.

2. The absolute value of twelve.

3. The absolute value of negative three-fourths.

Write each spot on the number line using the absolute value sign, then solve. H

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2

-1

E 3

A 7

4. A

5. B

6. C

7. D

8. E

9. F

10. G

11. H

10 11 12

Circle the expressions that are equivalent to the given number.

12. What expressions are equivalent to |-8|? 3+5

10 - 3

12 + 4

13. What expressions are equivalent to |4|?

11 � 3

1+5

10 � 6

1+4

9�5

14. |-8|

|3|

15. |-12|

16. |-7|

|15|

|7|

17. |5|

|-6|

Write a sentence: How would you describe absolute value to a friend?

Challenge Solve the following problems using absolute value.

18. In January the temperature in New York was -3ºF and in Arizona it was 65ºF. What is the difference in the temperature between these two locations?

Lighthouse Math

Level G

19. A dolphin is swimming at 20 feet below sea level (-20) and an owl is flying a 16 feet above sea level (16). What is the distance between the animals?

Chapter 6

Exercise 1

105

Use <, >, or = to compare the following numbers.

Chapter 6-2 Comparing & Ordering Numbers Place & label the numbers below on the number line.

Daily Review 1. A. �4

B. 5

C. |�3|

D. |�1|

-5

-4

-3

-2

-1

Learn and Connect Your class studies different cities around the world. You want to compare the coldest temperatures in these cities. You record the temperatures from five of the reports in the table to the right. Use the number line below to help order the cities from coldest to warmest. -60 -50 -40 -30 -20 -10

CITY

TEMPERATURE

New York

-52°F

Mexico City

40°F

Los Angeles

32°F

Toronto

-33°F

Chicago

-27°F

10 20 30 40

Apply Order the numbers from least to greatest. Use the number line, if needed.

1. -5, 3, 0, -2, -4, 1

-5

2. -8, |-4|, 3, |-1|, -2

3. -12, |-15|, -22, |6|, |-10|

-4

-3

-2

-1

-10 -8

-6

-4

-2

-25 -20 -15 -10 -5

20 25

Use <, >, or = to compare. 4. |-10|

-10

5. -8

6. |-4|

|4|

7. 8

8. |-1|

-10

9. |2|

|�2|

10. |-6|

-7

11. |-8|

|-5| |-5|

Vocabulary Absolute Value - the distance a value is from zero, the notation looks like |x| 106

Level G

Chapter 6

Lesson 2

Lighthouse Math

Exercise 6-2 Name Order the numbers from least to greatest. 1. 8, |-7|, 4, |-2|

2. -5, |-13|, 9, |20|

Order the numbers from greatest to least. 3. -8, |-10|, -5, |-14|

4. 19, |12|, |-5|, |8|

Use <, >, = to compare. 5. -8

-5

6. 4

9. -2

|-2|

10. 27

13. 9 � 4

14. |-20|

-5

7. -3

-4

-12

11. 6 + 4

|-25| 5�3

|-12 |

15. 9

|-9|

8. |-14|

|14|

12. |-16|

4�4

16. |-1|

|3|

In each number set: circle the largest number, box the smallest, and underline numbers that are opposites. 17. -7

|7|

-10

18. -1

�2

|-3|

|-1|

19.

Monday

-5°F

Friday

8°F

Wednesday

12°F

Saturday

-4°F

Use the thermometer to plot the temperatures during different days. Then, order the days from coldest to warmest.

Challenge Solve. 20. You take photographs and sell them to earn extra money. The amount you earn or spend each day is in the table to the right. Order the days from the most earnings to the least.

Lighthouse Math

Level G

Chapter 6

Exercise 2

Monday

$15

Tuesday

$-5

Wednesday

Thursday

$-10

107

Chapter 6-3 Coordinate Plane Daily Review Practice plotting points on a graph. Start at zero, follow the directions and plot the point.

y-axis

1. Over 1, up 3. Label this point A A=(1,3) 1. Over 3, up 0. Label this point B B=(3,0) 1. Over 2, up 1. Label this point C C= (2,1)

(0, 0)

x-axis

Learn and Connect When we are trying to find an exact location, like a subway or bus station, your friend's house or hidden treasure, it is helpful to have language to describe exactly where it is. With the coordinate plane, we use a coordinate point (x,y) to describe an exact location.

y-axis 4

Quadrant II

Quadrant I

3 2 1

-4 -3

-2

Plot two points in each quadrant. What do you notice about the numbers in the ordered pair (x, y)?

x-axis

-1 -1

-2

Quadrant III

-3

Quadrant IV

-4

Apply Draw an arrow to the quadrant that each point will be located in. Use the coordinate grid to help.

y-axis

Quadrant II

(-3, 4) (5, 3) (2, -2) (-3, -4) (4, -5) (-1, -1) (-5, 4) (-2, -2) (3, 4)

Quadrant I

3 2 1

Quadrant II -4 -3

Quadrant III

-2

-1 -1

x-axis 1

-2

Quadrant IV Quadrant III

-3 -4

Quadrant IV

Write a coordinate point that will be in each quadrant. 2. Quadrant I

3. Quadrant II

4. Quadrant III

5. Quadrant IV

Vocabulary X-axis - horizontal axis, left and right Y-axis - vertical axis, up and down Coordinate Point - a pair of numbers written as (x,y) that determine a specific point on a coordinate plane Origin - where the x-axis and y-axis intersect. It is always (0,0). 108

Level G

Chapter 6

Lesson 3

Lighthouse Math

Exercise 6-3 Name Use left/right & up/down to describe how you would plot the following points. 1. (-4, 5)

2. (6, -10)

3. (8, 6)

4. (-2, -3)

Look at the coordinate plane and write the coordinate point that describe each letters location. G

-4 -3

-2

-1 -1

D 1

-2 -3

-4

Which points are not in a quadrant?

Which quadrant(s) have the most points?

F B

Plot and label the following points on the blank coordinate plane. Then write what quadrant they are in. 10 Point

Quadrant

Point

L (-5, 9)

Q (1, 4)

M (3, -6)

R (-3, 0)

N (0, -4)

S (6, -2)

O (2, 8)

T (-1, -2)

P (-2, -7)

U (-8, 7)

Quadrant

6 4 2 -10 -8 -6 -4 -2

0 -2

0 -1 -1

-4 -6 -8 -10

Challenge Each grid line represents a block. Find the distance between the different locations on the town map.

Restaurant and Library

3 2

-4 -3

Playground and Library

-2

Fire Station and Post Office

Fire Station and Restaurant

-3 -4

Lighthouse Math

Level G

Chapter 6

Exercise 3

109

Chapter 6-4 Multiplying Integers Daily Review 1. Above Sea Level Withdraw Drop Deposit Spend Earn Underline positive number words and circle Raise Below Sea Level Sell Credit Buy Gain Loss negative number words.

Learn and Connect Tom buys lunch at school every day. He spends $5 each day of the week. How would you use integers to represent what he spends each day? An integer is a whole number that can be positive, negative or zero.

Write an expression to determine how much he would spend in a week.

How much would he spend in a month?

Apply Read through the integer multiplication rules and then solve the problems. 1. -2 • 5

Integer Rules: Same Signs +•+=+ �•�=+

Different Signs +•�=� �•+=�

� 3. -2 • -9

�

-3 � 4 = -12

-5 • -3 = 15

� 110

�

� 7. -30 • 10

Level G

Chapter 6

Lesson 4

�

� +

� 10. -5 • 7

�

� +

8. -6 • -4

+ �

�

� +

6. -6 • 7

9. -2 • -9

�

� +

5. -6 • -6

4. -20 • -4

+ �

This triangle can help when multiplying integers. Cross off a sign for each number. The sign left over is the sign of your answer.

2. -5 • 9

� +

�

Lighthouse Math

Exercise 6-4 Name Match the equations that have the same answers. 1.

-8 • -3

-2 • 2

1 • -4

-5 • -4

-6 • 3

12 • 2

-10 • -2

-21 • -3

-16 • 2

4 • -8

-9 • -7

9 • -2

How will you remember the sign of your answer when multiplying integers?

Write an expression to represent the scenario and solve. 3. On a hike your family descends from the mountain 35 feet an hour. If you hike for 4 hours, how far will you descend?

4. A fter the sun went down, the temperature dropped 2 degrees each hour for 5 hours. If it started at 82 degrees, what is the temperature after these five hours?

5. R ick is a marine biologist and he is studying deep sea animals. He is at sea level and goes down 10 feet per minute for 8 minutes. How far did he go down? What is his current location? © Lighthouse Curriculum. Copying strictly prohibited.

2. S amuel withdraws $45 from his bank account to pay bills each month. After 6 months, what was the change in his bank account?

Solve the problem doing one step at a time. 6. -4 • -3 • 5

7. -10 • -5 • -3

8. -3 • 2 • -6

9. -6 • 5 • 7

Solve the problem below step by step then answer the question. 10. -2 • -2 • -2 • -2 • -2 • -2

What do you notice when there is an even amount of negative numbers?

...an odd amount of negative numbers?

Lighthouse Math

Level G

Chapter 6

Exercise 4

111

Chapter 6-5 Dividing Integers Daily Review 1. -3 � 6 =

Solve. 2. -2 � -7 =

3. -9 � 10 =

4. -7 � -6 =

5. 5 � 9 =

Learn and Connect Tom gets his cafeteria bill at the end of the month which you can see to the right. If he has 5 weeks to pay, how much must he pay each week to balance his account so he does not owe money?

Thinking about the story, why does it make sense the answer is negative?

Apply © Lighthouse Curriculum. Copying strictly prohibited.

The integer division rules are the same as the integer multiplication rules! Integer Rules: Same Signs +•+=+ �•�=+ +�+=+ ��=+

1. -20 � 5 Different Signs +•�=� �•+=� +��=� ��+=�

� 3. -12 � -2

�3 � 4 = �12

�15 � �3 = 5

� 112

�

7. -30 � 10

Chapter 6

Lesson 5

�

� +

� 10. -32 � 4

�

� +

8. -16 � -4

+ �

6. -40 � 8

�

4. -22 � -11

9. -27 � -9

Level G

� +

5. -6 � -6 This triangle can help when dividing integers too. Cross off a sign for each number. The sign left over is the sign of your answer.

2. -45 � 9

� +

�

Lighthouse Math

Exercise 6-5 Name Match the equations that have the same answers. 1.

-8 • -6

-28 � 7

16 � -4

-5 • -5

-36 � 3

12 • 4

-50 � -2

-27 � -3

-36 � 6

48 � -8

-9 • -1

24 � -2

How will you remember the sign of your answer when dividing integers?

Write an expression to represent the scenario and solve. 2. M ickey's account balance is -$825. If he can pay $75 a month, how many months will it take to pay off his negative balance?

3. On a hike your family descends from the mountain 35 feet an hour. How long will it take you to descend 175 feet?

4. -72 � 8 =

5. 125 � -5 =

6. -56 � -8 =

7. -48 � -6 =

8. 132 � -12 =

9. -54 � 9 =

10. 256 � -8 =

11. 49 � -7 =

12. -50 � -5 � -2 =

Divide integers. Remember your integer rules.

13. 60 � -5 � -3 =

Solve the problem doing one step at a time. 14. -4 • -10 � 8

15. 10 � -5 • -3

16. -3 • -4 � -6

17. -60 � -5 � 3

Challenge 18. W ithout solving the problems, determine if they will be positive or negative, and write + or next to them. a) -5 • 3 • -2 • 7 • -5

Lighthouse Math

b) 100,000 � -10 � -10 � -10 � -10

Level G

Chapter 6

Exercise 5

c) (-5 • 2 • -6) � -10

113

Chapter 6-6 Multiplying & Dividing Rational Numbers Daily Review 1. 1 • 3 = 2 5

Solve. 2. 4 � 1 = 5 2

3. 3.2 • 0.5 =

4. 4.2 � 0.4 =

Learn and Connect Now that we have an understanding of multiplying and dividing integers with whole numbers, let’s practice this skill with fractions and decimals. Fraction Example:

- 51 · (- 43 )

Decimal Example: 2.16 � -12

1) negative · negative = positive

1) positive � negative = negative

- 51 · (- 43 )

-0.18 -12)2.16 � 12 96 � 96 0

1·3 5·4 3 20

Use the triangle if needed

+ �

�

Apply

Simplify the following expressions. Use the triangle if needed to determine if the answer is positive or negative. 1. - 32 � - 92 =

2. - 4 � - 3 =

1 8 4 • - 15 =

1 4. -2 • -1 4 =

5. -8 • 0.09 =

6. -9.3 • -5.1 =

7. -95.2 • -0.12 =

8. (-0.4)² =

7 9. -10 � 25 =

10. 41 � - 83 =

11. - 98 � - 98 =

12. - 51 � 20 =

13. -3.45 � -15 =

14. -0.18 � 0.03 =

15. 8.722 � -3.56 =

16. 14.4 � -4.8 =

Vocabulary Rational Number - any number that can be written as a fraction 114

Level G

Chapter 6

Lesson 6

Lighthouse Math

Exercise 6-6 Name Solve. 1. -18 • 24 =

2. 52 • -4 =

3. -38 • -11 =

4. 104 • -14 =

5. -512 � 32 =

6. -162 � -27 =

7. 280 � -14 =

8. -330 � -15 =

9. -1.2 • -15 =

10. 50 � -12 =

11. 4.6 • -3 =

12. -44 � 5 =

13. -3 • -15 � -9 =

14. 120 � -10 • -4 =

15. -7 • -12 � 4 =

16. -3 • -3 • -3 � -9 =

17. From sea level, a submarine descends 40 feet per minute. Where is the submarine in relation to sea level 5 minutes after it starts descending?

18. The price of one share of a stock fell 7 dollars each day for 4 days. How much value did one share of the stock lose after 4 days?

19. Donald joined a gym 8 weeks ago and he lost 1 lb 2 every week. How many pounds has he lost?

20. Eddie owns 15 shares of the stock from problem 18. How much money did he lose?

21. The same submarine from problem 17 increases its speed to descending 50 per minute. If it has to travel 600 more feet, how long will it take?

22. Each day the construction workers finish the tile in 5.5 apartments. How long will it take to finish 44 apartments?

Challenge Solve. 23. A test has 20 questions. The test awards 3 points if the answer is correct and takes away 1 point if the answer is incorrect. A student answered 5 questions incorrectly. How many points did the student lose? What was their final score?

Lighthouse Math

Level G

Chapter 6

Exercise 6

115

Write an expression and solve.

Chapter 6-7 Order of Operations with Negative Numbers Daily Review

Solve.

1. -4 • -9=

2. -64 ÷ 8=

3. 3 • -7 =

4. -40 ÷ -8 =

Learn and Connect Looking at the table to the right, what do you notice?

Using that information, try to identify the solutions to the expressions below: (-5)² =

(-10)³ =

EXPONENTS OF NEGATIVE BASES BASE

EXPONENT

OPERATION

RESULT

-3

(-3)1=-3

-3

(-3)2=(-3)(-3)

-3

(-3)3=(-3)(-3)(-3)

-27

-3

(-3)4=(-3)(-3)(-3)(-3)

(-5) = 3

(-10) = 4

(-2)² =

(-2) = 3

Apply

Complete the table given the provided information. BASE

EXPONENT

-6

-4

OPERATION

RESULT

-3 x -3 x -3 -5

25 -10 x -10 x -10 x -10

-2 -7

-2 x -2 x -2 x -2 x -2 3

-9

-9 x -9

Vocabulary Order of Operations - the order in which you do operations to simplify an expression PEMDAS Exponent - power which a number is raised to, squared = second power, cubed = third power Base - tells what number is being multiplied and is connected with the exponent 116

Level G

Chapter 6

Lesson 7

Lighthouse Math

Exercise 6-7 Name Use the order of operations to solve. 1. -5 • (32 ÷ �8)

2. -100 ÷ -5 ÷ -2 • -4

3. 54 ÷ -9 • 3

4. (2 • -8) ÷ (-2 • -2)

5. (-5)2 • (-14 ÷ -7)

6. 62 ÷ -4 • 3

7. -3 • (-2)2 ÷ -6

8. (-10)2 ÷ (-5)2

9. (-3)3 • -2 ÷ -9

10. -2 • (15 ÷ -3) • 6

11. 23 • (-3)2

12. 42 • 3 ÷ -12

13. Three times the quantity of -5 times 2.

14. The product of -6 and 5 divided by -2.

15. If each month you spend $15 on books, after 6 months how much have you spent?

16. A bank account has $-3. The account doubled by the next month. What is the amount in the account now?

Challenge Find at least two base and exponent combinations that equal the given number. 17. 81

Lighthouse Math

18. 64

Level G

Chapter 6

Exercise 7

117

Write an expression and solve.

Chapter 6-8 Review Daily Review

Solve.

1. -5 + 3 =

2. -5 � 3 =

3. -5 • 3 =

4. -15 ÷ -3 =

Learn and Connect Describe absolute value in your own words.

How would you write the absolute value of -6?

Solve.

Compare using <, >, =.

1. |�9|

5. |�3|

|10|

2. |6|

6. |�8|

|5|

3. |�25|

7. |�13|

|13|

4. |2|

8. |�4|

|0|

Order from least to greatest. 9. 6, �8, �10, |�5|, 0 10. |9|, �1, 4, |�10|, �5

Apply In the green boxes, label the quadrants & write the rule for the points for that quadrant. Quadrant

(

Quadrant )

(

)

11. Plot and label the following points.

12. Write the coordinate point for the blue dots on the plane.

A (5, 1)

B (�6,�3) C (9, �1)

W -10

-8

-6

-4

-2

D (0, �7)

-4

E (�5, 8)

-6

F (�4, �2)

-8

-10

Quadrant (

118

Level G

Z Quadrant

)

Chapter 6

(

Lesson 8

)

Lighthouse Math

Exercise 6-8 Name Multiplying & Dividing Integers. 1. What methods help you solve multiplication and division problems with negative numbers?

2. 3 • -7

3. 8 ÷ -4

4. 21 • -18

5. (-3)2

6. -5 • 8

7. -32 ÷-4

8. - 3 � - 4

9. (-5)3

10. -4 • -2

11. 4 ÷ (-4)

12. -1.2 • 4

13. (-7)2

14. -2 • -4 • -2

15. -22 ÷ 11

16. 0.25 ÷ -0.2

17. (-12)2

Word Problems. 18. The submarine starts at sea level and drops 12 feet a minute. If it has been 6 minutes, how many feet below sea level is the submarine?

21. T he water level in a water reservoir fell to -3 inches below surface and continued to fall 3 inches per day during a drought. If the drought lasted 9 days, how many inches below the water surface was the water level? © Lighthouse Curriculum. Copying strictly prohibited.

20. A family’s electric bill is $60 a month. After 4 months how much money has the family spent on electricity?

19. George’s account balance is -$84. He has 4 weeks to pay off his account. How much must he pay each week?

Order of Operations. 22. -12 ÷ 6 • (-3)2 =

23. -4 • -3 � 4 =

24. (15 • -3) ÷ -9 =

25. 42 • (-2)3 =

26. 7(-8) ÷ -2 =

27. (8 ÷ -4) • (16 ÷ -4) =

Challenge 28. W rite and solve an integer word problem involving temperature.

Lighthouse Math

Level G

29. Write and solve an integer word problem involving money.

Chapter 6

Exercise 8

119

Chapter 7

NYS NG Standards NY-6.EE.3 NY-7.NS.1

NY-7.NS.3 NY-7.EE.3

CC Standards 6.EE.A.3 7.NS.A.1

120

7.NS.A.3 7.EE.B.3

Chapter 7 reviews and builds skills with

Ratios, Negative Numbers and Solving Expressions with Negative Rational Numbers Now students will expand their understanding to include adding and subtracting rational numbers. Although multiplying and dividing negative numbers is similar to how students have learned these skills, adding and subtracting is different and can be a harder skill for students to pick up on. They will learn: • How to add expressions with negative numbers • How to subtract expressions with negative numbers • How negative numbers are represented in real life • How to use order of operations to solve expressions with negative numbers

The skills that they will gain through these lessons include: • Using number lines to represent negative quantities • Using number lines to show addition and subtraction expressions • Using order of operations to simplify expressions Some strategies that students will learn are using number lines for addition and subtraction problems and representing an expression with zero pairs. Although there is no new vocabulary for this unit, students will review integer, rational number and the real life negative and positive number vocabulary.

121

Chapter 7-1 Adding Integers with Number Lines Use the number line to show each problem below.

Daily Review 1. 3 + 5 1

2. 6 + 2 3

Learn and Connect You need to send a package to your cousin but you don't have any money. Your father tells you that he will pay for your things and you can pay him back later. You buy some stamps for $4.00 and then you also send a package which cost $3.00. How much money do you have now? package

stamps

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

After spending this amount at the post office, you found $2 outside. Use the number line to determine how much money you have now. Write an equation to show how you determined how much money you have.

Apply Use the number line to represent the following addition problem and solve. Adding same signs.

Adding different signs.

1. -3 + -5 =

3. 3 + -5 =

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

2. -1 + -7 =

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

4. -1 + 7 =

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Vocabulary Integer - a positive or negative number 122

Level G

Chapter 7

Lesson 1

Lighthouse Math

Exercise 7-1 Name 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Use the vertical number line to help solve the following problems. COLUMN A

1. -5 + 6 =

COLUMN B

2. 4 + 2 =

COLUMN C

3. -5 + 5 =

4. -2 + 1 =

5. -3 + -6 =

6. 2 + -2 =

7. -8 + 3 =

8. -2 + -8 =

9. -10 + 10 =

10. -4 + 7 =

11. -7 + -2 =

12. -7 + 7 =

What do you notice about the problems and answers in column A?

Column B?

Column C?

Write an expression and solve. 14. An elevator is on the 5th floor. It goes down 3 floors and then up 6 floors. At what floor does the elevator stop at?

13. Carl earns $27 from doing yard work in his neighborhood. Then he spends $6 on ice cream for his sister and him. How much money does he have now?

Solve the problem doing one step at a time. 15.

-4 + 5 + 3 =

16.

17.

-7 + 10 + �3 =

-10 + 4 + -2 =

Challenge Determine how much money is in Maxwell’s bank account. 18. Maxwell records his deposits and withdraws for the week. He started with $150 in his account and his bank record is to the right. How much money is now in his account?

Lighthouse Math

Level G

Monday

Deposit $15

Tuesday

Withdraw $30

Wednesday

Withdraw $60

Thursday

Deposit $25

Friday

Withdraw $35

Chapter 7

Exercise 1

123

Chapter 7-2 Adding Negative Numbers with Zero Pairs Daily Review

Solve.

1. 12 + -6 =

2. 3 + -9 =

3. -9 + -6 =

4. -5 + 4 =

Learn and Connect A Zero Pair is a set of numbers that when combined equals 0. For example -3 and 3 or 15 and -15. Look at the image to the right. How were Zero Pairs used to help solve 7 + -4?

Add integers using Zero Pair

7 + -4 = 3

7 + -4 =

How would you draw -4 + 2? What is the answer?

What would the picture for -3 + -1 look like? How many Zero Pairs? What would the answer be? Positive

Negative

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Draw a model of Zero Pairs and solve. 1.

7 + -4

-1 + -3

3 + -7

8 + -5

1 + -4

-3 + -3

3 + -6

-2 + 6

7 + -7

124

Level G

Chapter 7

Lesson 2

Lighthouse Math

Exercise 7-2 Name You can also use this method with numbers instead of chips. This is helpful when you have larger numbers. Study the model and then solve the practice problems. -30 + 12 = -18 P

30 � 12 18

Example: Notice we use subtraction to take away the zero pairs.

16 + -4

-10 + -3

4 + -9

18 + -5

1 + -7

-7 + -7

-4 + 4

-22 + 7

15 + -8

Solve the following problems using any strategy.

14.

- 68 � - 27

11. 5.3 � (-7.6)

15.

12. 3.4 � 1.4 � 7.2

- 57 � 68

16.

- 37 � - 92

13. -4 + 2.8 � (-6.4)

17.

4 7 8 + - 5

18. -11 � (-14) + 7

19. 7 + (-1) + 12 � 7

20. 6 + -7 + -5 � (-5)

21. -3 + 5 � (-4.6) + 12

22. 6.9 + (-3.7) � (-2)

23. -1.6 � 6.8 � 6.0

10. -4.1 + -4.6

Challenge Determine if the answer is correct or incorrect. If it is incorrect, find the right answer. 24. -15 + 10 = -25

Lighthouse Math

25. -8 + -10 = 18

Level G

26. 23 + -15 = 8

Chapter 7

Exercise 2

125

Chapter 7-3 Adding Integers Word Problems Daily Review 1. -8 + 6 =

Circle the expressions that are equal to -2. 2. -2 + 4 =

3. -1 + -1 =

4. -4 + 6 =

5. 3 + -5 =

Learn and Connect Two students solve the problem below. Who is correct and how do you know? It is 13 degrees outside on Wednesday but by Friday it dropped 18 degrees. What is the temperature now?

Student 1

Student 2

18 � 13

13 + -18

18 � 13 5

�5

Apply

Write an expression and solve. 1.

You park in a garage 3 floors underground and then get in the elevator and go up 12 floors. What floor are you on?

If your friend parked on a floor 5 levels below ground, how many floors do they need to take the elevator to meet you on floor 2?

Frank went to play golf. His scores were 2, -3, -6 and -1 for four rounds. What was his final score?

Frank's friend, Greg, also went golfing. His scores were -5, 3, -2, -1. In golf the lowest score wins. Who won, Frank or Greg, and by how many points?

A research team aboard an underwater research vessel descends 1,500 feet beneath the surface of the water. They then rise 525 feet. How many feet below sea level are they now?

Now the vessel descends another 350 feet. How many feet below sea level are they now?

126

Level G

Chapter 7

Lesson 3

Lighthouse Math

Exercise 7-3 Name Match the story with the correct equation and answer. 1.

A scuba diver swam 96 feet beneath the surface of the lake. He then climbs up 49 feet. What is his depth now?

The temperature was -3º C at dinner then it dropped 4º C. What is the temperature now?

A bank account has $-49 and someone deposits $96. What is the account balance?

It will be -12º F tonight. The weatherman predicts it will be 25º F warmer by noon tomorrow. What will the temperature be at noon tomorrow?

A boy owes his friend $3 for a toy he bought. His father gave him $4. Which equation shows how much money he has after paying his friend?

A. -25 + -12

1) 47

B. -96 + 49

2) -37

C. -12 + 25

3) 1

D. -3 + 4

4) -47

E. -3 + -4

5) 13

F. -49 + 96

6) -7

It costs $25 to go to the circus and $12 for snacks. How much did you spend in total?

Write an expression and solve. 7.

While buying supplies and selling lemonade, Rob recorded the money amounts in his journal as integers. He recorded 14, -7, and 9. What was the net gain or loss?

Milo has a $50 gift card. He spends $12.75 on a book and $7.50 on candy. What is his card balance now?

10. The local car wash reported losses of $475 each day for three days. What was the loss for the three days?

Challenge Write an expression and solve. 11. A local bookstore has 30 copies of a bestseller when it opens on Monday morning. On Monday, it sells 6 copies of the books. On Tuesday, it sells 3 copies. On Wednesday, it receives a shipment containing 24 copies of the books and also sells 8 copies. How many books does the store have at the end of Wednesday?

Lighthouse Math

Level G

Chapter 7

Exercise 3

127

Solomon has $75 to spend. The new car part he needs is $93. If he borrows the extra money that he needs, how much does he need to borrow?

Chapter 7-4 Subtracting Integers with Number Lines Daily Review

Solve.

1. 3 + -6 =

2. -3 + 6 =

3. 7 + -2 =

4. 2 + -7 =

Learn and Connect 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

At the aquarium, you are watching the sea lions play. One sea lion, Conner, is sitting on the edge and the second, Oliver, dives into the water. First Oliver dives down 5 feet but then he goes 4 feet lower to get a fish to eat. How would you describe Oliver's location?

If Conner jumps up on a rock that is 3 feet above the water, what is the difference in distance between Conner and Oliver? Write an expression and solve.

Apply Study the example, then solve. Use the number line if it is helpful.

-5 - 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

1. Start at -5

2. Subtraction means you need to flip the direction of the second number

3.+4 usually goes right but now will go left.

128

2. 4 � (-6) =

3. 3 � 8 =

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

-5 � 4 = -9

-1 � 6 =

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

4. -5 � 2 =

Level G

Chapter 7

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Lesson 4

Lighthouse Math

Exercise 7-4 Name Solve. Use the number line if it is helpful.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

-1 � 5 =

2. -6 � (-2) =

3. 5 � (-2) =

4. -4 � 9 =

7�1=

6. 4 � 3 =

9�5=

8. 5 � (-6) =

10. -1 � (-5) =

11. 1 � (-4) =

12. -3 � (-1) =

9. -7 � 9 =

Write an expression and solve. 14. Joseph has $47 left in his checking account. If he writes a check for $55, what will Joseph’s balance be?

15. The average temperature at the South Pole is -45º F. The average temperature on the Equator is 92º F. What is the difference in average temperatures?

16. An elevator is on the twentieth floor. It goes down 11 floors and then up 5 floors. What floor is the elevator on now? © Lighthouse Curriculum. Copying strictly prohibited.

13. If it is 5º F outside and the temperature will drop 17º F in the next six hours, how cold will it be?

Solve the problem doing one step at a time. 17. -4 � 5 + 3 =

18. -5 + 8 � 3 =

19. -10 � 4 � (-2) =

Challenge Find the location of the diver. 20. A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?

Lighthouse Math

Level G

21. How much longer will it take for the diver to reach sea level?

Chapter 7

Exercise 4

129

Chapter 7-5 Rewriting Subtraction Statements as Addition Daily Review

Solve.

1. -3 + 8 =

2. -8 + 3 =

3. 8 � 3 =

4. 3 � 8 =

Learn and Connect Mark noticed a pattern as he did his homework. Look at his work to the right. What do you see?

How would you describe how to rewrite a subtraction expression as an addition expression? What else changes?

How would you rewrite -4 � 6 as an addition expression?

5 � 6 = -1 5 + -6 = -1 -2 �(-9) = 7 -2 + 9 = 7 -3 � 5 = -8 -3 + -5 = -8

Apply

Rewrite the given subtraction problems as an addition problem and then solve. We can rewrite any subtraction problem as an addition problem by adding the inverse/ opposite. Study the example below: 1. Don't change the sign of the first number.

2. Change the subtraction sign to an addition sign.

Subtraction

2. 2 � (-1)

4. Now, use the rules of addition to get the answer.

3. -8 � 3 4. 4 � 7 5. -12 � 4

3. Change the sign of the second number.

6. -3 � (-5)

Here are some more examples:

7. 3 � 9

-6 � 2 =

5 � (-4) =

-2 � (-7) =

-6 + -2 =

5+4=

-2 + 7 =

Level G

Solution

1. -5 � 6

-5 - + 4 = -5 + - 4 = -9

130

Addition

Chapter 7

8. -4 � (-2)

Lesson 5

Lighthouse Math

Exercise 7-5 Name Solve the following expressions. Rewrite as addition if it is helpful for you. 1.

2. 5 � (-3) =

3. 6 � (-3) =

4. -4 � 14 =

5. 3 � (-9) =

6. -13 � (-2) =

8. 4 � (-8) =

9. -10 � 6 =

10. 1 � (-4) =

11. -3 � 13 =

-14 � 15 =

-2 � (-7) =

12. -8 � (-14) =

Write one addition and one subtraction expression based off the problem then solve. 13. George has $10 in his wallet and he earns $15 from watching his siblings. Then he spends $20 on a new art set. How much money does he have now?

16. Ken starts with 100 points. He is taking a test where you get 3 points given to you for every correct answer and 6 points taken away for every wrong answer. If he got 10 questions correct and 8 questions wrong, what is his score? © Lighthouse Curriculum. Copying strictly prohibited.

15. The temperature was -3 degrees in the morning, then it dropped 5 more degrees. What is the temperature now?

14. The football team loses 3 yards on the first play and then loses 6 yards on the second play. What is the total number of yards that they moved?

Solve the problem doing one step at a time. 17. �8 � (�5) + 2 =

18. �5 � 8 � 3 =

19. 3 � 8 � (�2) =

Challenge Find the difference in temperatures between the cities. 20. Paris & Moscow

Chicago

50C

Chicago & New York

Paris

70C

Paris & Rome

Rome

120C

Moscow & New York

Moscow

-60C

New York

-20C

Rome & Moscow

Lighthouse Math

Level G

Chapter 7

Exercise 5

131

Chapter 7-6 Word Problems with Negative Numbers Daily Review 1. combined

Write the operation (+, �, �, �) that the word represents. 2. per

3. product

4. decrease

5. all together

Learn and Connect It is feeding time for the polar bears. For each feeding, the zoo keeper brings in 165 lbs of food for all 4 polar bears. They have two feedings and get fed the same amount twice a day. How much do they eat per day?

If the zoo has 1,000 lbs. of food, how many feedings can they do with this supply?

How much does each bear eat per day?

Apply

Read the problem and circle important numbers, underline key vocabulary. Then write an expression to help you solve. 1.

Mt. Everest, the highest point on Earth, is 29,032 feet above sea level. The Dead Sea, the lowest point, is 1,385 feet below sea level. What is the difference between these two elevations?

A submarine was 800 feet below sea level. If it descends 250 feet, what is its new position?

Mitch owes his brother $35. Each of his 5 friends will help him pay off his debt. How much will each friend pay?

In the Sahara Desert it was 136°F. In the Gobi Desert it was -50°F. What is the difference between these two temperatures?

Bryan parks in the garage 4 levels down. He then takes the elevator up 9 floors to his office. What floor is his office on?

If each month the water bill is $15, how much will you pay in a year for water service?

132

Level G

Chapter 7

Lesson 6

Lighthouse Math

Exercise 7-6 Name Review integer operations. Remember your strategies for each operation. 1.

9 � (-4) =

2. -16 + 17 =

3. -12 � 5 =

4. -9 + -3 =

14 � 13 =

6. -6 � 0 =

20 � -2 =

8. -14 + -1 =

9. 4 + 5 =

10. -6 � -7 =

11. -15 + 3 =

12. 11 + -19 =

13. 8 + 1 =

14. 2 � 7 =

15. -17 � (-9) =

16. 18 � (-10) =

17. The temperature of a hot oven drops by 8°F every minute. If the temperature was 120° F, find the temperature after 4 minutes.

18. Jack runs for exercise. Every time Jack runs for exercise, it lasts for 30 minutes. Some days, he just walks for 45 minutes instead of running. If he walked 15 times this month and ran 12 times, what is the total amount of time he exercised?

19. Taylor lost 5 marbles to Max while playing a game. Max then lost 20 marbles to Taylor in the second round. If Max started with 25 marbles, how many does he have now?

20. Perry had 554 rocks in his collection. He sold 34 rocks from his collection. He decided to divide them all into 8 equal groups. How many rocks will be in each group?

Challenge Find the missing number. 21. A particular number was divided by 4 and then 14 was taken away from that quotient. Finally, this difference was multiplied by 5. Given the product was -60, what was that number?

Lighthouse Math

Level G

Chapter 7

Exercise 6

133

These are multi-step word problems, so you will need to do at least two steps to find the answer.

Chapter 7-7 Order of Operations with Integers Daily Review

Solve.

1. 5 + 6 � 7 =

2. 20 � 4 � 8 =

3. 2 � 4 (10 � 7) =

Learn and Connect Two students solved the following order of operations problem. Look through their work. Find any mistake and determine the correct answer.

ORDER OF OPERATIONS

PEMDAS

Frank’s work

Chip’s work

Your work

Parentheses, ()

-3 + 8 � (-2)²

Exponents, an

-3 + 8 � -4

-3 + 8 � 4

Multiplication or Division (left to right)

-3 + -32

5�4 AS

Addition or Subtraction (left to right)

-35

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Solve. 1. -32 ÷ 4(2 � 5)

2. 12 ÷ 3 + 7 × 4 ÷ 2

3. 16 ÷ 4 + 5² × 3

4. -16 + 2 � (-5) × 2²

6. 8(5 + -3) ÷ -4(-9 + 5)

7. (-8)² ÷ 4 � 3 × 9

8. -4 + 2 (32 � 15)

134

42 -6 + 3

Level G

Chapter 7

Lesson 7

Lighthouse Math

Exercise 7-7 Name Circle the step that you would do first. 1.

-4 × 32 + 8

3(13 – 6)

(9 + 2 × 2) – 15 ÷ 3

E MD

3 × (-2)² ÷ 6

8 – 4(2 + 5²) ÷ 12

18 6+3x7

Solve. 7.

(-5) − 2 × (-9) + 6

8 ÷ (-4) × (-6) + 6

[50 + 3(4 – 9)] ÷ -5

10. 4 × (-8) + 6 − (-2)

11. 3 × 10 + 8 − 4²

12. (-8)(-5) 22 − 15

13. 10 × 5 − (-6)² + (-8)

14. (10 ÷ (-5) − (-2)) × (-3)³

15. 16 − [3(6 − 3) − 12]

16. 32 + 5 × 3

2 + 8(35 ÷ 7)

18. 1 − (9 − 4) ÷ 5

20 ÷ -4 − (-7 + 2)

17. 8 × (-2) – (-4)²

36 ÷ 9 − 2 × 5

19. 8 − (-4)² + 4 × 5

7 − 3(4 − 5)

Solve each problem and compare using <, >, =.

Challenge Write two expressions that simplify to -5 using the integers: -10, 3, -2, 8, 12. Numbers can be used more than once. 20. Example: (12 + -2) = 10 = -5 -2 -2

Lighthouse Math

Level G

Chapter 7

Exercise 7

135

Chapter 7-8 Review Daily Review

Order the expressions from least to greatest.

-3 � 4

-4 + -3

3 � 12

25 -5

Learn and Connect Solve. 1.

85 + (-96)=

80 + 57 =

6 + (-47) =

-32 + 48 =

22 + (-41) =

-18 + (-45) =

86 + (-38) =

-78 + 69 =

6 + (-33) =

10. - 43 + 81 =

11. -4.6 + (- 7.2) =

12. -17 + 6 + (-22) =

13. 1 � 3 =

14. 2 � (-5) =

15. 9 � (-6) =

16. -12 � 3 =

17. -7 � (-1) =

18. -7 � 4 =

19. 3 � (-2) =

20. -5 � (-8) =

21. -1 � 9 =

22. 9 � (-2) =

23. 8 � (-1) =

24. -7 � 3 =

Rewrite and solve.

Vocabulary Integer - a positive or negative whole number Zero Pair - a set of numbers that when added together equal zero (-1 and 1 or -3 and 3) Order of Operations - set of rules that tells you which order to do operations within a problem (PEMDAS)

136

Level G

Chapter 7

Lesson 8

Lighthouse Math

Exercise 7-8 Name Write an expression and solve. 1.

A city recorded one of India's highest temperatures, 51°C. Another city recorded one of India's lowest temperatures, -40°C. What is the difference between the highest and lowest temperature in India?

Tim has $35. If he wants a pair of sneakers that cost $55, how much more money does he need to save?

Daniel buys tickets for himself and his 5 friends for a carnival and he spent $150. How much does each friend owe him?

Jay had $256 in his savings account. He took $78 from the to buy some running shoes and $54 for a gift. How much money is in his account now?

You remove frozen turkey. It is -17°C. The temperature is increasing by 3°C every five minutes. After 30 minutes what temperature will it be?

-0.9 + (�1.5) =

10. -5.6 � (+4.4) =

13. -6.1 � 3.22 =

14. -5.4 + 3.31 =

The bakery pays $225 a month in advertising fees. How much will they spend in 4 months?

-1 -6 4 + 2 =

11.

6 -1 2 + 7 =

8 2 12. -5 � 10 =

-5 1 -3 � 6 =

Order of Operations with Negative Numbers. Solve. 15.

-(-30) ÷ (-5) � (-3) =

16.

(-25) � (-3) ÷ (-5) �(-90) =

17.

-(-9) ÷ (-3) � (-7) =

Challenge Use the following four integers -1, -10, 40 and 50 to create as many equations as you can with an answer of 45. You can use each integer only once. 18.

Lighthouse Math

Level G

Chapter 7

Exercise 8

137

Rational Negative Numbers. Solve.

Chapter 8 NYS NG Standards NY-6.EE.2 NY-6.EE.3 NY-6.EE.4 NY-6.EE.6 NY-6.EE.7

NY-7.EE.1 NY-7.EE.2 NY-7.EE.3 NY-7.EE.4

CC Standards 6.EE.A.2 6.EE.A.3 6.EE.A.4 6.EE.B.6 6.EE.B.7

138

7.EE.A.1 7.EE.A.2 7.EE.B.3 7.EE.B.4

Chapter 8 takes students' understanding of working with

Negative Numbers and Simplifying Expressions to Learning How to Solve Equations In this chapter students learn the foundations of algebra which will be key in their future mathematics instruction. They will learn: • What an equation is • The parts of an equation • Inverse operations • The distributive property • Using like terms © Lighthouse Curriculum. Copying strictly prohibited.

The skills that they will gain through these lessons include: • Using inverse operations to isolate variables to solve equations • Checking their work by evaluating their answer • Simplifying expressions by using the distributive property and combining like terms Some strategies that students will use are: visualizing equations as a balance scale, using the area method for distributing, analyzing common errors following a fourstep process for solving algebraic equations.

139

Chapter 8-1 Expressions Daily Review Write the operation (+, -, �, ÷) that the word represents . Decreased By Sum

Half

Less Than

Difference For Every

Product Out Of

More Than

Double/Triple

Quotient Together

Per Total

Learn and Connect Tom ordered some cookies for his family. He paid a total of $16.75 for all of the cookies. He bought 5 peanut butter cookies for $1.25 and 10 chocolate chip cookies that cost a different amount. Which expression shows how to find CC, the cost of each chocolate chip cookie? To solve, consider what Tom would have to do to find the total if he didn’t already know it. A. 5p + 16.75 = CC B. 1.25 � 10 = 16.75

C. 1.25(5) + 10(CC) = 16.75 D. 1.25(5) + 10(16.75) = CC

Remember, he is missing a number and will have to use a variable to represent that number. A variable is a letter or symbol that can hold the place of a unknown quantity. Since we already know the total, we will have to work backward to find the variable. What is the price of each chocolate chip cookie?

Apply There are different parts to expressions. Study the example then complete the table. © Lighthouse Curriculum. Copying strictly prohibited.

Expression term

Expression

term

3x + 5 coeficient

variable

constant

9x + 8

3m + 8n - 9

6 + 4z - y

1 g+5 2

# of Terms

Coefficient

Variable(s)

Constant

Write an expression for the math sentence or word problem below. 5. The sum of seven and a number is 18.

6. Milo earns $8 per hour. In a week he earns $104. How many hours, h, did he work?

A third of the class, c, is in the play. If there are 9 students in the play, how many are in the class?

Vocabulary Variable - a letter or symbol that represents an unknown quantity Constant - a number whose value is always the same Coefficient - the number in front of a variable Term - a single mathematical expression 140

Level G

Chapter 8

Lesson 1

Lighthouse Math

Exercise 8-1 Name Match the sentence with the equation that represents that situation. 1.

The seventh grade class has eight more students than the 6th grade class. If there are 65 students in 7th grade, how many 6th grade students are there?

Eight more than half of a number is 50.

You and your brother together have $65. If you have 8 more dollars than him, how much does he have?

35 � p = 23

A chapter has 35 pages. If you have read 23, how many pages are left to read?

s + s + 8 = 65

Fifty is twice a number plus eight.

The temperature was 35 degrees. It decreases some amount and then was 23 degrees. How much did it decrease?

What variables are used in the expressions above?

2n + 8 = 50 s + 8 = 65

23 + p = 35

1 n + 8 = 50 2

How many terms does each expression have?

10. Seven students represent one third of the class. How many students are in the whole class?

11. To complete a science lab the temperature needs to be -5 degrees. Now it is 12 degrees. How much will it need to drop to do the lab?

12. The sum of a number and 15 is 42.

13. The product of a number and 8 is 48.

14. Half of a number take away 3 is 19.

15. There are 120 raffle tickets, and you divide them evenly between guests. If each person gets 8, how many people are there?

16. Of the 20 parks, 2 more than half have swing sets. How many have swings?

17. The field trip cost $3 per student. If the chaperone collected $42, how many students attended?

Morris earns $15 per bench he builds. How many benches will he need to build to earn $75?

Lighthouse Math

Level G

Chapter 8

Exercise 1

141

Write an expression to represent the situation or sentence.

Chapter 8-2 Combining Like Terms Write an equation for the scenario.

Daily Review

1. A number take away 18 is 34.

2. You earn $3.50 per batch of cookies sold. How many do you need to sell to earn $24.50?

Learn and Connect Harry volunteers at the local community garden. He went to pick some vegetables after school on Wednesday. He picks 5 tomatoes, 7 carrots and then picks 3 tomatoes from another tomato plant. He records what he takes home on his way out and he writes. 5t + 7c + 3t

Harry could have also written 8t + 7c. But he could not have written 15tc. Why does one expression work and not the other one?

Apply Study the example and then combine like terms to simplify the expressions.

Step 1

3x - 7 + 4y - x + 2

Step 2

3x -x

-7 +2

+4y

Step 3

-5

+4y

Hints: We included the operation before the constant or coefficient. Use your integer rules to help you combine!

142

8p � 6 � 3p

14m � 2 + 8m

4 � 5v + 1 + 10v

2t � 4t + 1 � 8t

9 + x � 5z + 6z � 6x

8h � 5z � 7 + 5z + 5 � 4h

2t � 4t + 1 + 8t2

-2h2 � 3h + 5 + 4h2 + 4

7c � 6 + 3a + 5 � 4c � a

10. 5g2 � 3g + 8 � g2 + 7g � 5

Level G

Chapter 8

Lesson 2

Lighthouse Math

Exercise 8-2 Name Draw a line to the expression with the correct simplified expression by combining like terms. 1.

a+b+a+a

2a + b

5a + 6

5a + b + b � 2a

3a + b

5a + 1 + 2 + 3 + 1

6a + 6

5a + 2b � b � 3a

3a + 2b

2 + 10a � 5a + 4

5a + 7

5b + a + a � b � b

2a + 3b

5 � 3 + 6a � a

6a + 7

b + 6a + b � 5a

a + 2b

3a + 1 + 1 + 1 + 3a + 4

5a + 2

5a + 1 + a + 5

-6g

3g2

5y2

-3y

-7y2

3h2

-7

-w

9w2

-2w

3w2

5ab

+4a

3ab

-2ab

-10r

13r3

-9r3

-x

-2x

10.

4m2

-m2

Circle the terms that can be combined in each row. In the last column simplify them into one term.

Challenge Combine like terms. 11. -8y + 7x + 9 � x2 + 12x + 10y + 5x2 � 4 � 7y + 14 � 3x

Lighthouse Math

Level G

Chapter 8

Exercise 2

143

Chapter 8-3 Distributive Property Circle terms that can be combined with 6x, box terms that can be combined with y2 . Then simplify the expression by combining like terms.

Daily Review

1. -4y2 + 8y + 5x - 3x2 - 8x + 3y2 - x

Learn and Connect Harry returns to the community garden on the weekend, but this time he packs boxes of vegetables for the community. Each box is the same and has 2 beets, 4 potatoes and one cauliflower. If he packs 5 boxes, how many of each vegetable did he pick? 2b + 4p + c represents how much was in one box. 5(2b + 4p + c) represents how many vegetables he uses in total.

10b

20p

So if we simplify 5(2b + 4p + c) = 10b + 20p + 5c. He picked 10 beets, 20 potatoes and 5 cauliflower.

Apply Complete the table using the distributive property.

Expression

Work

Example 7(4x � 6)

7 ∙ 4x � 7 ∙ 6

Simplified Expression

28x � 42

2(-2g + 8)

4 ∙ 7a + 4 ∙ 3b + 4 ∙ c

-3(3m + 5)

-5(4t � 8s + 4)

1 (10m + 6) 3

3 ∙ -m + 3 ∙ 7 � 3 ∙ 3n

1 1 3 ∙ 3g � 3 ∙ 12

Vocabulary Distributive Property - allows you to multiply a sum by multiplying each addend separately then add the terms. The example shows the distributive property can also be used in subtraction: 3(2x - 4) = 6x - 12

144

Level G

Chapter 8

Lesson 3

Lighthouse Math

Exercise 8-3 Name Place the letter of the simplified expression next to the expression. 1.

-4(-4x � 5)

-6(8x + 3)

2(3x � 8)

(2 � 5x)(-5)

1 2 (-2x � 6)

-9(x � 4)

(-5x + 1)(-2)

1 4 (-16x � 8)

- 31 (-9x + 30)

10.

(3x � 2)(-3)

Answer Choices: A -x � 3 B -48x � 18 C 16x + 20 D -9x + 6 E 6x � 16 F -4x � 2 G -10 + 25x H 10x � 2 I -9x + 36 J 3x � 10

Review the example. First use distributive property, then if needed combine like terms. Example:

11.

-2(n � 9) + 4

12.

-6 + 9(8 � 2b)

13.

6x � 3(2 � 3x)

14.

-8(-2r � 2) � 6r

15.

-3(a + 1) + 6

16.

-2(-3 � 3n) + 1

-3(5x � 4) + 7x

Distribute

-15x +12 + 7x

Combine

-8x + 12

-3(5x � 4) + 7x

Challenge Write an expression to represent the scenario, then simplify the expression. 17.

You are building picnic tables for the park. Each table needs 3 six foot boards, 5 two foot boards, 25 nails and 8 bolts. You are building 8 picnic tables. You want 20 extra nails and 2 extra bolts. How much of each material should you purchase?

Lighthouse Math

Level G

Chapter 8

Exercise 3

145

Chapter 8-4 Solving One-Step Equations Daily Review 1. 3 +

What would you put in the blank to make the equation true? 2. 10 �

3. 7 �

= 21

How would you figure out the value of the blue box, x, in the picture to the right?

x+2

We could take away 2 blue dots but to keep the scale balanced we need to do it to both sides. So x = 5. We could represent this algebraically by writing the following equation:

4. 30 �

Learn and Connect Inverse Operations

Addition

a·b

Multiplication

Subtraction

1 3

Division

Apply

x+2=7 �2�2 x=5

Determine the operation in the original problem, what the inverse operation is, then solve. Look at the first box for an example. Problem

Operations

Example

3x = 18 �3 �3 x=6 1. 10 = z + 6

2. q � 12 = 1

3. r = 7 3

Original: × Inverse: � Original: Inverse: Original: Inverse: Original: Inverse:

Problem

4. t � 19 = 2

5. 24 = 4c

6. 8y = 48

7. 18 = a 2

Operations

Original: Inverse: Original: Inverse: Original: Inverse: Original: Inverse:

Problem

8. 11 = m � 4

9. 1 + s = 3

10. v = 9 5

11. -m = 5

Operations

Original: Inverse: Original: Inverse: Original: Inverse: Original: Inverse:

Vocabulary Equation - two expressions or terms that are set equal to each other, 3x + 8 = 17 Inverse operations - operations that are the opposite of each other, addition & subtraction, multiplication & division Variable - an letter or symbol that represents an unknown quantity

146

Level G

Chapter 8

Lesson 4

Lighthouse Math

Exercise 8-4 Name x 1/2 is the same as ÷ 2

Solve the equation using inverse operations. 1.

2x = 8

p+4=1

m�3=4

1 g=7 2

y+6=4

-7t = 49

10k = 60

t = -4 3

12 = 2p + 4p

10. 51 w = -3

11. -48 = -10g + 2g

a = 24 12. -6

Write the number of the equation and letter of the solution for each scenario.

14. When Ethan stands on a box, he is 10 feet tall. If the box is 4 feet tall, how tall is Ethan? 15. A store is selling rulers in packages of 5 for $9. What is the cost of one ruler? 16. The speed limit in the city is 25 mph. This is half the speed outside of the city. What is the speed limit outside the city? 17. Arman has $40 in his savings account. He made 5 deposits of the same amount. How much was each deposit? 18. Each sandwich gets 1.5 ounces of turkey. If you have 15 ounces, how many sandwiches can you make?

Equations 1) 5x = 40 2) 10 � x = 3 3) 5x = 9 4) 4 + x = 10 5) 1.5x = 15 6) x � 2 = 25 Solutions A) x = 10 B) x = 6 C) x = 50 D) x = 1.8 E) x = 7 F) x = 8

Challenge If t = -3 and r = 4, find the value of the expressions. 19. 3t � 2r

Lighthouse Math

20. r � 2 � t

21. rt � 3t + 4r

Level G

Chapter 8

Exercise 4

22. -rt � -3

147

13. There is a total of 10 pages of homework. Ron worked on some pages on Monday. If he has 3 pages left, how many pages did Ron work on Monday?

Chapter 8-5 Two-Step Equations Daily Review

Solve the equations below.

1. -6x = 42

2. h 5 = 12

3. m � 8 = -5

4. 7 + p = 10

Learn and Connect How would you find the value of x in the image to the right? Use math vocabulary to explain what you would do.

2x + 3

x x

Knowing what we know about inverse operations, study how we would show this algebraically.

2x + 3 = 7 -3 -3 2x = 4 2 2 x=2

Apply Solve the problems and check your answer by plugging in the solution.

Problem Example

Check

n �8=1 3

27 � 8 = 1 3

+8 +8

n =9 3

Problem

Check

3. 1 - 4k � 10 = -5

9�8=1

�3 �3 n = 27 1. 5t - 4 = 16

4. 4p + 3 = 1

2. 8 + 4c = 48

5. 9 � y � 7 = 5

Vocabulary Inverse operations - operations that are the opposite of each other, addition & subtraction, multiplication & division 148

Level G

Chapter 8

Lesson 5

Lighthouse Math

Exercise 8-5 Name The first step will be to +/-. The second will be to x/÷.

Match equations that have the same answers . 1. 2. 3. 4. 5. 6. 7. 8.

Equation options: A. -10x + 5 = 55 B. 32 = -8 + 2x C. 4x � 30 = 34 D. -19 = -5x � 4 E. -x + 8 = 14 F. 4x + 12 = 60 G. x + 15 = -30 H. 12 = 8x � 4

-2x + 7 = 19 x � 8 � 10 = -8 1 x�9=-5 3 5 � m = 10 14 = -x � 3 � 1 -x + 13 = 10 10x � 10 = 10 -x � 4 + 7 = 2

Circle the error in the following problems, then solve them correctly. 10. 2x + 4 = 10 2 2 x+4=5 �4�4 x=1

4 � 2x = -2 +4 +4 2x = 2 2 2 x=6

11.

x � 5 + 8 = 18 �8 �8 x � 5 = 10 � 5 �5 x=2

When the fraction bar is under both terms, multiply by the denominator first.

Solve the equations. 12.

a+8 =3 9

13.

n + 31 =2 4

14.

w+6 =3 3

15. 0.4x + 2.9 = 1.5

16. v � 2.2 – 0.1 = 7.4

17. -1.3g + 1.9 = -11.1

18. - 32 p + 83 = -3p

19. 27 = 45 + 9q

9 20. 5 21 – u = 4

Challenge If -6x + 12 = 0 and 4y + 5 = 9, what is the value of x + y? 21. a) 3

b) -1

Lighthouse Math

c) 2

d) -4

Level G

Chapter 8

Exercise 5

149

Chapter 8-6 Multi-Step Equations Simplify the expressions.

Daily Review 1. -4(2x � 6) =

2. 3m � 9 + 4m + 5 =

3. 21 (6m � 10) � 4m + 5 =

Learn and Connect Looking at the problem to the right, how would you define what happened in each step? Step 1: Step 2: Step 3:

Step 1

6(1 + 2m) � 3m = 24

Step 2

6 + 12m � 3m = 24

Step 3

6 + 9m = 24 �6 �6 9m = 18 9 9 m=2

Step 4

Step 4: Following those steps, how would you solve: -4(2 + 3b) + 5b = 13

Apply

Solve the problems using the steps above. Note that not all problems will have all 4 steps. 1. 6c + 2(c + 3) = 38

2. 6y + 3(y � 4) = 33

3. 56 = 8(-x + 2)

4. 6(x + 4) + 3x � 2 = 58

5. 6 = b + 11 � 2b

6. 3x + 12 + 5 = 35

7. 5 (c + 2) = -20

8. -5x + 3(x + 1) � 4x = 45

9. 9y + 3(y � 6) = 30

10. 12a + 5 � 8a = -3

11. 2(x � 7) = 10

12. 5(a + 3) + 6(a + 1) + 8a = 40

Vocabulary Like Terms - terms that have the same variable and are raised to the same power Distributive Property - allows you to multiply a sum by multiplying each addend separately then add the terms. 3(2x - 4) = 6x - 12

150

Level G

Chapter 8

Lesson 6

Lighthouse Math

Exercise 8-6 Name These problems were solved incorrectly. Circle the incorrect steps and find the answer. 2.

2x + 6(x +3) = 34 2x + 6x + 3 = 34 8x + 3 = 34 �3 �3 8x 31 8 8 31 x= 8

6(x + 2) � 4x = 30 6x + 12 � 4x = 30 10x + 12 = 30 10x 18 10 10 4 x=1 5 1. Distribute 2. Combine 3. Remove constant 4. Remove coefficient

Solve the problems below. 3.

-152 = 4x � 4(-4x � 22)

4. 6x + 3(-6x � 11) = 39

4x � 3(-3x + 6) = -135

6. -3x + 2(-3x + 16) = 104

209 = -5x + 3(6x + 22)

8. -7x + 2(-2x � 18) = -135

7x + 3(-7x � 16) = 92

10. 7x + 5(4x � 14) = -205

Challenge 11. Write an equation with distributive property that is equal to 4.

Lighthouse Math

Level G

12. Write an equation with combining like terms that is equal to -2.

Chapter 8

Exercise 6

151

Chapter 8-7 Equation Word Problems Daily Review

Solve the equations.

1. 6a + 5a = -11

2. a − 2 + 3 = -2

3. 18 = 3(3x − 6)

Learn and Connect You have 52 balloons to give to the guests at your little brother's birthday. You save 10 for decoration and you give each guest 2 balloons. Write an equation to represent this scenario.

What is the most guests that can come if they each got 2 balloons?

What if you gave each person 3, how does the equation change? How many guests can come?

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Write an equation to represent the scenario. Then solve to find the solution. 1.

Abe took a taxi home from the airport. The taxi fare was $2.10 per mile, and he gave the driver a tip of $5. If Abe paid a total of $49.10, how many miles was his ride?

Each student in your class has an equal number of colored pens. Your teacher has seven colored pens. In total, there are 97 colored pens in the classroom. How many total colored pens does each student have?

Each of 5 gift bags contains pencils. Tyler adds 3 more pencils to each bag. Altogether, the gift bags contain 20 pencils. How many pencils are in each gift bag?

A printing company charged $38.50 to print your book. They charge $12 to have service and $0.25 per page. How many pages is your book?

152

Level G

Chapter 8

Lesson 7

Lighthouse Math

Exercise 8-7 Name Write a scenario that could be represented by the equation. Then solve and ensure your answer has the correct units based on the context of your scenario. 1.

8m = 56

t - 12 = 15

3m + 4 = 13

1 2 x + 5 = 10

Larry lends half his collection of hats to his brother, Ben. Larry then buys four more hats. If he has 12 hats now, how many hats did Larry have initially?

Peter bought 18 bottles of juice for the picnic. If he bought twice as much apple juice as grape juice, how much of each juice did he buy?

A car traveled 184 miles. If it was traveling at a rate of 46 miles per hour, how many hours did they drive?

At the antique fair, your uncle buys a lamp for $22, your dad buys a bench for $35 and you buy 3 books. If your family spend $75, how much was each book?

A new one-year membership at Rec Center costs $160. A registration fee of $28 is paid up front, and the rest is paid monthly. How much will you pay each month?

10.

The sum of the three angles of a triangle is 180°. If one angle is 50° and the other two are equal, how many degrees are the other angles?

Challenge The sum of three consecutive, in a row, numbers is 84. What are the three numbers? 11.

Lighthouse Math

Level G

Chapter 8

Exercise 7

153

Write an equation to represent the scenario. Then solve to find the solution.

Chapter 8-8 Review Daily Review

What operations are the inverse of the given operation?

1. Addition

2. Division

3. Multiplication

4. Subtraction

Learn and Connect Simplify the expressions by combining like terms. 1. What two things must be the same to be like terms?

3m + 4n � 6n

12 + 9x � 6x � 19

4g + 6g � 3g

y2 + 3y2 � 6y + 4y2

15f � 5 + 2f

2 � 5t + 8 + 5t �8

Simplify the expressions by distributing and combine like terms if needed.

8. Describe distributive property in your own words.

4( x + 7 )

10. 31 (3x � 6 + 12y)

11.

1 2 (6m � 4 + 2m)

12. -(-4x + 15)

Use inverse operations to solve the equations below. 13. When solving equations, how can you check to see if your answer is right?

14. 4x = 32

15. M � 6 = -2

Vocabulary Inverse Operations - operations that are the opposite of each other: addition & subtraction, multiplication & division Variable - an letter or symbol that represents an unknown quantity Like Terms - terms that have the same variable and are raised to the same power Distributive Property - allows you to multiply a sum by multiplying each addend separately then add the terms 3(2x + 4) = 6x + 12 154

Level G

Chapter 8

Lesson 8

Lighthouse Math

Exercise 8-8 Name Using inverse operations, solve the equations below. 1. When solving 2-step equations what term do you start with first? What is the second step?

2x � 1 = -5

-3 = 5k + 7

b 2=7+ 4

5. What order do you use to complete the steps for multi-step problems?

4(x + 7) = -12

18 = 3(3x - 6)

16 = -7x � 5x � 8

-19 + 3x � 11 + 2x = 5

10. 2(x + 5) + 3x = 20

11.

1 3 (9x � 15) + 8 = 27

Write an equation then solve the equation to find the answer. 12. Rick is building a multistory house made of 336 wooden sticks. Each story of the house uses 56 plastic sticks. If he has already built 4 stories, how many more sticks does he have?

13. The Elk Grove Ice Cream stand offers a special. Each cone costs $2.50, and ice cream scoops cost $2. You spent $14.50 total. How many scoops of ice cream did you get?

14. The bill for the repair of a car window was $179. The cost for parts was $44, and the labor charge was $45 per hour. How many hours did it take to repair the car window?

15. You and three friends go to the town fair. You have a coupon for $20 off. If the total bill to get into the fair was $100, how much does one regular price ticket cost?

Lighthouse Math

Level G

Chapter 8

Exercise 8

155

Solving multi-step problems.

Chapter 9 NYS NG Standards NY-6.RP.1 NY-6.RP.2 NY-6.RP.3 NY-7.RP.1

NY-7.RP.2 NY-7.RP.3 NY-7.G.1

CC Standards 6.RP.A.1 6.RP.A.2 6.RP.A.3 7.RP.A.1

156

7.RP.A.2 7.RP.A.3 7.G.A.1

Chapter 9 reviews and builds

Skills with Ratios Students will expand their understanding of ratios to include equivalent ratios, proportions and scale. Students will review what ratios are and the different ways to write them. They will learn that there are multiple ways to solve proportions including finding unit rate/unit ratio and see how this can be helpful to solve certain problems. Then students will apply these concepts to scale to find missing sides of figures and in real world contexts.

They will learn: • How to find equivalent ratios • How to find and use unit rate • How to find scale factor • How to solve proportions The skills that they will gain through these lessons include: • Finding factors the create equivalent fractions • Cross multiplying to solve proportions • Identifying unit rate • Finding the scale factor • Using scale factor to solve problems The key vocabulary terms for this unit are: ratio, per, unit rate / unit ratio, unit price, equivalent ratios, proportion, scale image, scale factor

157

Chapter 9-1 Introduction to Ratios Daily Review

Use the image of the marbles to answer the questions.

How many marbles are… 1. White

2. Striped

3. Black

4. Total Marbles

Learn and Connect Thomas and his mom are baking cookies for their neighbors. Here is the recipe card. One batch makes 20 cookies. Flour

2 cups

Sugar

3 4 cup

Eggs

Vanilla

2 tsp

Baking Soda

1 tsp 2

Butter

3 cup 4

What is the ratio of flour to eggs? What is the ratio of flour to sugar? What is the ratio of vanilla to eggs? What is the ratio of cookies to eggs? What is the ratio of baking soda to butter? What is the ratio of vanilla to cookies?

Apply 1. To make a gallon of green paint, we need 5 pints of blue and 3 pints of yellow. Yellow : blue Gallons : yellow

Blue : yellow Blue : total pints

2. The class has 10 students with glasses and 13 students without glasses. With glasses : without glasses Without glasses : with glasses Total students : with glasses

3. A recipe calls for 1 cup of sugar for every 3 cups of flour for 12 muffins.

Sugar : flour Flour : muffins

Flour : sugar Sugar : muffins

4. In the park, there are 3 oak trees to every rose bush. Oak trees : rose bushes Rose bushes : oak trees Total plants : rose bushes

Vocabulary Ratio - a ratio is a way to compare two quantities or amounts. They can be written in three ways - 3:2, 3/2, 3 to 2 158

Level G

Chapter 9

Lesson 1

Lighthouse Math

Exercise 9-1 Name Determine the ratio indicated based on the set of images.

1. Tomatoes to onions

2. Chairs to furniture

3. Glasses to mugs

4. Pumpkins to vegetables

5. Short sleeve to long sleeve

6. Camels to animals

Read the scenario and write the ratio as a fraction. 8. The store sells hats and shoes. For every 10 purchases made 3 are hats. What is the ratio of…

9. T he library has 80 new books. Of those books, 25 are non-fiction and the rest are fiction. What is the ratio of…

a. sunflowers to tulips

a. shoes to hats

a. non-fiction to fiction

b. flowers to sunflowers

b. hats to purchases

b. fiction to non-fiction

c. tulips to flowers

c. purchases to shoes

c. books to fiction

Challenge E

10.

What is the ratio of states that touch an ocean to states that do not touch an ocean?

D y/ K

Lighthouse Math

Level G

Chapter 9

Exercise 1

159

7. A bouquet has 15 flowers. 5 are sunflowers and the others are tulips. What is the ratio of…

Chapter 9-2 Equivalent Ratios Daily Review

Write the ratio.

James was picking up shells. For every 4 shells he picked up, 2 of them had holes in them. What is the ratio of total shells to shells with holes in them? Write the answer 3 ways.

Learn and Connect Thomas and his mom are baking cookies for their neighbors. Each batch makes 20 cookies. One batch uses 2 cups of flour and 1 egg. Fill out the table below based on the number of batches. Batches

Flour (c) Eggs Cookies

If you wanted to make 200 cookies, how many eggs and flour would you need?

Apply Study the example and then write 4 sets of equivalent ratios for each ratio provided. 2:3

2 3

1. 2 5

2�2 4 3�2 � 6

4:6

2�5 10 3 � 5 � 15

10 : 15

2:3 and 4:6 and 10:15 are all equivalent ratios

2. 3 to 4 3. 1 : 5 4. 4 to 10 1

5. 3 6. 3 : 7 7. 25 8. 8 to 9

Vocabulary Equivalent - equal Equivalent Ratios - a set of ratios where one ratio is a multiple of the ratio. 1 is equivalent to 3 2 6 160

Level G

Chapter 9

Lesson 2

Lighthouse Math

Exercise 9-2 Name Fill out the tables to make equivalent ratios. �4

�6 6

7 9

�6 �4

108

128

5. 5 6

40 54

6. 3 7

15 35

9 24

12 32

8. 5 6

9 21

9. 30 36

5 6

10. 8 3

40 15

11. 18

4 45

12. 5

3 5

13. 5

4 9

Read the story problem, set up an equivalent ratio and solve. 14. Crackers cost $1.05 for 3 packs. How much would 6 packs cost?

15. Oliver ran 5 km in 27 minutes. How long would it take him to run 15 km?

16. F or every 5 people that walk to school, 3 ride their bike. If 20 people walk, how many ride their bike?

Challenge 9 cm

What is the ratio of…

18. Length : perimeter

4 cm

17. Length: width Hint: A= L x W, P=Add all 4 sides

19. Perimeter : area

Lighthouse Math

Level G

Chapter 9

Exercise 2

161

Are these equivalent ratios? Write = if they are and ≠if they are not.

Chapter 9-3 Unit Rate & Unit Ratio Daily Review 1.

Find the missing number in the equivalent ratios.

1 3 = 9

2 4 5 =

3 5 = 15

= 50

Learn and Connect Brad, Jordan, and Harry go to the carnival and buy tickets to play games. Write the ratio of tickets to dollars: They spend $8 on tickets, how many tickets did they buy?

What is the price per ticket? Per means for 1.

How many tickets can you buy per dollar?

Apply Study the example, then find the unit ratio for each of the following problems. If Charlie can write 100 words in 2 minutes, how many words can he write per minute?

1. 3 in. of snow in 7 hours

2. 11 paper towels cost $16

3. $6 for 2 cans of soup

4. Mowed 4 yards for $25

5. 145 miles on 8 gallons of gas

6. 4 pans for $120

7. $ 16 for 8 books

8. 7 circus tickets for $31.50

9. 5 pillows for $12

1. Write your original and unit ratio 100 words �2 2 minutes = � 2 =

(

) words 1 minute

2. Find the factor you need to divide your ratio by to get the unit ratio 3. Divide to find the answer 100 � 2 50 words per minute

Vocabulary Per - for every one, division. 55 miles per hour = 55 miles in 1 hour Unit Rate/Unit Ratio/Unit Price - the amount for 1 of something 162

Level G

Chapter 9

Lesson 3

Lighthouse Math

Exercise 9-3 Name Find the unit price for each option and compare to find the best buy. COLUMN A

UNIT RATE A

COLUMN B

1 apple for $0.19

3 apples for $0.60

20 pounds of pet food for $15

50 pounds of pet food for $38

A car that travels 308 miles on 11 gallons of gasoline

A car that travels 406 miles on 14 gallons of gasoline

10 pens for $9

25 pens for $19.75

1-gallon can of paint for $14

5-gallon can of paint for $67.45

UNIT RATE B

BEST BUY (A OR B?)

Find the unit rate and use it to find the missing information. 6. Jeremiah bought 3 pairs of shoes for $71.40. A. Find the unit rate. B. How much would 8 pairs cost?

C. How much would 2 pairs cost?

7. Howard received 42 tickets from playing 3 games.

B. How many tickets would Howard win in 5 games?

A. If he received an equal amount of tickets per game, how many tickets did he win in one game? C. In 6 games?

8. Andy drove 840 miles in 12 hours. A. How many miles did he drive per hour? B. How far could he drive in 3 hours?

C. In 8 hours?

Challenge 9. Peter drives 825 miles to California. The trip takes 17 hours. He uses 38 gallons of gas on the trip, which costs him $125 in all.

Lighthouse Math

Find his speed. Find his gas mileage. Find the unit price he paid for gas.

Level G

Chapter 9

Exercise 3

163

Chapter 9-4 Introduction to Proportions Fill in the missing numbers in the tables to make equivalent ratios.

Daily Review 1.

3 4

2 7

Learn and Connect Nathan is going to take the train to his aunt’s house. Look at the sign for the different ticket options. How much is each ride if he buys the 10 ride pass?

If he needs to take 4 rides today, find the cost with the 10 ride pass.

Here is another method to solve. What do you notice?

$ 12 ? ride 10 = 4

12 � 4 = 10 � ? 48 10 � ? 10 = 10

x = $4.80

Each ride costs ___________if you a buy a package of 10 ride.

Apply Study the example and then solve the problems provided. x 2 9 = 3

Cross-Multiply

(x) (3) = (2) (9)

Set the cross-product equal to each other

3x 18 3 = 3

x=6

Divide both sides by 3 to get x by itself.

12 1. 2r = 18

50 5 2. 20 = h

3d 3. 16 6 = 9

x 4. 45 27 = 3

v 2 5. 84 = 21

8 6. b8 = 64

26 7. 13 3 = c

72 8. 27 15 = a

5 9. 15 n = 12

Vocabulary Proportion - comparison between two amounts can be solved by cross multiplying 164

Level G

Chapter 9

Lesson 4

Lighthouse Math

Exercise 9-4 Name Decimals can also be used in proportions. Solve these proportions and round to the nearest hundredth if needed. 1.

12 8 n = 3

5.6 n 2 = 4

n 1 3.5 = 7

3.6 1.2 15 = n

2.8 n 7 = 4

18 n 25 = 7

n 4 3.7 = 29.6

1.5 1.2 n = 7

Study the example and steps. Solve the proportions below. Steps: 1. Cross Multiply 2. Distribute 3. Solve using inverse operations

3 x�3 6 = 8

10. x � 1 = 2

11. x + 3 = 7 4

12.

7 a�6 12 = 4

13. x + 7 = 15

14. 3 =

6 x+3

-4

12(3 + x) = 7 (8) 36 + 12x = 56 -36 -36 12x = 20 12 12

3+x 7 8 = 12

x = 1 32

Challenge Find the ratio of area to perimeter for each square. 15.

16.

1 in

2 in

Lighthouse Math

17.

18.

3 in

Level G

4 in

Chapter 9

Exercise 4

165

Chapter 9-5 Proportion Word Problems Daily Review 1.

Solve the proportions.

2 3 x = 9

60 x 3. 100 = 80

x 2 3 = 8

Learn and Connect Ben and Tom both solved the following problem correctly, but their work is different. What do you notice about how they set up the problem?

For every 12 students on the field trip the school needs 1 chaperone. If 60 students go, how many chaperones are needed? BEN

TOM

students : chaperone

students chaperone

12 60

What do you notice about their work?

= x1

�5 12 60 1 = x

�5

12x 60 12 = 12

1�5=5

x=5 5 chaperones

5 chaperones

Apply

Read the scenario, write the proportion and solve. 1. Seth reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall?

2. One cantaloupe costs $2. How many cantaloupes can you buy for $6?

3. A cookie recipe calls for 3 eggs and makes 4 dozen cookies. How many (dozen) cookies could you make with a dozen eggs?

4. Before going to Samoa, Mitchell did some research and the exchange rate is 6 Tala for $2. How many Tala would he get if he exchanged $12?

5. An outdoors club uses 12 batteries on a three-night camping trip. If they are planning a seven-night trip, how many batteries should they bring?

6. There are 6 cups of detergent in a bottle. If 1 3 cup is need for 1 load of laundry, how many loads can be cleaned with one bottle of detergent?

166

Level G

Chapter 9

Lesson 5

Lighthouse Math

Exercise 9-5 Name Proportions are used with exchange rates when traveling or doing business with other countries. Use the charts to determine the amount of money in different locations. 1. How many pesos do you have if you exchange $25 USD?

3. Y ou have $50 USD. How much is that in Australia?

2. I f an item costs ¥28, how many USD is it?

EXCHANGE RATE FOR $1 USD Euro

4. I f an item costs £12.96, how many yuan is that?

€ 0.85 (euro)

Australia

﹩1.33(aus. dollar)

England

£0.72 (pound)

Mexico

$20.00 (peso)

China

¥6.48 (yuan)

USD is “U. S. Dollars”

5. A bag of 8 apples costs $1.50 at Sam’s Orchard.

6. A rnold can ride his scooter 18 miles in 50 minutes.

7. Will’s Widgets can produce 2 21 tons of widgets in an 8 hour day.

a. At this same rate, how much would 18 apples cost?

a. At this same speed, how far can he ride in two hours?

a. H ow many widgets can they produce between 8am & noon?

b. H ow many apples could you buy for $5.00?

b. H ow long would it take for him to ride 4 miles?

b. How many work days will it take to make 17 tons of widgets?

c. W hat is the unit cost per apple?

c. What is his unit rate in miles per hour?

c. What is the unit rate of hours per ton of widgets?

Challenge Set up a proportion to help you solve. 8. The ratio of boys wearing white and boys wearing blue in Mr. Alper’s math classes is 5 : 7. If there are 60 students in all of his classes, how many are wearing white? How many are wearing blue?

Lighthouse Math

Level G

Chapter 9

Exercise 5

167

Use proportions to help you solve and then round to the nearest cent or tenth. Be sure to round to what makes sense in the situation (You cannot buy part of a product).

Chapter 9-6 Scale Figures Find 3 ratios that are equivalent to the given ratio.

Daily Review 1.

Learn and Connect Let’s see if the following shapes are scale models of each other. Scale models are like equivalent ratios, because the ratio of the sides are equal. Fill in the table of side lengths. A base

height

If D is a scale figure of the others, what would the missing side be? How did you find the side?

Are shapes A & B scale images?

B & C?

A and C?

Apply Set up a proportion to help find the length of the missing side. 15 10

12 25

Scale factor from A to B = 2:7

10 14

5 6

Scale factor from A to B = 5:6

Vocabulary Scale - Increase or decrease the size or quantity of something 168

Level G

Chapter 9

Lesson 6

Lighthouse Math

Exercise 9-6 Name Set up a proportion to solve for the missing dimension. 1. If 4 inches represents 100 miles on a scale drawing, how long would a line segment be that represents 50 miles?

2. On a map drawn to scale, 7 cm represents 280 km. How many kilometers are represented by a line 8 cm long?

3. On a scale drawing, 4 inches = 25 miles. If a line on the drawing is 6 inches long, what distance does this represent?

4. On a map drawn to scale, 2 cm represents 800 km. How many centimeters would 200 km represent?

5. If 3 inches = 90 miles, how long would a line be that represents 240 miles?

6. A sketch of a conference room represents 6 feet with 1 inch. How wide is the conference room if the drawing is 3 inches?

Find the missing side. Remember to check that you are using the correct, equivalent side. K 6

? 48

11. 34

12.

x y

B 3 A

X= 91

13.

14.4

5 Y

10.

?= 15

9. J

14. 12.5

91 x

5 4

7 11 4

Challenge Draw 2 images that are scale copies of the provided image and 1 that is NOT a scale copy. Label the side lengths.

Lighthouse Math

C 7 cm A

6 cm

Level G

4 cm B

Chapter 9

Exercise 6

169

Chapter 9-7 Scale Factor & Scale Word Problems Daily Review

Determine the new dimensions of the rectangle on the right for each scenario.

1. Sides are double

2. Sides are tripled

3. Sides are halved

Learn and Connect Leon went to the park to climb his favorite tree. He was wondering how tall it is, but he can’t climb all the way to the top to measure. He is 4.5 feet tall and his shadow is 2 feet long. If the shadow of the tree is 10 feet long, how tall is the tree?

Scale is the factor that is used to make equivalent ratios or helps us solve a proportion. What is the scale between the boy and the tree?

10 ft 2 ft

Study the example then find the scale factor and use it to find the missing side.

9 ft

3.6 km

C 6.6 ft

6 ft

1. 7f

Apply

10.08 km

8.8 km

7.2 ft

5.1 ft

5.61 ft

scaled figure original figure

9 6 = 1.5

4. 39.5 ft

scale factor = 1.5

6.6 � 1.5 = 9.9 7 � 1.5 = 10.5

3.4 m

8.16 m

8.1 ft D

98.75 ft D'

38.7 ft

2.6 m

Vocabulary Scale Factor - the amount by which a quantity is changed, whole number increases, fraction/decimal decreases 170

Level G

Chapter 9

Lesson 7

Lighthouse Math

Exercise 9-7 Name Use the given scale factor to identify the missing side lengths. y

2. y

12 in

4 ft

3. S

20 yd 5 in

9 ft

scale factor A to B is 1 : 2 5 1 x = 2

scale factor Q to P is 1 : 3

10 yd

scale factor S to T is 4 : 1

5 y 10 = 12 y = 6

x = 10

2 in

5. H

7 in

scale factor G to H is 1 : 7

D x

3 ft

scale factor C to D is 5 : 1

8 yd

35 ft

88 yd

scale factor N to M is 8 : 1

A new school is being built. A scaled drawing, using 9 6 inches to represent 2 feet, was created to reflect the sizes of each room. Complete the table with the missing dimensions. ROOM

DRAWING LENGTH

Lobby

Principal’s office

Library

10.

School Room

3 inches

11.

Science Lab

1.5 inches

12.

Cafeteria

13.

Music Room

4 inches

14.

Gymnasium

13 inches

15.

Auditorium

16.

Teacher’s Lounge

ACTUAL LENGTH 16 ft

1.25 inches © Lighthouse Curriculum. Copying strictly prohibited.

20 feet

48 feet

56 feet 1.75 inches

Challenge Use the conversion chart to find the missing information. 17. c =

tsp

19. 3 c =

Lighthouse Math

fl. oz.

18. 32 Tbsp = 20. 16 oz =

fl. oz. ml

Level G

Cup =

Teaspoon Fluid Ounce Tablespoon = = = Milliter (ml) (Tbsp) (tsp) (fl. oz.)

16 Tbsp

Chapter 9

48 tsp

Exercise 7

8 oz

237 ml

171

Chapter 9-8 Review Circle the ratios that are equivalent to 2:3.

Daily Review 1. 1:3

2. 4:6

3. 3:2

4. 20:30

5. 10:15

6. 4:3

7. 22:30

Ratios 2. T o make purple paint you add 3 pints of red and 1 pint of blue. What is the ratio of…

1. What is the ratio of…

3. A salad calls for 1 head of lettuce, 2 carrots and 0.5 cucumber. What is the ratio of…

Cookies : Desserts

Red / total pints

Lettuce to vegetables

Cookies : Cupcakes

Total pints / blue

Carrots to cucumber

Desserts : Cupcakes

Red / blue

Vegetables to carrots

Equivalent Ratios Write the equivalent ratios in the same format as the problem.

4. W rite 2 ratios equivalent to 4 : 6

5. I f 5 pounds of cherries cost $35, how much do they cost per pound?

7. Complete the table. 3 5

6. A rnold builds 3 picnic tables in 1 month. How long will it take to build 9 picnic tables?

8. Carl earns $8 per lawn mowed. How many lawns will he need to mow to earn $40?

Unit Rates Find the unit rate for each scenario. 9. Alex can run 24 miles in 3 hours. What is his average speed per hour?

10. Here are different orange juice options. Which is the best buy? (lowest price per ounce) Amount

11. If 10 bushels of apples cost $100, how much does one bushel of apples cost?

172

Level G

Chapter 9

Lesson 8

Total cost

16 oz

$1.28

32 oz

$1.92

64 oz

$2.56

96 oz

$3.36

Rate

Cost per ounce (unit cost)

Lighthouse Math

Exercise 9-8 Name Solve the proportions. 1.

3 x 5 = 25

12 x 36 = 24

5 x 25 = 100

16 x 64 = 36

x 10 9 = 45

9 18 x = 14

x 8 6 = 12

x 6 6 = 2

9. Geologists find an average of 7 meteorite fragments in every 500 tons of gravel. How much gravel must they study to get 100 fragments?

11. I f you can buy four bulbs of elephant garlic for $8, then how many can you buy with $32?

10. A 20-pound turkey serves 28 people. How many people will a 30-pound turkey serve?

12. I f there are 3 cups of sugar in 24 cookies, how many cups of sugar are there in 72 cookies?

Scale figures. 13.

14.

15. The scale for a house plan is 1 inch = 10 feet. How many feet wide is the bedroom, if the drawing is 2.5 inches?

X= 16. 10

17.

36 126

X= 19.

18. If 2 cm represents 75 miles on a scale drawing, how long would a line segment be that represents 60 miles?

X= x

11 12

20.

10 60

21. A giraffe is 18 feet tall and casts a 12 foot shadow. If Corry casts a 4 foot shadow, how tall is he?

Challenge Determine which is the better buy.

Lighthouse Math

7 lbs of fish food for $9.10

5 magic beans for $5.50

5 lbs of fish food for $6.00

7 magic beans for $8.40

Level G

Chapter 9

Exercise 8

173

Chapter 10 NYS NG Standards NY-7.RP.3 NY-7.NS.3 NY-7.EE.2

NY-7.EE.3 NY-7.EE.4

CC Standards 7.RP.A.3 7.NS.A.3 7.EE.A.2

174

7.EE.B.3 7.EE.B.4

Chapter 10 continues to

Review and Build Skills with Ratios Students will expand their understanding of ratios & proportions and apply this to percentages. Students will review what percentages are and how to convert between fractions, decimals and percents. They will learn how to use percentages to find the percent of a scenario and the missing part or whole in a scenario. Then students will apply these concepts to real world uses of percentages like tax, tip, markdown and simple interest. They will learn: • How to find a percent • How to convert between percent, decimal and fraction • How to find percent in a scenario • How to find a missing part or whole given a percent

The skills that they will gain through these lessons include: • Converting between fraction, decimal and percent • Applying proportions to percent problems • Using double number lines with percentages • Writing equations to solve percent problems

Students will learn three strategies to solve percentage problems. One strategy is to write an equation and convert the percent to a decimal. The second strategy is to use a double number line to organize the given information and solve. The third strategy is to set up a proportion using part ÷ whole = percent ÷ 100 model. Sometimes students will use the proportion method after they organize their information with a double number line.

175

Chapter 10-1 Introduction to Percentages Daily Review

Solve.

1. What is half of 10?

2. What is a third of 30?

3. What is a fourth of 20?

Learn and Connect Per cent (%) Out of

100

Percents or percentages are numbers similar to fractions that tell us part of a whole, but the whole is always 100. Looking at the soup can label to the right, or any food label, you will see a lot of percents. Your daily nutrition on the soup can label is shown out of 100%, how much of your daily value are you getting of: Vitamin D

Calcium

Iron

What do you get the most of and least of in a can of soup?

Apply Study the example. Set up and solve a proportion to find the percent. 1.

6 out of 10 6 10 � 10 6 x 10 = 100 � 10

percent always out of 100

6 � 10 = 60

3 out of 20

8 out of 10

45 out of 50

5 out of 25

30 out of 50

4 out of 5

1 10

60 100 = 60%

22 25

37 50

18 10. 20

11.

1 5

12.

9 10

Vocabulary Percent (%) - amount out of 100 (% / 100) 176

Level G

Chapter 10

Lesson 1

Lighthouse Math

Exercise 10-1 Name Write the percentage that is shaded in the diagram. 1.

10.

11. O f the 20 students in class, 8 were in the play. What percent were in the play?

12. Of the 10 days Greg worked, he bagged groceries for 3 days. What percent is this?

13. On the 5 point quiz, Mark got 3 correct. What was his percent?

14. O f the 25 classes offered, 10 were science classes. What percent were NOT science?

15. I n the past 100 days, it has rained 17 times. What percent is this?

16. There are 50 different animals at the zoo, and 35 are mammals. What percent is this?

17. Of the 20 deliveries for the day, 5 were complete. What percent of deliveries were completed?

18. T here were 10 old cars at the show and 4 were red. What percent were red?

19. There are 25 homework problems. If you have done 15, what percent is this?

Write a proportion to represent the scenario and find the percent.

Challenge Name the percentage. 99 0.99 = 100 =

1.25 =

1.06 =

1.00 = 100 100 =

1.09 =

150 =

101 1.01 = 100 =

1.8 =

2.00 =

Lighthouse Math

Level G

Chapter 10

Exercise 1

177

Chapter 10-2 Fractions, Decimals and Percents Daily Review

Write as a percent.

1. 4 out of 5

2. 7 out of 10

3. 19 out of 20

4. 18 out of 25

Learn and Connect Fractions, decimals and percents are all ways to write numbers that have a part and a whole. We can convert between each of these numbers since different numbers are used in different situations.

Divide 1�2 1 2

fraction

Use the chart below to find the equivalent fractions, decimals and percents. FRACTION

DECIMAL

2)1 0.5

4 5

50%

decimal

Write as fraction + simplify "five tenths

PERCENT

� 100

percent

� 100

5 = 10 = 21 "

0.84

Apply Complete the table with equivalent numbers. © Lighthouse Curriculum. Copying strictly prohibited.

FRACTION

DECIMAL

PERCENT

FRACTION

1 20

DECIMAL 0.5

0.1

60%

0.2

70% 0.75

0.25

3 10

80% 0.9

40%

2 5

0.35 75%

15%

4 5

0.08

178

PERCENT

Level G

Chapter 10

Lesson 2

Lighthouse Math

Exercise 10-2 Name Study the examples for repeating decimals. Solve the problems and use the repetition bar or round to the nearest hundredth. repetition bar

FRACTION

1 3 = 0.3 = 33%

0.33 3)10 – 9 10 –9 1

0.2857 7)20 – 14 round 60 – 56 40 – 35 5 *keeps going

*keeps going

PERCENT

1 7 2 3 5 9 5 7 1 3 7 9

2 7 = 0.29 = 29%

(33.3%)

DECIMAL

0.1

35%

9 20

3 4

0.8

55%

75%

0.2

65 100

10%

1 5

0.9

1 4

90%

0.55

7 10

4 10

70%

0.45

6 10

65%

0.4

50%

1 2

95 100

1 3

0.85

85 100

0.25

9 10

30%

0.6

0.3

95%

80%

0.35

Challenge Write the equivalent fraction, decimal and percent for the given numbers. 1. 0 .5%

2. 2.2

7 3. 1000

4. 150%

5. 0.003

6. 47

Lighthouse Math

Level G

Chapter 10

Exercise 2

179

Use colors or shapes to identify the equivalent fractions, decimals & percents.

Chapter 10-3 Percent of a Number Daily Review 1.

Fraction

Find the equivalent fractions, decimals and percents. Decimal

Percent

Fraction

4 5

Decimal

Percent

1 3 0.65

0.55

Learn and Connect Three students answered the following question. What is 30% of 40? Student 1 30% � 40 0.3 � 40 40 � 3 120 x = 12

Student 2 x 30 40 = 100 100x 1200 100 = 100

Student 3 4

10%

30%

100%

x = 12

Method 2

Method 3

What is 75% of 36?

Method 1

Apply Use any strategy to find the missing PART. 1. What is 27% of 600?

2. W hat is 86% of 950?

3. What is 26% of 150?

4. What is 58% of 300?

5. What is 9% of 200?

6. W hat is 13% of 100?

7. What is 71% of 1,000?

8. What is 51% of 200?

180

Level G

Chapter 10

Lesson 3

Lighthouse Math

Exercise 10-3 Name Study the example, then use any strategy to find the missing WHOLE. 1. 20% of a certain number is 3. What is the number?

If 40% of a number is 8, what is the number? Strategy 1

Strategy 2

2. Find a number so that 92% of it is 139.

Convert percent to decimal first.

8 40 x = 100

3. 75% of what number is 33?

40% · x = 8

40x 800 40 = 40

0.4 · x 8 0.4 = 0.4

x = 20

4. 50% of a certain number is 44. What is the number? 5. 50% of what number is 31?

Strategy 3 4

6. 60% of what number is 27?

7. 25% of what number is 34? 20%

40%

60%

80%

8. 30% of what number is 27?

100%

9. What percent of 200 is 28?

10. What percent of 700 is 364?

11. What percent of 500 is 195?

12. What percent of 1,000 is 200?

13. What percent of 950 is 931?

14. What percent of 50 is 13?

15. What percent of 575 is 161?

16. What percent of 300 is 111?

Challenge Find the following percents of 50. What patterns do you notice? 17. 10%

18. 1%

19. 0.1%

20. 50%

21. 5%

22. 0.5%

Lighthouse Math

Level G

Chapter 10

Exercise 3

181

Find the missing PERCENT (%).

Chapter 10-4 Part, Whole and Percent Word Problems Daily Review

Solve. Round to the tenths place if needed. 2. 42 is what percent of 60?

1. What is 55% of 80?

3. 25% of what number is 27?

Learn and Connect On my quiz I got a 95%. There were 20 questions on the test. How many questions did I answer correctly?

We can use the key below to help us solve word problems with percentages. % part = 100 whole Step 1

Identify the part, whole and percent.

Step 2

Identify the missing piece.

Step 3

Set up proportion (% always over 100)

Step 4

Cross multiply & solve

Part =

Whole =

Percent =

part % = whole 100

% = out of 100. 95 So 95% = 100

x 95 20 = 100

If a student got a 65%, how many questions did they answer correct?

100x = 1900 100x 1900 100 = 100

If a student got 17 correct, what was their percentage on the quiz?

x = 19 19 questions correct

Apply © Lighthouse Curriculum. Copying strictly prohibited.

Use the organizer to help you solve the following problems. 1. A student answered 78 problems on a test correctly and received a grade of 97.5%. How many problems were on the test?

2. A park is made up of 8 mango trees; the rest are palm trees. 66.6% of the park are mango trees. How many trees are in the park?

3. Ben earns $12,800 a year. About 15% is taken out for taxes. How much is taken out for taxes?

Part =

Whole =

Percent =

100

Vocabulary Part / Whole - ratio used to help solve percent proportion problems Percent - amount out of 100 (% / 100) 182

Level G

Chapter 10

Lesson 4

Lighthouse Math

Exercise 10-4 Name Look at the example and then solve. (Round to the nearest tenth.) What is 90% of 130 inches? % p(is) = 100 w(of) x 90 130 = 100

100x = 90(130) 100x 11,700 100 = 100

x = 117

1. What percent of 29 is 3?

2. What percent of 33.5 is 21?

3. What percent of 55 is 34?

4. 41% of 78 is what?

5. 2 8% of 63 is what?

6. 58% of what is 63.4?

7. 1 is what percent of 52.6?

8. What percent of 38 is 15?

9. Twelve of the students in the school choir sing solos. These 12 students make up 24% of the choir. How many students are in the choir?

10. There are 12 red fish in the 11. 240 books are nonfiction. tanks, and these red fish These 240 books make make up 40% of the total up 80% of the collection. fish. How many red fish How many books are are in the tank? there total?

12. If there are 50 students in the choir and 28 are youth choir members, what percent is this?

13. If there is a class of 30 14. 60% of the class has met students and 9 are absent, their fundraising goal. If what percent are absent? the class has 30 students how many met the goal?

15. In a 50 person choir, 78% have been singing for multiple years, how many does this represent?

16. 34 students in Mr. Jones' math class passed the final exam. There are 40 students in class. What percent of students passed?

Challenge Your plant is 5 in tall. Each week it grows 10%. 17. Complete the table for the height after different lengths of time.

Lighthouse Math

Level G

WEEKS

HEIGHT

5 in

Chapter 10

Exercise 4

183

Write a proportion in the part/whole = %/100 format and solve.

Chapter 10-5 Tax and Tip Daily Review

Solve. Round to the tenths place if needed.

1. What is 40% of 38?

2. What is 45% of 120?

3. 36 is what percent of 48?

Learn and Connect A family goes to order pizza and the total is $37.50. The tax that will be added is $3. What percent does this represent?

If your dad wants to leave a 20% tip on the pre-tax amount, how much tip should he leave?

What will the total bill with tax and tip be?

Would the tip be different if he used the post-tax amount?

Apply Look at the two examples. Solve the problems to find the amount of tax or tip. 1. Food bill before tax: $30

10% tax on a $18.30 purchase Example 1 x 1.83

18.30 � 10

Example 2 18.3

x 18.30 10 = 100

100x = 183 % 10%

100 100 � 10

100x 183 100 = 100

$1.83

x = 1.83

18.30 � 10% 18.30 � 0.10 18.3 � 0.1 1.83 $1.83

Sales tax: 6.4% Tax = 2. Food bill before tax: $80 Tip: 20% Tip = 3. Food bill before tax: $45 Sales tax: 7.9% Tax =

Vocabulary Tax - a required amount determined by the government added onto the purchase of certain goods, services and wages Tip - additional amount paid on top of a service to show gratitude 184

Level G

Chapter 10

Lesson 5

Lighthouse Math

Exercise 10-5 Name Look at the two examples. Solve the problems to find the total bill with tax or tip. Total bill for $18.30 purchase with 10% tax Example 1

Example 2

20.13 x 18.30

18.30 � 110% 18.30 � 1.10

18.3 � 1.1 183 1830 2 0.1 3

100% 110% 18.30 x 100 = 110 100x 2013 100 = 100

$20.13

1. Food bill before tax: $24

2. F ood bill before tax: $62

Sales tax: 7.3% Total =

Sales tax: 8% Total =

10% tax added

$20.13

3. Food bill before tax: $35 Tip: 21% Total =

4. A bicycle is on sale for $189.50. The sales tax rate is 5%. What is the total price?

5. A family is eating out for dinner. The bill was $45.80. They leave a 20% tip. How much is the tip?

6. Eric bought a canoe for $333.75. The sales tax was 5.25%. What was his total cost?

7. The cost of the meal is $45.22. You leave a 22% tip. How much tip do you leave?

8. A snowmobile is priced at $2,800. The sales tax rate is 8.2%. What is the sale price including tax?

9. At a restaurant you order a drink for $1.50 and a slice of pie for $6.50. If the tax is 8%, how much tax do you pay?

Challenge Sales tax is different among towns. Which is the better buy? 10. Town A $4.35 for a 6 pack of juice boxes Tax rate 9.3%

Lighthouse Math

11. Town B $4.42 for a 6 pack of juice boxes Tax rate 8.5%

Level G

Chapter 10

Exercise 5

185

Use any strategy to solve. Determine what you need to find the tax/tip OR total cost.

Chapter 10-6 Discount & Markdown Daily Review

Solve.

1. 10% of 30

2. 50% of 30

3. 10% of 65

4. 20% of 65

1. Crayons $1.20 25% off

2. Book $18.00 Discount 20%

3. Microscope $150 Sale 30% off

4. Shirt $22.50 Discount 40%

5. Sandwich $5.80 Coupon 10% off

6. Desk - $58.00 35% off

Learn and Connect Joseph and his mom were at the supermarket. They buy 3 pounds of strawberries and 2 watermelons for a picnic. Both are on sale. Let’s find how much they will pay. How much will 3 pounds of strawberries cost?

How much will the first watermelon cost? How much will the second watermelon cost?

What is their total at the store?

Apply Study the examples. Find the discount amount. 35.00 � 25% 35.00 � 0.25 $8.75 $

100

x 35 25 = 100

100x 8.75 100 = 100

x = $8.75

Vocabulary Discount - the amount or percent an item is marked down, on sale or % off 186

Level G

Chapter 10

Lesson 6

Lighthouse Math

Exercise 10-6 Name Study the examples and then find the sale price. 35.00 � 75% 35.00 � 0.75 $26.25

* 25% off pay 75% of original price

x 35

75 100

x 35 75 = 100

100x 2625 100 = 100

1. Markers $1.20 50% off

2. Magazine $1.80 3. Television Discount 10% $1500 Sale 30%

4. Pants $32.50 Discount 50%

6. Carpet $158 5. Pizza $15.80 28% off Coupon 10% off

7. Hat $14.75 Sale 22% off

8. Sofa $680 Sale 15% off

9. Painting $183 Coupon 5% off

x = $26.25

Study the examples. Find the missing infromation. Sale $37.10

37.10

100

37.10 53 x = 100

53x 3710 53 = 53

Paid 70% Sale $21

x = 70%

Sale 30%

11. Original $58.50 Sale $35.10 Discount

12. Original $ Sale $28 Discount 15%

13. Original $ Sale $43.50 Discount 20%

14. Original $120 Sale $78 Discount

15. Original $ Sale $12 Discount 30%

Discount 25%

100

21 x 75 = 100

10. Original $45 Sale $36 Discount

Original $53.00

75x 2100 75 = 75

x = $28

Challenge Find out how much you would pay for your final bill. 16. M eal costs $35.50

Coupon for 10% off

Tax of 8.5% (applied after coupon)

Tip of 20% on the original meal cost

Grand Total = Lighthouse Math

Level G

Chapter 10

Exercise 6

187

Chapter 10-7 Simple Interest Convert between years and months.

Daily Review 1. 3 years =

2. 5 years =

months

3. 48 months =

months

4. 96 months =

years

Learn and Connect Interest is the amount of money one pays to borrow money or earns from investing money. Interest will depend on three things - principal (amount you borrow or invest), interest rate and the length of time. Study the example on the right. Your turn! $6,000 at 5% for 10 years

$4,500.00 at 9.5% for 6 years I=Prt I = (4,500.00) (0.095) (6) I = $2,565.00 I

Interest - fee for borrowing ($)

Principal - borrow amount ($)

Rate - interest rate (%)

Time - years

Step 1: Set up the equation. x principal

x rate as a decimal

time in years

Step 2: Solve. The interest earned on $6,000 at 5% for 10 years is

Apply Find the amount of interest for each scenario. 1. $450 at 7% for 2 years.

2. $2,400 at 5.5% for 5 years.

3. $5,200 at 4% for 3 years.

4. $15,600 at 3% for 2 years.

5. $1,300 at 5% for 6 years.

6. $1,200 at 5.5% for 4 years.

7. $5,400 at 3.5% for 6 months.

8. $1,600 at 4.5% for 9 months.

9. $600 at 4% for 9 months.

10. $12,000 at 2.2% for 5 years.

11. $1250 for 3 years at 3.2%.

12. $4,800 for 4 years at 1.2%.

Vocabulary Interest - a fee paid for borrowing money Simple Interest - interest that is only calculated on the initial amount of a loan Principal - the total amount of money borrowed or invested 188

Level G

Chapter 10

Lesson 7

Lighthouse Math

Exercise 10-7 Name Complete the table given the information using the formula I = Prt. 1.

Interest (I)

Principal (P)

Rate (r)

Time (t)

$5,500

3.5%

36 months

5.65%

5 years

$850 $9,975

$50,000

2.85%

$3,050

4.8%

$9,000

$12,500

$2,880

$15,000

8 years 120 months

3.2%

2. Jack borrows $150,000 to buy a house. The interest rate is 6.75% over 30 years. How much interest will he pay?

3. Kenny is buying a car. The loan is $22,500 for 5 years with an interest rate of 5%. How much interest will he pay?

4. Leo is doing home improvements. He gets a loan for 5 years with an interest rate of 11.25%. Leo pays $4,500 in interest. What was his loan amount?

5. Marc borrows $6,500 with a rate of 4.5%. He pays $2,632.50 in interest. Find the time on his loan.

6. J ack borrowed $33,000 to pay for school. His rate is 7% and his goal is to pay his loan in 36 months. How much interest will he pay?

7. Steven’s loan is $36,000 at 8.5% for 20 years. How much will he pay back in total (principal + interest)?

Challenge 8. Victor puts $2,400 in the bank for 5 years. He makes $9.20 in interest every month. What is the annual interest rate?

Lighthouse Math

Level G

Chapter 10

Exercise 7

189

Use the I = Prt formula to solve the following problems.

Chapter 10-8 Review Daily Review Order the numbers from least to greatest. 4 9 1. 10 , 35%, 0.37, 20 , 0.42, 42.5%

Learn and Connect Fractions, decimals and percents can show the same value in different ways. They all represent a part of something. Percent is always out of 100; fractions are out of 1. Practice converting between fractions, decimals and percents to recognize how they can show the same amount in different ways. When we need to find a percent of a number, we can convert to decimals or fractions to solve.

3 = 0.30 x 100 = 30% 10 5 = 0.625 x 100 = 62.5% 8

Apply

Find the equivalent percent. 1. 3 out of 5

2. 3

3. 8 out of 25

4. 47

5. 3 red marbles out of 10, percent are red

6. T hree boys of four siblings, percent boys

7. 2 rainy days in 20, percent not rainy

8. 37 wins in 50 games, percent lost games

Convert the given number to find equivalent fractions, decimals or percents. FRACTION

DECIMAL

9. 10.

PERCENT

FRACTION

12.

45%

1 3

11.

DECIMAL

0.3

13.

0.08

14.

Find the missing part, whole or percent.

PERCENT 12.5%

2 9

0.2 0.6

part = % whole 100

15. 2 % of 250

16. 7 5% of 396

17. 9 1 is what percentage of 140

18. 2 9 is what percentage of 58

19. What percentage of 4 is 3?

20. 2 0% of what number is 7?

21. 4 0% of a certain number is 48. What is that number?

22. 50% of a certain number is 74. What is that number?

190

Level G

Chapter 10

Lesson 8

Lighthouse Math

Exercise 10-8 Name Find the amount of tax or tip and the total amount. 1. Your family ate at a restaurant. The meal cost $47.25 and you left a 20% tip. Tip:

Tax:

Total:

3. Calvin left a 15% tip for a $9.42 meal. Tip:

2. Frank bought a new bicycle for $129. The sales tax was 8%. Total:

4. Henry bought snacks for $1.49, 0.89¢, and $2.25. He paid 6% sales tax. Tax:

Total:

Find the discount and then final cost. 5. Marc found a dining table on sale for 45% off. The original price was $1,250. Discount:

Discount:

Final cost:

7. Larry purchased a pair of jeans for $35. He had a 10% off coupon. Discount:

6. Sam bought a board game that usually sells for $68, but he paid $57.80.

Final cost:

Percent:

8. George wants to purchase new shoes for an original price of $50.00, and they are marked down 20%. Discount:

Final cost:

9. $250 deposited for 5 years with rate of 7.5%. Find the interest earned.

10. $24,000 borrowed for 3 years with interest paid of $3,600. What is the rate?

11. Borrow $7,500 at a rate of 2.85% for 12 years. How much interest will be paid?

12. What amount was borrowed if interest paid was $4,991 for 7 years at a rate of 6.2%?

Use the formula I = Prt to solve the following problems.

Challenge Which scenario will cost you less money? Option B Borrow $15,000 4 years 4%

Option A Borrow $15,000 5 years 3.8%

Lighthouse Math

Level G

Chapter 10

Exercise 8

191

Chapter 11

NYS NG Standards NY-6.EE.6 NY-7.G.5

NY-7.EE.3 NY-7.EE.4

CC Standards 6.EE.B.6 7.G.B.5

192

7.EE.B.3 7.EE.B.4

In Chapter 11 we will review

Geometry Concepts We will explore angles and the use of transversals across parallel lines. We will use what we know about measurements of angles to solve missing angles. Classifying angles • We will review the concept that angles can be acute, obtuse, right or straight based on their angle measurements. Supplementary and complementary • We will learn that supplementary angles are created when a right angle or straight angle is cut into two. Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. © Lighthouse Curriculum. Copying strictly prohibited.

Find missing angles • We will use our knowledge of a right angle measurement of 90° and a straight angle of 180° to find a missing angle measurement. Interior angles of triangles • We will use our knowledge of a triangular angle sum of 180° to find a missing angle measurement. Writing equations for missing angles • We will use our knowledge of angles to solve for an unknown number. Transversal vocabulary and transversal angles • We will learn about transversals and how to find the angle measurements of a transversal over parallel lines.

193

Chapter 11-1 Classifying Angles Daily Review 1. A ray:

Sketch each of the examples. 2. A point:

3. A line segment:

4. A quadrilateral:

Learn and Connect The image shows an angle. An angle is formed by two rays with a common endpoint.

The rays intersect at the vertex. When naming an angle, we use the vertex as the middle point. Therefore, this angle would be known as: • angle ABC or ABC • angle CBA or CBA • angle B or B

Angles are measured in degrees, which we show using this symbol (°) after a number. We identify the type of angle based on its degree measurement.

Types of Angles

Name: Right Degree: 90°

Name: Acute Degree: less than 90°

Name: Obtuse Name: Straight Degree: more than 90° Degree: 180°

Apply Write each of the three different ways to name the angle. Then, identify if it is right, acute, obtuse, or straight. Q

Q M

194

Level G

Chapter 11

Lesson 1

Lighthouse Math

Exercise 11-1 Name Draw a line from the name to the correct angle. 1.

ABC

BCD

BAC

DFE

EFD

D B

10.

11.

12.

13.

14.

15.

Sketch an example of each. 16. An angle named QRS that is acute.

17. An angle named LMN that is obtuse.

18. An angle named PQR that is right.

19. An angle named T that is acute.

Challenge Identify the name and type of angle being described. 20.

21.

T 135°

35° Q

Lighthouse Math

Level G

Chapter 11

Exercise 1

195

Identify the angle as acute, obtuse, or right.

Chapter 11-2 Supplementary, Complementary and Adjacent Angles Daily Review

Sketch each of the examples.

1. An angle labeled ACF

2. An acute angle

3. An obtuse angle

4. A right angle

Learn and Connect Adjacent angles are a pair of angles that share the same vertex and are bound by the same pair of lines but are opposite of each other.

A D

Trace ABD and DBE These angles are adjacent angles.

Adjacent angles can be supplementary or complementary. Supplementary a pair of angles that add up to 180 degrees.

Complementary a pair of angles that add to 90 degrees.

= 180°

40°

= 90°

140°

60°

30°

Apply Complete the chart. Supplementary or Complementary?

Angle 1: Name and Angle Type

Angle 2: Name and Angle Type

A B

T M

196

Level G

Chapter 11

Lesson 2

Lighthouse Math

Exercise 11-2 Name Use the figure below to answer the questions. 1. Which angle is complementary to

D C

hich angle is W supplementary to

DBC?

ABD?

3. Name an acute angle in the figure. 4.

Name an obtuse angle in the figure.

Name a right angle in the figure.

Use the figure below to answer the questions. M

L K

6. Which angle is supplementary to

KLM?

7. Which angle is supplementary to

NLJ?

8. J

Name an acute angle in the figure.

10. Name a right angle in the figure. Sketch the example described. 11. S upplementary angles: an acute angle labeled DFG and an obtuse angle labeled GFE.

12. Complementary angles: an acute angle that is 33° labeled PRT and an acute angle 57° labeled SRT.

13. S upplementary angles: an acute angle labeled QRS and an obtuse angle labeled PRQ.

14. Complementary angles: an acute angle that is 45° labeled ABD and an acute angle 45° labeled DBC.

Lighthouse Math

Level G

Chapter 11

Exercise 2

197

9. Name an obtuse angle in the figure.

Chapter 11-3 Find Missing Angles Daily Review

Sketch each angle. Label with measurements of your choosing.

1. Angles that are supplementary

2. Angles that are complementary

Learn and Connect ABC is missing a measurement. What is the missing measurement?

175°

A C

To find the measurement, consider what is the relationship between ABC and DBC. Are they supplementary or complementary? Because we know that they make a straight line, they are supplementary. The total of both angles equals to 180° which makes the following true: 180 =

ABC +

DBC

Therefore, to solve we can use our understanding of fact families and inverse operations. Solve using the expression. 180 = ABC + 175 ABC = 180 – 175

Therefore,

ABC is

Apply Find the missing angle. 1.

4. ?

69°

30°

82°

65°

52° ?

198

33°

Level G

Chapter 11

110°

Lesson 3

63°

Lighthouse Math

Exercise 11-3 Name Find the missing angle. 1.

3. ?

52° 35°

83°

105°

8. 36°

41° ?

37°

135°

9. Complementary angle to 5° =

10. Supplementary angle to 65° =

11. Complementary angle to 50° =

12. Supplementary angle to 85° =

13. Complementary angle to 75° =

14. Supplementary angle to 95° =

15. Complementary angle to 23° =

16. Supplementary angle to 121° =

Determine if the angle measurements are complementary, supplementary or neither. 17.

36° and 28°

18. 180° and 90°

19.

78° and 12°

20. 40° and 65°

21. 120° and 75°

22. 45° and 45°

23. 137° and 43°

24. 106° and 74°

Challenge Find the complementary or supplementary angle for each listed angle. 25. Complementary angle to 23.25° =

Lighthouse Math

26. Supplementary angle to 110.273° =

Level G

Chapter 11

Exercise 3

199

Determine the complementary or supplementary angle to the listed angle.

Chapter 11-4 Identify Missing Angles in Triangles Find the missing angles and determine if the angles are complementary, supplementary or neither. 2.

Daily Review 1. ?

140°

60°

Learn and Connect A

A triangle is a three sided figure made of three angles. The triangle in the image has three angles: ABC, BAC, and BCA or A, B, C. To find the missing angle, we need to write an expression. We know that a triangle's angles add up to a total of 180°. Therefore, the following is true: 180 =

A+

B+

90°

35°

To find the missing angle, we can use our understanding of fact families and inverse operations. Solve using the equation. 180 = A + 90 + 35 A = 180 – 90 + 35

Therefore,

A is

You can distinguish the type of triangle by its angles and the length of its sides.

Equilateral Triangle All three angle measurements and sides are equal.

Scalene Triangle None of the angle measurements or side lengths are equal.

Isosceles Triangle Two angle measurements and two side lengths are equal.

Apply Calculate the missing angle measurement. Identify if the triangle is equilateral, isosceles or scalene. 1.

60° ?

2. 60°

23°

75°

50°

42°

90°

45°

Type of triangle:

Missing angle:

200

Level G

Chapter 11

Lesson 4

Lighthouse Math

Exercise 11-4 Name Calculate the missing angle measurement. Identify if the triangle is equilateral, isosceles or scalene. 2.

71°

56° ?

? 60°

24°

54°

60°

Type of triangle:

Missing angle:

40°

96° ?

69° 70°

42°

15°

Type of triangle:

Missing angle:

Identify if the angle measurements create an equilateral, isosceles, scalene or is not a triangle. 7.

86°, 53°, 41°

70°, 22°, 68°

10. 65°, 78°, 37°

11. 79°, 79°, 22°

12. 11°, 101°, 60°

13.

14. 75°, 75°, 30°

60°, 60°, 60°

28°, 28°, 100°

Challenge Identify the missing angle measurement for triangles below. 15. 35.67°, 58.236°,

Lighthouse Math

16. 102.326°,38.837°,

Level G

Chapter 11

Exercise 4

201

Chapter 11-5 Equations for Missing Angles Daily Review

Identify the missing angle for a triangle with the given angles. Identify if the triangle is scalene, isosceles or equilateral.

C = 35°,

D = 28°,

R = 90°,

S = 45°

M = 30°,

N = 30°

S = 32°,

T = 101°

Learn and Connect We can use our understanding of angles to solve for “x.” We use x in place of a missing number when writing equations. In the model, we know the entire line CF is equal to 180° and, therefore, BDF and BDC are supplementary.

B 20° C

2x° D

To solve for x, we can use the following equation: 180 = 2x + 20 We can use inverse operations to solve for x by moving all other numbers to the other side of the equal sign and leaving x.

First, remove the 20 by subtracting from the total: 180 – 20 = 160

180 = 2x + 20 –20 160 = 2x ÷2 80 = x

Since the 2 and x are next to each other, this indicates multiplication. To separate them, we need to do the inverse operation of division: 160 ÷ 2 = 80 Therefore, x = 80. So the missing angle labeled 2x = 160°.

Apply Use your understanding of angles to create an equation and solve for x. 1.

33°

3. 125°

5x - 20°

x + 15°

3x + 3°

Equation:

5. x°

45°

45° 89°

95° 40 + x°

2x°

Equation:

202

Level G

Chapter 11

Lesson 5

125°

43°

Lighthouse Math

Exercise 11-5 Name Use your understanding of angles to create an equation and solve for x. 1.

15°

3. 5 + x°

88°

4x°

115°

2x - 5°

Equation:

45°

113°

22 + 3x° 35°

Equation:

9. 99°

165°

32°

6 + x°

5x°

90°

66°

x + 32°

Equation:

10.

11.

12.

52°

x + 100° 23°

22°

3 - x°

15°

9°

Equation:

Lighthouse Math

Level G

Chapter 11

Exercise 5

x+11°

x°

3x + 5°

203

Chapter 11-6 Transversal Vocabulary Daily Review

Solve for x.

1. 1 80 = 2x + 25 + 123 x=

2. 90 = x +35 +18 x=

3. 123 = 3x x=

4. 90 = 15 + x – 25 x=

Learn and Connect Read the vocabulary and definition. Highlight the portion of the example that indicates the vocabulary word based on its definition. Example

3 7

5 8

1 2 4

1 2 3 4 7

204

5 8

Vertical Angles

3 7

5 8

1 2 3 4

A pair of adjacent angles formed when two lines intersect.

Level G

Chapter 11

1 2 4

Linear Pair

Lesson 6

5 8

Interior Angles

Exterior Angles Angles that lie on the outside of the parallel lines.

3 5

1 2 4

Corresponding Angles Two angles that lie the same relative position at each intersection (and have the same angle measurement).

Vocabulary and Definition

Angles that lie on the inside of parallel lines.

3 7

1 2 4

Transversal A line that intersects two or more other lines.

3 5

Example

A pair of opposite angles made by intersecting lines.

3 7

1 2 4

Vocabulary and Definition

Alternate Interior Angles Angles that are formed on opposite sides of the transversal and inside the two lines.

Alternate Exterior Angles Two exterior angles on opposite sides of a transversal which lie on different parallel lines.

Lighthouse Math

Exercise 11-6 Name Use the word bank below to identify each angle pair. Word Bank Alternate Interior Alternate Exterior

Same-side Interior Same-side Exterior

Corresponding Vertical

Use the transversal across parallel lines below to answer the questions.

3 7

5 8

Lighthouse Math

1 2 4

7. Name two acute angles.

8. Name two obtuse angles.

9. Name a pair of supplementary angles.

10. Name two vertical angles.

11. Name a pair of alternate interior angles.

12. Name a pair of angles with the same measurement.

Level G

Chapter 11

Exercise 6

205

Chapter 11-7 Transversal Angles Daily Review 1. Transversal

Sketch an example of each. 2. Corresponding Angles

3. Interior Angles

4. Vertical Angles

Learn and Connect Based on your knowledge of supplementary and complementary angles, determine the missing angle measurement for each of the following angles.

C G

Hint: We know that angle A and B are supplementary. Therefore, when combined, they equal to 180.

Hint: We know that angle A and E are corresponding angles. Therefore, they are equal.

E H

A D

140°

Hint: Angle A and angle H are alternate exterior angles.

Apply For each set of parallel lines, you are given the measurement of an angle. Use your knowledge of parallel lines and transversals to find the measures of each other angle. 1.

3. 90°

92° 43°

Solve for x. 4.

6. 70°

128° 2x°

115° x + 16°

206

5x°

Level G

Chapter 11

Lesson 7

Lighthouse Math

Exercise 11-7 Name For each set of parallel lines, you are given the measurement of an angle. Use your knowledge of parallel lines and transversals to find the measures of each other angle.

46°

112° 27°

Solve for x. 5. 120°

6°

+ 3x

113°

3°

107°

88°

10. °

° 27

x° 2+ 175°

Lighthouse Math

12.

23° x-

11. 146°

23°

11x°

65°

x°

Level G

Chapter 11

Exercise 7

207

Chapter 11-8 Review Daily Review Write the supplementary or complementary angle to the listed angle. 1. S upplementary angle measurement for 78°

2. Complementary angle measurement for 35°

Learn and Connect Use the diagram of parallel lines cut by a transversal to answer the questions. What is the measurement of angle F? Hint: F is supplementary to A

112° A B C D

What is the measurement of angle H? Hint: H is a corresponding angle to A

E F 2x + 4° G H

Name the four interior angles. , , Hint: the word “interior” means inside

Name an angle that is supplementary to H Hint: supplementary angles add to 180° What is the value of x based on the location of angle G? Hint: G is a corresponding angle to A

Apply Find the measures of each other missing angle in the figure. 1.

123° 32°

25°

48°

Write an expression and solve for x. 4.

98°

22 + x°

14°

42°

3x°

8x - 4°

Equation:

208

Level G

Chapter 11

Lesson 8

120°

Lighthouse Math

Exercise 11-8 Name Find the measures of each other missing angle in the figure. 3.

1. 65° 115°

22°

35°

74°

147°

45°

6°

Write an expression and solve for x. 9.

103°

110°

16° 32°

5x°

3 + x°

2x - 6°

Equation:

Draw a sketch of each description. 10. A n angle named LMF that is acute.

11. An angle named PQT that is obtuse.

12. An angle named TOL that is right.

13. An angle named R that is acute.

Identify the types of triangles below as equilateral, isosceles or scalene. 14.

15.

16.

48° 47°

60° 60°

60°

Lighthouse Math

64°

85°

64°

Level G

Chapter 11

Exercise 8

209

Chapter 12 NYS NG Standards NY-6.G.1 NY-6.G.2 NY-6.G.4

NY-7.G.4 NY-7.G.6

CC Standards 6.G.A.1 6.G.A.2 6.G.A.4

210

7.G.B.4 7.G.B.6

Chapter 12 reviews and builds skills in

Area and Perimeter Students will review area and perimeter of rectangles and triangles. Then students will expand their understanding to include area and circumference of circles and area of composite shapes. Students will then move to 3D figures and find the surface area and volume of rectangular prisms. They will learn: • How to find area of rectangles, triangles, parallelograms and circle • How to find circumference of circles • How to find surface area of rectangular prisms • How to find volume of rectangular prisms

Students will learn formulas for area of 2 dimensional shapes including circles. They will also learn the formula for circumference of circles. They will then use a decomposing strategy to find the area of composite shapes, where they need to add 2 shapes or subtract 2 shapes. Students will use nets to find surface area of rectangular prisms. They will use the idea that volume is the area of the base times the number of layers which they will utilize for rectangular prisms. It also can be applied for other shapes in the future.

211

Chapter 12-1 Perimeter Daily Review

Solve.

1. 42 =

2. 2(3 × 4) =

3. 2(4 + 5) =

4. 82 =

Learn and Connect Ryan is part of garden club in his neighborhood. They are building 3 new garden beds and installing a new fence around each garden. The perimeter is the length around the edge of a shape, like the fence around the edge of the garden. If the entire garden space is 12 feet long and 18 feet wide, how much fencing would the garden club need to enclose all 4 sides?

The sides of the small triangle bed are: 2ft, 3ft, and 5 ft. What is the perimeter?

The sides of the small rectangle bed are: 3ft and 2.5ft. What is the perimeter?

Apply Find the perimeter of each shape below. 18 ft

5 in

18 ft

3 in

18 ft

Perimeter =

6. 8 yd

212

Perimeter =

6 in

Perimeter =

Lesson 1

14 yd

6 in

Perimeter =

Chapter 12

9 in

12 in

Level G

7 ft

19 in

3 yd

Perimeter =

15 in

7 ft

9 yd

7. 16 in

4. 13 yd

13 yd

5 in

Perimeter =

8 yd

9 yd

Perimeter =

Lighthouse Math

Exercise 12-1 Name Write an equation and find the perimeter. 1. Norman is a sunflower farmer. He uses a plot of land that is 3 km by 4.3 km. How much fence would he need to enclose his sunflowers?

2. Joseph created a triangular shaped vegetable garden. What is the perimeter if the sides are 1.4 m, 2.6 m and 3.7m?

3. A square bedroom measures 10.5 feet in length. If you need to install baseboard around the edge of the room, how much will you need?

4. A border will be painted around a mural which is 6 1 ft � 3 1 ft. What is the 4 2 total length of the border?

5. If the park is a rectangle with lengths 0.5 miles by 0.75 miles and Conner walks around the park 2 times, how far did he walk?

6. A hexagon bookshelf has sides that are 8 21 inches. What is the perimeter of the bookshelf?

Perimeter = 34

Perimeter = 22

Perimeter = 38

10. Perimeter = 16

11. Perimeter = 18

12. Perimeter = 28

2 5

10.

11.

12.

List the missing sides given the information.

Challenge Find the perimeter of these figures, find the missing side(s) first. 3 cm

6 ft

13.

14.

2 ft

8 cm

4 cm

5 ft

5 cm

3 ft

Lighthouse Math

Level G

Chapter 12

Exercise 1

213

Chapter 12-2 Area of Rectangles and Parallelograms Find the perimeter of the following shapes.

Daily Review 4 cm

4 cm

6 ft

4 cm

2 ft

7 ft

7 ft 7 ft

4 cm

Learn and Connect The garden club has built all the beds and now they are ready to get started planting. Ryan is responsible for cutting the tarp to place at the bottom of the bed to help prevent weeds. In order to know how much tarp he needs, he will need to find the area of the bed. The rectangular bed is 3ft by 2.5ft. To find area of a rectangle we use the formula: Area = length � width. What is the area of the rectangle garden bed?

What is the area of the whole garden which is 12 feet long and 18 feet wide?

Apply Study the example of how to find the area of a parallelogram and then find the areas of the shapes below. 1.

4 cm

2. 4 ft

5 cm

10 m 5.3 m

4 ft

A = bh A=6·4 A = 24cm2

The height is not always the side, it is always perpendicular (90°) from the base.

8.7 yd 11 yd

10 m

5.9 m

6 cm

4 ft 6.1 ft

4 km

5.9 km

6. 6 km

5 in

11 in

5 in

Vocabulary Area - the amount of space a 2 dimensional shape covers, measured in units squares (in2, cm2, ft2) 214

Level G

Chapter 12

Lesson 2

Lighthouse Math

Exercise 12-2 Name Find the missing side given the area. 1.

15 m

Area is 28 cm2 and the height is 4 cm.

4. Area is 63 km2 and the length is 21 km.

ft 16 ft

A = 180 m2 5.

6.5 cm

A = 60.45 cm2 9.

A = 128 ft2 7.

Area is 84 in2 and the base is 12 in.

A = 1.26 m2

cm 5.1 cm

A = 16.32 cm2

10. Area is 102 m2 and the height is 17 m.

0.7 m

11.

ft 90 ft

A = 8,100 ft2

Area is 28 mm2 and the height is 4 mm. w=

12. Area is 48.5 cm2 and the width is 5 cm. w=

Find the missing information in the table given the provided information Shape

Dimensions

13.

Racquetball

Rectangle

w= ft. l = 40 ft.

14.

Basketball

Rectangle

w = 50 ft. l = 94 ft.

15.

Ice hockey

Rectangle

w = 85 ft. l= ft.

16.

Volleyball

Rectangle

w= ft. l = 60 ft.

17.

Dodgeball

Rectangle

w = 180 ft. l = 330 ft.

18.

NCAA soccer

Rectangle

w = 225 ft. l = 360 ft.

Perimeter

Area A = 800 sq. ft.

P = 570 ft. A = 1800 sq. ft.

Challenge Find the area based on the story. 19. The base of a parallelogram is 10 in. The height is 2 in. more than half the base. Find the area.

Lighthouse Math

Level G

20. The height of a parallelogram is 4.5 cm. The base is twice the height. What is the area?

Chapter 12

Exercise 2

215

Game

Chapter 12-3 Area of Triangles Daily Review 1.

Circle the number that is the height and then find the area. 2.

10 m

7 ft

11.5 ft

12.5 ft 5 ft

12 ft

25 m

Learn and Connect Now, Ryan is ready to cut tarp for the triangular garden bed. The sides of the triangle bed are 2ft, 3ft, and 5 ft. Ryan sketched it out below. He did not remember the formula for the area of a triangle but he did remember area of rectangle is A = L � W.

5 ft 2 ft 3 ft

He noticed that the triangle was half of the rectangle.

Knowing this, what would the area of the triangular garden bed be?

Apply Study the example and both formulas. Then use either formula to find the areas. 1.

3 7

= 10.5

216

4. 18 in

= 2 ·7·3

12 yd

8 mm

A= 2 ·b·h

21 = 2

12 yd

5 mm

7 cm Just like rectangles & parallelograms, sometimes the height is a side and other times it is not a side. **It has to be perpendicular to the base**

Level G

20 cm

16 in

6. 8 ft 17 ft

Chapter 12

Lesson 3

3 in 8 in

Lighthouse Math

Exercise 12-3 Name Find the area based on the scenarios below. 1. Mark is carpeting his dining room. It is a 5 yd by 10 yd rectangle. How much carpeting does he need?

2. A triangular mural is being repainted. How much paint is needed if the base is 12 ft and the height is 18 ft?

3. A field is 0.5 miles wide and has an area of 8 square miles. How long is the field?

4. If a triangle has a base of 5 cm and an area of 25 cm2, what will the height be?

5. How much material is needed to make a parallelogram shaped rug, 10 ft long by 6.5 ft. tall?

6. What is the area of a triangular yard with a base of 15 yards and a height of 12 yards?

Study the example then find the area of the composite shapes. 4

6 cm

4 ft

5 cm

14 cm 6 ft

2 b·h 3·2 6 = = =3 2 2 2

We don’t have a formula for this shape but we can split it into shapes we know, find the areas and then add them together!

10.

8 cm

3 cm 3 cm

13 cm

4 cm

7 cm

1) Determine the shapes you see 2) Find the areas of each 3) Add areas together

16 cm

10 cm

Challenge Find the area of each figure. Then, list the shapes in order from greatest area to least. 11. 10 cm 12.5 cm 8 cm

Lighthouse Math

Level G

6 cm

Chapter 12

10 cm

Exercise 3

217

LxW 3·4 12

75 ft

A = 15

Chapter 12-4 Circles Daily Review

Find the area of the triangles with the given bases and heights.

1. b =12 in, h = 20 in

2. b = 4.5 in, h = 8 in

3. b = 60 in, h = 32 in

Learn and Connect When working with circles, we use different vocabulary. Look at the image and definitions, then answer the questions below.

If the diameter of a circle is 6 cm, what would the radius be?

et er

Radius

Center

Write the formula for circumference. Circumference

If π = 3.14, what would the circumference be?

Radius Diameter

Write the formula for area.

Circumference Area

If π = 3.14, what would the area be?

Pi (π)

center to edge, half of the diameter across the circle through the center, two times the radius around the edge of the circle, perimeter C = 2rπ or C = πd space taken up by the circle, inside A = πr2 constant used to measure circles π=3.1415… it goes on 22 forever but we round to 3.14 or 7

Apply Find the radius or diameter. 1. r = 8 m d =

2. r = 24 cm d =

3. r =

d = 10 ft

4. r =

5. r = 3.5 in d =

6. r =

7. r =

d = 14 ft

8. r = 32 in d =

10.

d = 11 mm

d = 2 km

12.

11.

12 cm

5 mm

Vocabulary Radius - the distance from the center of the circle to the edge Diameter - the distance from one side of a circle to the other through the center Circumference - distance around a circle, similar to perimeter of polygons

218

Level G

Chapter 12

Lesson 4

Lighthouse Math

Exercise 12-4 Name Find the circumference of circles. 1.

d = 8 in

3. 6 cm

7 in

r = 4 in C = d · π or C = 2 · r · π C = 8π C=2·4·π C = 8(3.14) C = 8π

22 ft

9 in

C = 25.12 in

Find the area of the circles. 7.

d = 8 in

7 in

9. 5m

6 cm

r = 4 in

10.

11.

12.

9 in

22 ft

Complete the table, leave your answers for circumference and area in terms of π (Ex. 8π or 20π) 13.

Radius

Diameter

Circumference

Area

5cm 30 in 12 ft 3m

Challenge Complete the table.

14.

Radius

Diameter

Circumference

Area 49π in2

20π cm 64π mm2

Lighthouse Math

Level G

Chapter 12

Exercise 4

219

A = π · r2 A = π · 42 A = 16π A = 50.24 in2

Chapter 12-5 Composite Area Write the formula.

Daily Review

1. R adius to Diameter

2. Diameter to Radius

3. Circumference

4. Area of Circle

Learn and Connect 5 in

Henry and William both solved this problem with area differently. Look through their work. Then answer the problem below using each of their methods.

10 in

6 in

8 in

Henry 2m

Henry

William

3 4

1 1

William

8 · 10 - 4 · 3 80 - 12 68 in2

6·8+5·4 48 + 20 68 in2

Apply

16 in

5 in

8 in

16 in

4 yd

12 in

8 in

6 yd

Area = 5.

6. 9.8 yd

15.3 yd

13.4 yd

6.1 yd

Area =

17.4 yd

5.1 yd

5.7 yd

Area =

4. 8.2 yd

Determine what shapes you see. Then, find the area of each figure by adding the areas of the smaller figures.

4.6 yd

9.8 yd

Area =

Vocabulary Composite/Compound Figures - multiple shapes that are put together or overlap Semicircle - half of a circle, has half of the area

220

Level G

Chapter 12

Lesson 5

Lighthouse Math

Exercise 12-5 Name Study the shaded area example and then solve the following problems. 1.

2. 19 yd

6 cm 3 cm

6 cm

d 5y

5 cm

4 cm 16 yd

πr2 - L · W π62 - 5 · 3 36π - 15 113.04 - 15 98.04 cm2

3 cm

12 cm

8 cm 12 cm

8 cm

3 cm

5 cm

4 cm 9 cm

5. A rectangular backyard is 22 feet by 15 feet. There is a circular brick patio in the middle. The diameter is 8 feet. If the yard that is not the brick patio is grass, how much grass is in the backyard?

6. Gregory is repainting a dining room table. It is 3 feet by 6 feet. He is going to paint a border around the edge that is 0.5 feet wide. The border will be black and the interior rectangle will be blue. How much black and blue paint will he use?

You are painting a mural. Yesterday you painted the blue rectangle that is 5 ft by 7.5 ft. Today you paint a triangle next to the rectangle, the height is 7.5 ft and the base is 3 ft. How much have you painted over the two days?

Challenge 8. Find the area of the shaded part of the figure. 32 cm

Hint: You can use division to find the diameter of each circle.

Lighthouse Math

32 cm

Level G

Chapter 12

Exercise 5

221

Read the scenario, draw a picture and then solve to find the area.

Chapter 12-6 Surface Area of Rectangular Prisms Daily Review

How many faces do the following 3D shapes have?

Learn and Connect Surface area is the sum of the areas of all of the faces in a 3 dimensional shape. To find surface area (SA) we can make a net which is a map of the shape if it were unfolded.

lw h l

Study the example. It’s similar to composite area. The units are squared, u2.

l = 5 in w = 3 in h = 4 in

SA = 2(gr. rect) + 2(purp. rect) + 2(blue rect) SA = 2(l · w) + 2(l · h) + 2(w · h) SA = 2(5 · 3) + 2(5 · 4) + 2(3 · 4) SA = 2(15) + 2(20) + 2(12) SA = 30 + 40 + 24 SA = 94 in2

Try to find the surface area of the shape below:

4 cm

8 cm

Apply Find the surface area of the following rectangular prisms. 1. 4 in

Surface Area =

2. 15 yd

4.7 m 5.9 m

Surface Area =

20 yd

7 in 12 in

Surface Area =

7.4 m

13 yd 12 yd 8 yd

Surface Area =

4 ft

Surface Area =

7 ft

17 yd 2 ft

9.4 m

Surface 3 m Area =

4.1 m

Vocabulary Surface Area - sum of the areas of all of the faces in a 3 dimensional shape Rectangular Prism - 3D shape with all rectangular faces Faces - 2D shapes that make up a 3D figure, sides

222

Level G

Chapter 12

Lesson 6

Lighthouse Math

Exercise 12-6 Name Complete the table. 3D Figure

Net

Equation & Solve

i 15

9 in 12 in 3 in

2. 3 in

6 in

6 in 8 in

6 in

SA = 2(5in x 6in) + 2(5in x 9in) + 2(6in x 9in)

4. A gift box is 18 in long, 7 in wide, and 3 in tall. If you need to wrap the present, how much wrapping paper do you need to cover the whole box?

5. You are painting a rectangular cabinet. It is 2.5 feet long, 1 foot wide, and 3 feet tall. What is the total area you need to paint?

6. A pool is 20 feet by 14 feet and is 5 feet deep. You are hired to repair the cracks in the sides and bottom. What is the total surface area you are responsible for repairing?

Challenge 7.

How much glass and plastic would you need to make the fish tank if the top and bottom are plastic and the four sides are glass?

14 in

12 in

Lighthouse Math

Level G

Chapter 12

Exercise 6

25 in

223

Write an equation then find the surface area for the following scenarios.

Chapter 12-7 Volume of Rectangular Prisms Use the surface area formula to find the SA of this prism.

Daily Review 1.

3 in 9 in

13 in

Learn and Connect Ryan is back in his garden. A new bed was built and he needs to figure out how much dirt is needed to fill the bed. The space in which a 3 dimensional shape occupies (how much can fit inside) is called volume. If the bed is 4 feet by 3 feet and 2 feet tall, how much dirt will we need?

First we find the area of the base (l � w) 3 � 4 = 12 Then we multiply it by the height (amount of layers) 12 � 2 = 24

3&4

Therefore, the volume = 24 ft3

3&4&2

Apply Look at the example and find the volume. Round to the tenths if necessary.

4m 13 m

1. 4 in

2. 15 yd

7 in

20 yd

l·w

4.7 m 5.9 m

V = Area of base · height V=

12 in

7.4 m

13 yd

·h

V = 13 · 4 · 5

12 yd

4 ft

8 yd

V = 52 · 5

7 ft

17 yd

V = 260 m3

9.4 m

2 ft

4.1 m

Vocabulary Volume - the amount of space a 3D object occupies, units are cubed, u3 224

Level G

Chapter 12

Lesson 7

Lighthouse Math

Exercise 12-7 Name Determine how many unit cubes are needed to fill the rectangular prism. 2.

Complete the table to find the missing information Length

Width

4 cm

5 in

2 in

8 ft

Height

4 cm 5m

Volume

Units

cm3

3 in 512

1.5 km

10 km

37.5

10. A gift box is 18 in long, 7 in wide, and 3 in tall. If you need to fill the present with candy, how much candy will you need to fill the box?

11. You are filling a rectangular cabinet with canned food. It is 2.5 feet long, 1 foot wide, and 3 feet tall. How much space do you have to place cans?

12. A giant sandbox is 3 feet by 6 feet and is 1 foot deep. If you need to refill the sandbox with sand, how much sand is needed?

Challenge Find the volume of this composite rectangular prism. 20 cm

13.

5 cm

5 cm 15 cm

Lighthouse Math

Level G

Chapter 12

Exercise 7

225

Write an equation and then find the volume for the following scenarios.

Chapter 12-8 Review Daily Review

What is the formula for...

1. Area of Rectangle

2. Area of Triangle

3. Area of Circle

4. Circumference

Learn and Connect Find the perimeter of the following shapes. 40 cm

40 cm

60 cm

35 cm

30 cm

20 dm 25 dm

30 dm

35 cm

24 dm

Find the area of the following shapes. 5.

15 m 16 m

15 mm

10 in

40 cm

12 m

12 in

32 mm

Find the missing information about the circles and leave the answers with pi. 9.

10.

11.

t 6f

12.

13.

60 cm

226

Level G

Chapter 12

Lesson 8

Lighthouse Math

Exercise 12-8 Name Find the area of the composite figure or shaded area. 1.

15 ft

5 in 6 in

6 ft

4 in

7 ft

2m 9

20 ft

Find the surface area of the following rectangular prisms. 5.

4 yd

13 in

15 yd

7 ft 4 in

2 ft 12 ft

6 in

8 yd

Find the volume of the rectangular prisms. 9.

4 yd

10.

13 in

15 yd

7 ft 2 ft 12 ft

4 in 6 in

8 yd

Determine if you are finding surface area or volume then solve. 11. How much cardboard is needed to make a cereal box that is 2 in by 10 in by 8 in?

Lighthouse Math

12. How much cement will fill a hole that is 2.75 feet wide, 3 feet long and 1.5 feet deep?

Level G

Chapter 12

13. How much space is in a suitcase that is 18 in � 36 in � 14 in?

Exercise 8

227

Chapter 13 NYS NG Standards NY-6.SP.3 NY-6.SP.4 NY-6.SP.5c NY-6.EE.9

NY-7.SP.4 NY-7.SP.5 NY-7.SP.8

CC Standards 6.SP.A.3 6.SP.B.4 6.SP.B.5 6.EE.C.9

228

7.SP.B.4 7.SP.C.5 7.SP.C.8

In Chapter 13 will

Review Data in Many Different Contexts Students will be introduced to probability, analyze data by finding the mean, median, mode, and range of data sets, and display data in graphs. They will also be introduced to input/ output tables and connect linear functions to points on the coordinate plane. They will learn: • How to find the probability of events • How to find sample space • How to find mean, median, mode and range • How to create dot plots and histograms • How to complete input/output tables • How to graph a linear relationship from an input/output table

The skills that they will gain through these lessons include: • Multiplying probabilities to find the probability of multi-step problems • Create dot plots & histograms • Using function rules to complete input/output tables • Given an input/output table finding the function rule • Given an input/output table how to graph a linear function • Matching equivalent equations, input/output tables, and graphs This chapter does not have as many new strategies but has more new contexts where students will apply strategies and skills they have learned previously. They will review addition, subtraction, division, multiplying fractions and evaluating expressions.

229

Chapter 13-1 Introduction to Probability Daily Review

Find the product and simplify.

1. 1 � 4 = 3

2. 3 � 2 =

3. 1 � 1 =

4. 4 � 2 = 7

Learn and Connect Mark goes to a carnival and he is deciding which games to play. He wants to win 200 tickets to get a new hat. There is a spinner game, which is shown to the right. How would you describe Mark’s chances to win 100 tickets playing this game?

What outcome is most likely from the spin?

In the other game, you roll a 6 sided number cube with numbers 1 - 6. If you roll an even number you get 20 tickets, if you roll an odd number you get 10 tickets. Which game is Mark more likely to win tickets?

Apply Look at the table of how we can explain the likeliness, or chance, of an event occurring. Decide which word fit the provided situations. You have a 100 page book...

1. After Thursday it will be Friday.

Impossible: opening to page 140

2. A student will be out of class tomorrow.

Unlikely: opening to page 35

3. I will go in a spaceship tonight.

Equally likely: opening to page 50 or less

4. If I flip a penny I will get heads.

Likely: opening to page less than 80

5. It will rain tomorrow.

Certain: opening to page less than 500

6. I will forget my backpack tomorrow.

Vocabulary Chance - the likeliness of something happening - impossible, unlikely, equally likely as not, likely, certain Sample space - all the possible outcomes of an event 230

Level G

Chapter 13

Lesson 1

Lighthouse Math

Exercise 13-1 Name Sample space are all the possible options from an event. Find the sample space for the following situations. 1. A spinner can land on either red, blue or green.

2. A bagel shop has three types of bagels: blueberry, raisin and plain.

3. The custodian cleans the classroom Monday, Tuesday or Wednesday.

4. A spinner is spun and it lands on a random odd number greater than 1 & less than 9.

5. Two number cubes (1-6) are rolled.

6. You toss two coins: head or tails.

7. Each day the custodian can come in at 3 or 4 o’clock.

8. You also choose cream cheese for the bagel - plain or strawberry.

Determine how many possible outcomes there are for each situation draw a list, tree diagram or table to help.

Tree diagram H T

10. Two dice are rolled.

T H

11. You have a set of cards numbered 1-6. You choose two even cards.

T Table H

9. A spinner can land on either red, blue, or green. You spin twice.

H T

2�2=4 4 possible outcomes (count the sample space)

Example: You flip two coins.

12. You choose one random month of the year. 13. A jewelry store sells gold and platinum rings with a ruby, sapphire, emerald or diamond stone.

Challenge 14. Write at least one event for each that are: impossible, equally likely as not, and certain.

Lighthouse Math

Level G

Chapter 13

Exercise 1

231

Chapter 13-2 Finding Probability of a Single Event With a 6-sided number cube, numbered 1-6, what is the chance of the following events (impossible, unlikely, equally likely, likely, or certain)?

Daily Review

1. Rolling an even

2. Rolling a 4

3. Rolling a 10

Learn and Connect Mark’s friend comes to look at the game with him. They are trying to find the probability of getting each of the spins. How many total options are there? Of the total options, how many will you land on 25 tickets? What is the probability of winning 25 tickets? What is the probability of landing on 100 tickets? What is the probability of landing on try again?

Apply Find the probabilities of the following events. P(A) means find the probability of A. C C A

C A

P(C) -

P(green) -

P(vowel) -

P(A) -

P(not purple) -

P(not S) -

P(not B) -

P(blue or green) -

P(S or O) -

P(A or B) -

P(blue) -

P(not L) -

O M

Vocabulary Probability - the likelihood of something happening, usually written as a fraction (probable outcome/total possible outcomes)

232

Level G

Chapter 13

Lesson 2

Lighthouse Math

Exercise 13-2 Name Use the images to determine the probability. 1.

P(2) : P(odd): P(1 or 5) : P(L) :

2. Letters in the word CHALLENGE are placed in a bag.

P(A) : P(vowel) : P(not 3) :

3. Cards with the numbers 1 - 10 are placed face down on a table

P(odd) : P(multiple of 3) : P(white) :

P(striped) : P(black or stripe) :

Which marble is most likely? P(3) :

P(not 2) : P(even) :

P(not 3) :

Which number is least likely?

Challenge 6. Create a spinner & situation where you are likely to win.

Lighthouse Math

7. Create a bag of marbles & situation where you are likely to lose.

Level G

Chapter 13

Exercise 2

233

Chapter 13-3 Probability of Multi-Step Events Daily Review

Using the letters in MATHEMATICS find the probabilities.

1. P(A) =

2. P(not vowel) =

3. P(M or A) =

4. P(H) =

Learn and Connect Mark and his friend go to a new game. Here they spin the spinners two times. To win the large prize you need to spin gold and 2. To win an extra spin you need to spin blue or red. What is the probability of spinning gold? What is the probability of spinning 2? To find the probability of multiple events we multiply the two probabilities. What is the probability of spinning gold AND 2?

Complete the table for the given scenarios. Event 1

Pull a letter from

Event 2

Probability of both

P(black)

P(even)

P(black & even)

P(white)

P(2)

P(white and 2)

P(not black)

P(not 1)

P(not black and not 1)

P(vowel)

P(odd)

P(vowel & odd)

P(m or n)

P(2)

P(m or n and odd)

P(not d)

P(not 4)

P(not d and not 4)

P(A)

P(3)

P(A and 3)

MONDAY Pull a number between 1 - 5

234

Level G

Chapter 13

Lesson 3

Lighthouse Math

Exercise 13-3 Name Sometimes we have events where the total changes from Event 1 to Event 2. Look at the example and then solve the problems. Event 1

Event 2

Prob

Bag with 7 chips - 3 red, 2 blue, 2 green. Find probability of blue then blue without replacement

Find the probability of pulling a black and WITHOUT replacing it, drawing a white. 2 4 8 10 � 9 = 90

**If we pull one marble out and do not replace it there are now 9 marbles

Letters - ABCDE. Probability of vowel then C without replacement. Card with numbers 1-8. Probability of even then odd without replacement Bag of marbles to the left. Probability of stripe & without replacement stripe Letters in SUNSHINE. Probability of S then N without replacement.

1. Flip a quarter and roll a number cube. P(heads & 4)

2. L etters - LMNOP 3. Bag of chips - 4 - pull consonant, white, 3 black, 1 keep it, and pull red. P(red) put the another consonant. chip back P(white).

Use this for the next 3 problems.

5. Pulling blue marble, putting it back then pulling red.

4. On any day the chance of rain is 1 . What is the 8 probability that it rains two days in a row?

6. Pulling green, 7. Pulling a non-green keeping the marble marble, replacing it, and pulling another and then pulling an green. orange.

Challenge 9. You flip a penny, nickel, dime, and quarter. What is the probability of all landing on heads?

8. If you roll 2 number cubes and then multiply the numbers, what is the probability of the product being an even number?

Lighthouse Math

Level G

Chapter 13

Exercise 3

235

Solve the following compound probabilities and determine if there is replacement or not.

Chapter 13-4 Mean, Median, Mode, Range Daily Review

The colored chips to the right were placed in a bag.

1. P(yellow)

2. P(red or blue)

3. P(red) then P(red)

Learn and Connect The class takes a math test and the scores are below:

MEAN

MEDIAN

7, 3, 4, 1, 7, 6

95 70 85 100 55 80 85 90

Sum of numbers divided by the total numbers

Arrange in order and pick the middle value

In order to understand the data let’s analyze it by finding the…

Mean = (7 + 3 + 4 + 1 + 7 + 6) = 28 6 = 4.66

1, 3, 4, 6, 7, 7 Median = 4 + 6 = 5 2

Mode MODE

RANGE

7, 3, 4, 1, 7, 6

Most common number

Difference between highest and lowest

Range Median

7, 3, 4, 1, 7, 6

Mean/Average

Range = 7 - 1 = 6

Mode = 7

Apply Find the mean, median, mode and range for each data set. Mode

Range

Median

Mean/Average

24, 31, 12, 38, 12, 15

5, 28, 16, 32, 5, 16, 48, 29, 5, 35

53, 13, 34, 41, 26, 61, 34, 13, 69

85, 58, 72, 85, 46, 93

92, 63, 22, 80, 63, 71, 44, 35

39, 82, 74, 96, 64, 52, 74

236

Level G

Chapter 13

Lesson 4

Lighthouse Math

Exercise 13-4 Name Find the mean, median, mode and range from each situation. 1. At Oliver's Bakery, in the 6 hours they were open, they sold the following number of pies: 55 blueberry, 57 chocolate, 50 strawberry, 51 pecan, 61 pumpkin and 50 custard. Mean

Mode

Median

Range

2. Dave counted the number of times people sharpened their pencils in class for a week. He counted: 4, 13, 4, 1, 14 and 11. Mean

Mode

Median

Range

3. Victor was selling chocolate for a school fundraiser. The first week he sold 75, the second week he sold 67 and the third week he sold 75. In the fourth week he sold 70 and in the last week he sold 68. Mean

Mode

Median

Range

4. The of a numerical set of data is the difference of the greatest value and the least value.

5. The of a numerical set of data is the middle number when the numbers are written in numerical order.

of a numerical 6. The set of data is the value that occurs most frequently.

is the average of 7. The a set of data, calculated by dividing their sum by the number of data points.

Challenge You and your friend are having a friendly competition about the scores on your math quizzes. Both of your scores for the first five quizzes are given below: Your quiz scores: 18, 16, 19, 15, 17 Friend’s quiz scores: 20, 20, 13, 12, 17 8.

Who has the higher range?

Who has the higher mean?

Lighthouse Math

Level G

Chapter 13

Exercise 4

237

Fill in the word that fits the description.

Chapter 13-5 Data Use this data set 120, 135, 118, 142, 112, 128, 120 to find the following.

Daily Review 1. Mean

2. Median

3. Mode

4. Range

Learn and Connect A survey was sent to the 7th grade students asking how many books they read over the summer. Here are the results: 0, 4, 6, 1, 2, 2, 3, 6, 4, 3, 3, 1, 0, 2, 2, 4, 0, 3, 2

Dot Plot

One dot per data point, label the axis.

Using the dot plot & histogram answer the questions. Notice which graph is helpful for different questions. 0

1. How many students were surveyed?

2. How many students didn’t read any books?

3. How many students read exactly 3 books?

4. How many students read less than 3 books?

Number of students

5. What was the most books read by any student?

6. How many students read more than 5 books?

Histogram Equal groups (each bar represents 3 numbers), gathers data to see trends

6 4 2 3-5

0-2

Bonus: How many books were read in all?

6-8

Books Read

Apply Answer the questions based on the provided graph. Distribution of Math Test Scores

Dot Plot of the number of Children in a Family

Number of Students

Number of Books Read

8. How many more students read 2 books than 1 book?

7. How many students read more than 2 books?

12 10 8 6 4 2 0

Number of Children in a Family

41-51

51-60 61-70 71-80 81-90 91-100 Test Scores

1. How many families have 3 or more kids?

238

2. W hat is the most number of kids in a family?

Level G

Chapter 13

3. How many students earned 81 or higher?

Lesson 5

4. How many students earned less than 61?

Lighthouse Math

Exercise 13-5 Name Given the data, find the frequency of the given intervals then create a histogram. Each student brings a bag of trail mix to class, and they then count the number of chocolate candies in their bag. The amounts are recorded below: 44, 63, 100, 46, 67, 42, 99, 79, 83, 42, 77, 38, 72, 54, 52, 67, 83, 34, 98, 86, 44 Histogram

Chocolate Candies per Bag of Trail Mix 10 9 8 Frequency table:

7 6

Interval

# of values

1-20

21-40

3 2

41-60

61-80

0 1-20

21-40

41-60

61-80

81-100

The height of 20 teachers, in inches, are given below. 68, 70, 70, 71, 75, 80, 81, 82, 84, 75, 75, 80, 75, 77, 75, 80, 83, 80, 71, 70

2. What is the range of the data?

3. What is the mode of the data?

4. How many teachers are greater than 70 inches tall?

5. What is the probability that a random teacher chosen will be 74 inches or shorter?

Challenge 6. Explain when or how a dot plot is more helpful than a histogram.

Lighthouse Math

Level F

7. Explain when or how a histogram is more helpful than a dot plot.

Chapter 13

Exercise 5

239

Given the data, create a dot plot and answer the questions.

Chapter 13-6 Input/Output Tables Evaluate the following expressions if x = 3.

Daily Review 1. 5 x–6=

2. x2 – 4 =

3. 7x – 2x =

4. x – 15 =

Learn and Connect A function is a rule or expression that relates two values. We input a number into a function, do the rule and then get an output.

x=8 input

Looking at the image to the right, the function is y = 2x + 5, the input is x and the output y.

y = 2x + 5

If we input 8, x = 8, what will our output be?

y output

We usually show the inputs and outputs in a table, and then complete the table with our given function. x

-2

Apply

Complete the tables given the function. 1.

y = 9x x -2 -3 -5 -7 6

x 5 -3 -9 3 6

4. y = -2x – 7 x -6 -2 -7 -5 1

5. y

y = -7x – 4 y

x -3 3 -5 -4 -2

x 7 -8 9 -5 -7

y=x+7 y

y=x+3 y

y = -6x x 7 6 -6 -9 1

Vocabulary Function - rule that takes our input to an output Input - x, the number we put into our function Output - y, the number that comes out of our function

240

Level G

Chapter 13

Lesson 6

Lighthouse Math

Exercise 13-6 Name Complete the table for the perimeter of the rectangle (y), and then answer the questions. Input, x

5 3

Output , y x

1. Write the rule and equation, that describes the function.

2. Use your equation to find y if x is 20.

3. Use your equation to find the value of x when the perimeter is 50.

Write a rule and complete the table. 4. The output is 1 less than input. Input, x

5. The output is twice the input. 5

Output , y

Input, x

6. The output is 5 more than the input. 9

Input, x

Output , y

Input, x

Output , y

What is the input for y = 15? 9.

Input, x

Output , y

What is the input for y = 20?

Input, x

Output , y

What is the input for y = 15?

10.

Input, x

Output , y

What is the input for y = 15?

Challenge Complete the inputs given the function and output. 11. y = 3x – 2

Lighthouse Math

12. y = 3x – 2

x -2

x y

Level G

Chapter 13

Exercise 6

241

Write the rule. Use the rule to solve for the input, given the output.

Chapter 13-7 Graphing Functions Complete the table given the function.

Daily Review 1. y = x + 2

-6

-3

2. y = 3x + 1

-6

-3

Learn and Connect We can also graph functions. Given an equation: y = 2x + 3

First complete the table: x

-2

-1

6 4

2 y

x -10

-8

-6

-4

-2

Then use the table as coordinate points (x,y). Plot the 5 points in the table and connect them with a line.

-4 -6

Use the equation, table or graph to find.

What is x if y is 13?

-8

What is y if x is –4?

-10

Apply Find the different representations given the table or equation. 1. Equation:

y=5+x

-3

-1

242

18 y 16 14 12 10 8 6 4 2 -3 -2 -1 -2

2. Equation:

10 8 6 4 2 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10

x 1 2 3 4 5 6 7

Level G

Chapter 13

Lesson 7

1 2 3 4 5

Lighthouse Math

Exercise 13-7 Name Match the graphs with the equation and the tables, place the letter for the matching table and number for matching graph in the equation table. Equation

y = 1x - 3 2

y = -3x + 2

y = 2x - 3

y = 3x + 2

y = -2x - 3

y = -2x + 3

Table Graph

-2

-4

-3

-2

-1

-2

-1

-5

-2

-4

-2

-4

-10

Lighthouse Math

Level G

Chapter 13

Exercise 7

-2

-7

-3

-2

-3

-7

-11

243

Chapter 13-8 Review Daily Review Complete the table for the equation y = 3x + 2.

-3

-1

5 2

Learn and Connect Using sample space find the number of possible outcomes. 2. There are 4 shirt options and 2 pants options for a uniform.

1. You can order black or green tea and get it sweet or unsweet.

3. Spinner with 5 sections -red, blue, green, pink, yellow and it is spun 3 times.

Find the probability of the following events. Each of the following names is placed in a hat. Mark

Jeremy

4. P(4 letter name)

Bob

Maxwell

Bill

Jack

Jerry

Tito

Conner

Joe

5. P(name starting with J or B)

6. P(name starting with T)

7. P(7 letter name)

8. P(name starting with S)

9. P (name ending with Y)

Apply Find the probability from the following scenarios. Using the letters:

P(A) then P(vowel)

P(S) then P(A)

P(R) then P(T)

P(even) then P(even)

P(3) then P(5 or 10)

P(multiple of 3) then

AUSTRALIA With replacement

Number Cards with numbers 1 - 10 without replacement

244

P(less than 4)

Level G

Chapter 13

Lesson 8

Lighthouse Math

Exercise 13-8 Name Complete the table. 1.

Mode

Range

Median

Mean/Average

89 , 76 , 85 , 76 , 77 , 84 83 , 97 , 85 , 84 , 96 , 80 , 80 , 87 , 91 30 , 36 , 47 , 50 , 50 , 50

Given the data make a dot plot and histogram. 2. T he ages of 20 students in a karate class are given below. 11, 5, 9, 13, 8, 9, 9, 11, 10, 8, 6, 7, 12, 11, 13, 12, 7, 6, 11, 12 7 6 5 4 3 2 5

1 0

5-6

7-8

9-10 11-12

13-14

Complete the equations, table or graph given one piece of information. x

-2

-4

-2

-1

Equation:

Equation: y = 2x – 5

10 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6

6 5 4 3 2 1

8 6 4 1 2 3 4 5 6

-6 -5 -4 -3 -2 -1

2 -6

-4

-2

1 2 3 4 5 6

-2 -3 -4 -5 -6

-2 -4

Lighthouse Math

Level G

Chapter 13

Exercise 8

245

Chapter 14 NYS NG Standards NY-7.RP.1 NY-7.RP.2 NY-7.RP.3 NY-7.NS.1 NY-7.NS.2 NY-7.NS.3 NY-7.EE.3

NY-7.EE.4 NY-7.G.1 NY-7.G.4 NY-7.G.6 NY-7.SP.5 NY-7.SP.8

CC Standards 7.RP.A.1 7.RP.A.2 7.RP.A.3 7.NS.A.1 7.NS.A.2 7.NS.A.3 7.EE.B.3

246

7.EE.B.4 7.G.A.1 7.G.B.4 7.G.B.6 7.SP.C.5 7.SP.C.8

In Chapter 14 we will

Review all Concepts. We will practice using the order of operations with rational numbers. We will also practice all operations using integers and delve back into ratios, percentages, and interest. We will practice geometry concepts and create functions and graphs.

• Order of operations with rational numbers and exponents • We will review the steps of the order of operations which include parentheses, exponents, multiplication and division, followed by addition and subtraction • Integer operations • We will practice adding, subtracting, multiplying, and dividing negative and positive numbers • 1-2 step equations • We will solve 1-2 step equations by solving for unknown numbers • Ratio and proportions • We will practice developing and identifying ratios and proportions • Percent, tax/tip, interest • We will use what we know about percentages to find taxes, tips, and interest • Geometry • We will review what we know about geometrical concepts • Probability • We will find the probability of different situations • Functions/graphs • We will create graphs using tables that we create using basic operations

247

Chapter 14-1 Order of Operations Review Daily Review 1. 15 +

What would you put in the blank to make the equation true?

= 21

2. 4 �

3. 8 �

= 20

4. 25 �

= 18

Learn and Connect PEMDAS helps us remember the order of operations. When working with the order of operations, parentheses and exponents come first. Then, it is multiplication and division from left to right, followed by addition and subtraction. Consider the following equation: (52 + 3 ∙ 31 ) + 5.24 � 2

First, work out the exponents:

+ 3 ∙ 31 ) + 5.24 � 2

( (

) + 5.24 � 2

Then, solve any multiplication and division from left to right.

+ 5.24 � 2 +

Therefore, (52 + 3 ∙ 31 ) + 5.24 � 2 =

Next, complete the other operations in the parentheses, starting with multiplication and then addition. Last, solve all addition and subtraction from left to right.

Apply Use the order of operations to solve the following equations. 1.

1 ( 32 + 41 ) + 12 =

(2.3 + 5) ∙ 2.3 � 7 =

2.5 + 3.78 ∙ 4 � 7.8 =

( 21 + 42 ) � 83 =

3 ÷6+2∙ 1 = 7 2

22.08 ÷ 6.9 + (3 �2.1) =

248

Level G

Chapter 14

Lesson 1

Lighthouse Math

Exercise 14-1 Name For each expression, determine the next step. 1. Step1: 2 + 3 + 7.2 ∙ 4 � (8 ∙ 3) 2. Step 1: (8.5 + 3.7 ∙ 3) � 62 + 3 Step2: 2 + 3 + 7.2 ∙ 4 � 24 Step 2: (8.5 + 11.1) � 62 + 3 Step 3: 19.6 � 62 + 3 a. 3 + 7.2 b. 4 � 27

c. 7.2 ∙ 4 d. 2 + 3

a. 19.6 ∙ 3 b. 3 � 62

3. Step 1: (6 + 51 ∙ 3) + 45 � 25

c. 62 + 3 d. 62

Step 2: (6 + 35 ) + 45 � 25 a. 6 + 35

c. 45 � 25

b. 35 + 45

d. 45

Circle the example that correctly solved the expression. 4.

15 � ( 51 + 6 ÷ 21 )

15 � (6 51 ÷ 21 )

15 � ( 51 + 12)

15 � 12 25

15 � 12 51

2 35

24 5

3 ∙ (72.5 ÷ 5) � 5 =

4 �(2 � 1)+4= 6 3 6

15 ÷ 51 � 5 ∙ 2 =

200 � 3.25 ∙ 5 + 2.8 =

1 + 3 � 3 = 8 4 12

10.

2 + (1 � 1 ) ∙ 1 = 5 5 4

12. 2 � 41 + 21 ∙ 41 =

11. 13 � 25.2 ∙ 12 + 23 =

Lighthouse Math

Use the order of operations to simplify expressions.

Level G

Chapter 14

Exercise 1

249

Chapter 14-2 Integer Operations Review Daily Review

Solve using the order of operations.

1. 2.35 + 6 ÷ 3 � 1 =

3. 21 � 4 ÷ 2 + 43 =

2. 42 � 3.27 � 2 + 3 =

Learn and Connect Integer Rules Addition

Subtraction

Same signs: Add & keep the sign

Add the opposite (change the sign of the second number and follow the addition rules) Example: -65 - 24

Examples: 12 + 3 = 15 -12 + (-3) = -15 Different signs: Subtract and keep the sign of the larger number

Multiply & Divide Same sign = positive answer Different sign = negative answer

Examples: -10 + 23 = 13 10 + (-23) = -13

-65 + -24 = -89

Example: -4 � -5 = 20 ; 4 � -5 = -20

Apply Solve the following problems using the number line below if necessary. 1.

5 � (-4) =

(-5) + 7 =

(-6) � 1 =

(-2) � 7=

(-2) + 2 =

(-4) � (-4) =

4 � (-7) =

(-24) ÷ 8 =

(-2) � (-9) =

10.

9 + (-7)=

11.

(-6) ÷ 3 =

12.

(-72) ÷ 9 =

13.

8 ÷ (-4) =

14.

(-6) � (-6) =

15.

(-2) � (-5) =

16.

(-6) � (-1) =

17.

(-4) ÷ (-1) =

18.

63 ÷ (-9) =

19.

(-2) + 2 =

20.

(-2) + (-7) =

21.

1� 2 =

250

Level G

Chapter 14

Lesson 2

Lighthouse Math

Exercise 14-2 Name Solve the following problems using the number line below if necessary.

-8

-7

-6

-5

-4

-3

-2

-1

8 + (-10) =

16 ÷ (-2) =

(-2) � (-2) =

3+8 =

(-12) + (-15) =

(-48) ÷ (-6) =

(-7) � 5 =

(-2) � (-9) =

(-10) + 4 =

10.

(-9) + 3 =

11.

(-7) � (-2) =

12.

(-4) + 7 =

13.

(-28) ÷ 7 =

14.

6 ÷ (-3) =

15.

(-6) � 7 =

16.

(-1) + 6 =

17.

7 + (-11) =

18.

(-35) ÷ (-5) =

19.

(-4) � 2 =

20.

15 + 9 =

21.

(-11) + 14 =

22.

(-9) ÷ (-9) =

23.

3 � (-9) =

24.

(-7) � 0 =

25.

(-8) + (-4) =

26.

(-6) ÷ (-3) =

27.

(-15) + (-9) =

28.

3 + (-15) =

29.

6 + (-1) =

30.

56 ÷ (-8) =

31.

(-14) ÷ 7 =

32.

(-3) � (-4) =

33.

(-1) � (-7) =

34.

(-7) � (-4) =

35.

1+3=

36.

(-5) � 8 =

Draw a line from the story problem to the correct expression used to solve it. 37.

Charlie has a balance of $-47 in his checking account. If he deposits a check for $55, what will Charlie’s balance be?

(-47) + 55 = 8

38. James wants to buy a board game that cost $55. He currently has $47. How much more money does he need?

47 -55 = -8

39. The temperature in Montana fell 55 degrees last night. If the temperature started at 47° F, what was the temperature after it fell?

55 -47 = 8

Lighthouse Math

Level G

Chapter 14

Exercise 2

251

-10 -9

Chapter 14-3 Equations Review Daily Review

Solve.

1. 9 � (-4) =

2. (16) + 17 =

3. (-9) ÷ (-3) =

4. (15) ÷ 3 =

Learn and Connect How to Solve Multi-step Equations 4(x + 2 ) � 10 = 2(x + 4) 4x � 2 = 2x + 8

Step 1: (Distributive Property) Simplify each side as much as possible Step 2: (Combine like terms) Eliminate the variable from one side

2x � 2 = 8

Step 3: (Inverse operations) Eliminate the constant term from the side with the variable

2x = 10 x=5

Step 4: (Inverse operations) Divide each side by the coefficient of the variable

Apply

Use the strategy above to solve the equations. 1.

13x � 9x + 20 = 30 + 2

2(4 � y) � 3(y + 3) = -11

4(x + 6) � 11 = 25

14 + 13y = 20y � 21

8q + 6 = 4q � 14

-15b + 21 + 5b = -19

-3(7p + 5) = 27

7 � (5t � 13) = -25

252

Level G

Chapter 14

Lesson 3

Lighthouse Math

Exercise 14-3 Name

-16 + 5n = -7(-6 + 8n) + 3

24 + 8x = 8(5x+8) + 8x

-4k + 2(5k − 6) = -3k − 39

-4 − 4(-x − 1) = -4(6 + 2x)

-3(1 + 6r) = 14 − r

5(n − 6) = 4(n − 7)

-3(4r − 8) = -36

24 = 4(p − 7) + 8(1 − 6p)

3 = x + 3 − 5x

10. -57 = -6(4 + 5v) − 3

11. -12 = 2 + 5v + 2v

12. -3(1 + 4a) = 33

13. -11 + 10(p + 10) = 4 − 5(2p + 11)

14. -7 = 7r − 6r

15. -24 = 4n + 4n

16. 9= -3(-5 − 2n) − 6(1 − 5n)

17. 3(x – 4) = 2(-2x + 1)

18. 13x − 9x + 20 = 30 + 2

Lighthouse Math

Level G

Chapter 14

Exercise 3

Use the strategy taught in the lesson to solve the equations.

253

Chapter 14-4 Ratio, Scales, Proportions Review Daily Review

Solve for x.

1. 8(6.9x – 0.7 + 1.1x) = 7.2

2. 8 + 1.7x = -2x – 4 – 0.3

Learn and Connect Proportion, Ratio and Scale Explanations Proportion

Ratio

Scale

Statements that express two equivalent ratios. Proportions can be written as a fraction (a/b = c/d), or using a colon (a:b = c:d).

An expression of how much of one thing there is compared to another.

A scale drawing is an illustration of a real object which has been reduced or enlarged, but still proportional to the real object. The proportion by which the drawing of an object is changed is called the scale ratio.

Can be written as a fraction using the word “to” or with a colon (:).

Example: To check whether two ratios are proportional, they can be cross multiplied.

3 4 � 3 4

Example: There are 20 students in a class, and 13 are wearing red shirts and the rest are wearing blue.

Example:

4 in

The ratio of red to blue shirts is 13:7.

2 in 1 in 2 in

Apply Determine the ratio reduced to lowest terms. 1.

The ratio of

Complete the proportional ratios. 4.

254

= 3

1 = 4 2 4

Level G

Chapter 14

= 16

Lesson 4

5 = 15 6 18

1 = 2 6 4

Lighthouse Math

Exercise 14-4 Name Use the diagram below to answer questions 1-2. 1.

Kevin’s Apartment

Living Room

Kevin made a scale drawing of his apartment. If he drew his bathroom as 4 in long and 3 in wide, what is the actual length and width of his apartment?

Bathroom Kitchen

2. The kitchen in Kevin’s apartment is 8 ft long and 12 ft wide. What is the length and width of the kitchen to scale?

Bedroom

Scale: 1in = 4ft

For each of the rectangles below, find the ratio of the width to the length reduced to lowest terms. 3.

5. 2 in

5 ft 25 ft

30 in

1 ft 8 ft

2 in

3 in

Determine the ratio described below. 8.

Quadrilaterals to other figures:

Blue to green stars:

Complete the proportional ratios. 9.

= 5 2

10. 19 = 3 57

11.

= 8

12.

27 = 72 6 40

13.

15 = 5 36 4

Solve. 14.

Martin is drawing a scale model of his sister’s doll house that is 4 ft tall. If he uses a scale of 2 ft to 5 in, how tall will he need to draw his sister's dollhouse?

Lighthouse Math

Level G

Chapter 14

Exercise 4

255

Chapter 14-5 Percent, Tax, Interest Review Daily Review

Determine whether each pair of ratios are proportional.

1. 56 , 7

2. 19 , 1

72 9

3. 10 , 25

24 60

Learn and Connect Calculations Cheat Sheet Percents

Interest

Example: 60% of 50

Part % = Whole 100

X 50

Steps: • Set up the problem • Cross multiply • Solve for x

I=P·r·t

60 100

3000 100x = = 30 100 100

Interest - an additional fee for borrowing money

30 is 60% of 50

Principal - amount of money borrowed

Tax & Tip

Rate of Interest - percent charged

Tax - a required amount you have to pay for goods or services Tip - optional additional money given for a service

Time - amount of time borrowed

Example: $20 with a 3% tax 3% = 0.03 0.03 � 20 = 0.6 $20 + 0.6 = $20.6

Steps: • Turn percent into decimal • Multiply • Add to original cost

Example: $4,500 at 9.5% for 6 years I = (4,500)(0.095)(6) I = $2,565

Apply Determine the amount. 1.

90% of 70 =

70% of 60 =

60% of 70 =

20% of 30 =

7% of $45 = $

3% of $28 = $

Determine the total cost including tax/tip. 5.

5% of $30 = $

8% of $18= $

Find the total interest paid for the given information using the formula above. 9.

256

10. $6,500 at 3.2% for 3 years

$10,000 at 3.8% for 5 years

Level G

Chapter 14

Lesson 5

11. $3,500 at 4.3% for 10 years

Lighthouse Math

Exercise 14-5 Name A store has several items on discount. The list below shows the items and their discounted rate. Find the price of the item after the discount. ITEM

ORIGINAL PRICE

DISCOUNT

Red shirt

$22

10% off

Basketball

$7.50

20% off

Paint set

$62

52% off

Sandals

$25.88

25% off

Lamp

$23

15% off

NEW PRICE

Jonathan is comparing prices on car loans. Determine the total cost he will pay by the end of each loan. LOAN OPTION 1 Principal Interest rate

Duration (time)

$45,000 5%

10 years

LOAN OPTION 2 Principal

$45,000

LOAN OPTION 3 Principal

Interest rate

4.5%

Interest rate

Duration (time)

5 years

Duration (time)

Interest paid:

Total cost:

$45,000 8%

8 years

Challenge 9.

Four friends went to a bakery. Their bill came out to $43.30. If they want to leave a 20% tip and then split the bill evenly with each other, how much will each person pay?

Lighthouse Math

Level G

10. Mr. Smith has a car loan for his $25,000 car. He has an interest rate of 5%. How much money will he save if he pays off his car in 5 years instead of ten?

Chapter 14

Exercise 5

257

Chapter 14-6 Geometry Review Daily Review

Determine the amount.

1. 50% of 70 =

2. 20% of 40 =

3. 15% of 80 =

4. 100% of 20 =

Learn and Connect Geometry Formulas Perimeter The measurement of distance all the way around an object. P=S+S+S+S P=1+1+1+6+3+5 P = 17 1

P = (2 × W) + (2 × L) P = (2 × 4) + (2 × 2) P = 12

1 5

Area of a rectangle: A=L×W A=5×2 2 A = 10

Volume

Circles

The amount of space a 3D object occupies.

Circumference C = 2πr or C = πd C = (3.14)(6) C = 18.84

V= L × W × H V=3×2×4 V = 24

Area The measurement of the entire surface of a figure.

Area of a triangle: A = 1 (B × H) 2

Area A = πr2 A = (3.14)32 A = 28.26

Area of a parallelogram: A=B×H A=7×3 3 A = 21 7

A = 1 (3 × 4)

Radius am e 6 te r

A=6

Circumference

Apply Find the perimeter and area of the figures. 6 in

1. 13 in

5 in 6 in 8 in

6 in

12 in

C= 4 in

258

C= 12 in

Level G

A= 3 in

Find the volume of the figures.

11 in

4 in

Find the circumference and area of the circles. 4.

5 in

2 in

Chapter 14

Lesson 6

5 in

9 in

3 in

Lighthouse Math

Exercise 14-6 Name Find the perimeter and area of the figures. 1.

6 in

4 in 4 in

9.2 in

2.5 in

12 in

8 in 10 ft

6.8 in

4.8 in

13 in

20 in

3.6 in

Find the circumference of the circles. 5.

23.4 in

16 in 7 in

11.8 in

10.

11.

12. 12 in

2.1 in

1.4 ft 6.3 in

4.6 in

9 in

10.5 in

2.2 in 5 ft

2.32 ft

Find the area of the shaded composite figures. 14.

2 in

15.

16.

8 in

7 in

5 in

Lighthouse Math

6.6 in

8 in 9 in

13.4 in

13.

4.6 in

6.6 in

Level G

Chapter 14

Exercise 6

259

Find the volume of the figures.

Chapter 14-7 Probability Review Find the circumference and area of the following circles.

Daily Review

1. Circle with D = 10 in C =

2. Circle with r = 10 in C =

3. Circle with D = 3 ft C =

Learn and Connect Probability Cheat Sheet Probability

Single Event

Multiple Events

The probability of something occurring means how likely it is to happen. We can create a sample space to show the likelihood of something occurring.

The probability of a single event occurring can be represented as a fraction:

Independent event: events that do not affect each other.

Example: The tree diagram below shows the sample space for flipping a coin twice. H

T H

HT TH

# of chances to get outcome total possible outcomes

Example: If you have 5 cards labeled A, B, C, D, E, the probability of choosing the card labeled A at random is: 1 5

Example: If you pull a red card from a deck and then replace it, you do not change the probability of pulling a red card a second time. Dependent event: events that do affect each other. Example: If you pull a red card from a deck and then do not replace it, the chances of you pulling a red card a second time decreases.

Apply Determine if the probability is dependent or independent from the result of the first action. Explain. 1.

You choose a marble from a bag and replace 2. it. Then, you choose another marble.

Your teacher chooses a student to stand in the front of the line. She then chooses a student to stand at the back of the line.

Find the probability of each of the outcomes using the image. 3. What is the probability of randomly choosing a blue flower?

260

Level G

4. What is the probability of randomly removing a blue flower and then a pink flower?

Chapter 14

Lesson 7

Lighthouse Math

Exercise 14-7 Name Write the total possible outcomes for each scenario. 1.

A bag contains 3 blue spheres, 2 green spheres, and 5 purple spheres. If a ball is randomly selected from the bag, how many outcomes are possible?

There is a set of 10 blue cards numbered 1-10 and 10 red cards numbered 1-10. If a card is selected from the mixed set, how many possible outcomes are there?

Create a tree diagram to list all the possible outcomes. Write all the possible outcomes as a sample space. Show the possibilities you have to choose one crust and two fillings. You can choose to double a filling. For example, you can have double the strawberries. Pie crust type: chocolate or regular Pie fillings: strawberries, pecans, custard

4. Chocolate

3. Regular

Use the spinner to determine the possibilities. Consider each occurrence if both spinners are spun. 5.

Possibility of both digits being the same

Possibility both spinners land on an odd number

5 1

2 4

Possibility that spinner A lands on 2 and spinner B lands on an even number

3 B

Find the probability that two cards are picked without looking at not replaced. 8.

Picking A and then C.

Picking either D or F.

10. Picking C and then D.

Lighthouse Math

Level G

Chapter 14

Exercise 7

261

Chapter 14-8 Functions and Graphs Review Draw a tree diagram and find the probability.

Daily Review

1. What is the sample space of possible outcomes for tossing three coins, one at a time?

2. What is the probability that all 3 coins will land on heads?

Learn and Connect The grid below shows the location of 4 students from school. Use it to answer the questions below. N 1.

Key

Fill in the chart below based on the locations of each home. Student

6 5

Lucas

Matt

Matt Logan

Ron

Logan

To get from the school to Logan’s house, you have to move -6 units on the x-axis and -5 units on the y-axis. Explain how to get from Lucas’s house to Ron’s house.

-6 -5 -4 -3 -2 -1

-1

3 4 5

-2

Ron

-3 -4

School

-5 -6 S

Matt left his house and walked 3 units north and 6 units west. Write the coordinate pair that shows where Matt is now.

Apply Complete the table and graph the ordered pairs on the coordinate plane. Draw a line through the points.

8 6 4

MULTIPLY BY 2 -8 -6 -4 -2 x

-4

-2

-2 -4

-6 -8

262

Level G

Chapter 14

Lesson 8

Lighthouse Math

Exercise 14-8 Name Complete the tables and graph the ordered pairs on the coordinate plane. Draw a line through the data points for each table. 1.

MULTIPLY BY 5

2 x

-5

-2

15 10

5 5

-25 -20 -15 -10 -5

10 15 20 25

-5

SUBTRACT 5

-10 x

-10

-5

-15 -20

-25

Use the equation to complete each table, then, graph the equation. Draw a line through the data points for each table. 3.

Y=X+6

8 x

-2

-6

6 4

-10 -8 -6 -4 -2 -2

Y = 8 -X

-4 x

-1

-6 -8

-10

Identify the coordinate needed to complete the shape. 5.

6. -6 -5 -4 -3 -2 -1

Lighthouse Math

-1 -2 -3 -4 -5 -6

Isosceles triangle: (

)

Level G

4 3 2 1 -4-3 -2 -1 -1 -2 -3 -4

Chapter 14

Diamond:

1 2 3 4

Exercise 8

(

) (

)

263

Glossary Absolute value

Circumference

the distance a value is from zero, the notation looks like |x| 104 6-1

distance around a circle, similar to perimeter 218 12-4

Alternate exterior angles

1 2 3 4 7

5 8

Coefficient the number in front of a variable

140 8-1

Common denominator a common multiple of the denominators of a set of fractions 70 4-2

Composite/Compound Figures two exterior angles on opposite sides of a transversal which lie on different parallel lines 204 11-6

Alternate interior angles angles that are formed on opposite sides of the transversal and inside the two lines 204 11-6

multiple shapes that are put together or overlap 220 12-5

Constant a number whose value is always the same

140 8-1

Coordinate plane y axis

Area

4 cm

6 cm

the amount of space a 2 dimensional 5 cm shape covers, measured in unit squares (in.2, cm2, ft2) 214 12-2

Base

2 1 -4 -3

-2

-1 -1

x axis 1

-2 -3 -4

the factor that is being multiplied when using an exponent 116 6-7

a plane that has two perpendicular axes (x and y) intersecting at the point (0,0) 108 6-3

Chance

Coordinate point

the likelihood of something happening impossible, unlikely, equally likely as not, likely, certain 230 13-1

264

Level G

Glossary

a pair of numbers written as (x,y) that determine a specific point on a coordinate plane 108 6-3

Lighthouse Math

Glossary Corresponding angles

Equation

Two angles that lie the same relative position at each intersection (and have the same angle measurement) 204 11-6

two expressions or terms that are set equal to each other, 3x + 8 = 17 146 8-4

equal, the same value even if written with different numbers 160 9-2 68 4-1

Diameter the distance from one side of a circle to the other through the center 218 12-4

Discount the amount or percent an item is marked down, on sale or % off 186 10-6

30%

Distributive property allows you to multiply a sum by multiplying each addend separately, then add the terms. 3(2x - 4) = 6x - 12 144 8-3

Dividend

Equivalent ratios a set of ratios where one ratio is a multiple of the other ratio. 1/2 is equivalent to 3/6

2 10 3 = 15 160 9-2

Expanded form a number form that writes each digit multiplied by the place value of that digit; 400 + 50 + 3 14 1-1

Expanded notation a number form that writes each digit as a product of the digit and the place value; 4x100 + 5x10 + 3 14 1-1

the number in a division problem that is being divided 58 3-5

Exponent

Divisor

number is raised to, squared = second power, cubed = third power 40 2-5

any number that divides another number

52 3-2

Dot plot

number of times we are 3 the multiplying the base; power which a

Exterior angles Angles that lie on the outside of the parallel lines 204 11-6

Faces 0

a number line graph to show distribution of data 239 13-5

Lighthouse Math

2D shapes that make up a 3D figure; flat sides of a 3D figure 222 12-6

Level G

Glossary

265

15 Denominator the bottom number of a 25 fraction

Equivalent

Glossary Factor

Inverse operations

a number you multiply with another number to get an answer in a multiplication problem 32 2-1

operations that are the opposite of each other, addition & subtraction, multiplication & division 146 8-4

Frequency

Least Common Multiple (LCM)

how often something occurs

239 13-5

Function rule that takes our input to an output; relationship that involves more than 1 variable 240 13-6

Greatest Common Factor (GCF) the greatest factor that both numbers have in common 68 4-1

Improper fraction

19 a fraction where the is larger than 4 numerator the denominator 70 4-2 © Lighthouse Curriculum. Copying strictly prohibited.

Input x, the number we put into our function

240 13-6

122 7-1

a fee paid for borrowing money; often a percentage 188 10-7

266

5 8

1 2 4

3x + 2 + 4x + 1 = 7x + 3 terms that have the same variable and are raised to the same power 150 8-6

Linear pair a pair of adjacent angles formed when two lines intersect 204 11-6

Mean sum of the values divided by the number of values in the set 236 13-4

the middle number when values are arranged from least to greatest 212 12-1

Mode

Interest

Like terms

Median

Integer a positive or negative whole number

the smallest multiple that each number has in common 70 4-2

Interior angles angles that lie on the inside of parallel lines 204 11-6

Level G

Glossary

most common number; the number that occurs most often 212 12-1

Multiple The products of multiplying one whole number by other numbers. Example: 8 and 16 are multiples of 4 32 2-1

-3 a number that is

Negative number less than zero

104 6-1

Lighthouse Math

Glossary Proportion

the top number of a fraction

68 4-1

Order of Operations set of rules that tells you which order to do operations within a problem (PEMDAS) 116 6-7

a comparison between two amounts; the relationship of one thing to another in terms of number or quantity 164 9-4

Radius

Output

Radius

y, the number that comes out of our function 240 13-6

Part / Whole ratio used to help solve percent proportion problems 182 10-4

Per for every one, division. 55 miles per hour = 55 miles in 1 hour 162 9-3

Percent (%) out of 100

176 10-1

Range difference between the highest and lowest values in a set 212 12-1

Ratio a ratio is a way to compare two quantities or amounts. They can be written in three ways - 3:2, 3/2, 3 to 2 158 9-1

Rational numbers any number that can be written as a fraction using two integers, a/b where b ≠ 0

Perimeter 5 in 3 in

3 in

distance around an object

114 6-6

Rectangular prism 3D shape with all rectangular faces

5 in

212 12-1

Principal the total amount of money borrowed or invested 188 10-7

Probability the likelihood of something happening, usually written as a fraction (probable outcome/total possible outcomes) 232 13-2

Lighthouse Math

the distance from the center of the circle to the edge 218 12-4

222 12-6

Sample space all the possible outcomes of an event

230 13-1

Scale increase or decrease the size or quantity of something 168 9-6

Level G

Glossary

267

Numerator

Glossary Scale factor

Unit Rate/Unit Ratio/Unit Price

the amount by which a quantity is changed, whole number increases, fraction/decimal decreases 170 9-7

the amount for 1 of something

Semicircle half of a circle, has half of the area 220 12-5

Simple interest interest that is only calculated on the initial amount of a loan

I = Prt 188 10-7

Surface area sum of the areas of all of the faces in a 3-dimensional shape 222 12-6

Tax a required amount determined by the government added onto the purchase of certain goods, services and wages 184 10-5

Variable a letter or symbol that represents an unknown quantity 146 8-4

Vertical angles a pair of opposite angles made by intersecting lines 204 11-6

Volume the amount of space a 3D object occupies, units are cubed 224 12-7

Written Form (Word Form) a number form that writes each number using words 14 1-1

X-axis y-axis 4 3 2

Term

a single mathematical expression. It can be a single number, a single variable, several variables multiplied but never added or subtracted. 140 8-1

Tip additional amount paid on top of a service to show gratitude, usually calculated as a percentage of the total 184 10-5

Transversal a line that intersects two or more other lines 204 11-6

268

162 9-3

Level G

Glossary

-4 -3

-2

-1 -1

x-axis 1

-2 -3 -4

horizontal axis, left and right

108 6-3

Y-axis vertical axis, up and down

108 6-3

Zero pair a set of numbers that, when added together, equal zero (-1 and 1 or -3 and 3) 136 7-8

Lighthouse Math

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