ANSWER KEY & ACTIVITIES COMMON CORE GPS

ANSWER KEY & ACTIVITIESFOR

MASTERING THE GRADE 6COMMON CORE GPS

IN

MATHEMATICSSeptember 2012

Erica DayColleen Pintozzi

Mary Reagan

Reviewed By:Angela Redman

AMERICAN BOOK COMPANYP. O. BOX 2638

WOODSTOCK, GA 30188-1383TOLL FREE 1 (888) 264-5877 PHONE (770) 928-2834 FAX 1 (866) 827-3240

Web site: www.americanbookcompany.com

Grade 6 Common Core GPS Mathematics

Ratios and Proportional Relationships 6.RP

Understand ratio concepts and use ratio reasoning to solve problems.

1. Understand the concept of a ratio and use ratio language to describe a ratio relationshipbetween two quantities. For example, “The ratio of wings to beaks in the bird house at the zoowas 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received,candidate C received nearly three votes.”

2. Understand the concept of a unit rate a/b associated with a ratio a : b with b 6= 0, and use ratelanguage in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cupsof flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for15 hamburgers, which is a rate of $5 per hamburger.”

3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoningabout tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole number measurements, findmissing values in the tables, and plot the pairs of values on the coordinate plane. Use tablesto compare ratios.

b. Solve unit rate problems including those involving unit pricing and constant speed. Forexample, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could bemowed in 35 hours? At what rate were lawns being mowed?

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 timesthe quantity); solve problems involving finding the whole, given a part and the percent.

d. Use ratio reasoning to convert measurement units; manipulate and transform unitsappropriately when multiplying or dividing quantities.

The Number System 6.NS

Apply and extend previous understandings of multiplication and division to divide fractions byfractions.

1. Interpret and compute quotients of fractions, and solve word problems involving division offractions by fractions, e.g., by using visual fraction models and equations to represent theproblem. For example, create a story context for (2/3)÷ (3/4) and use a visual fraction modelto show the quotient; use the relationship between multiplication and division to explain that(2/3)÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b)÷ (c/d) = ad/bc.) Howmuch chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land withlength 3/4 mi and area 1/2 square mi?

1

Compute fluently with multi-digit numbers and find common factors and multiples.

2. Fluently divide multi-digit numbers using the standard algorithm.

3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithmfor each operation.

4. Find the greatest common factor of two whole numbers less than or equal to 100 and the leastcommon multiple of two whole numbers less than or equal to 12. Use the distributive propertyto express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum oftwo whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).

Apply and extend previous understandings of numbers to the system of rational numbers.

5. Understand that positive and negative numbers are used together to describe quantities havingopposite directions or values (e.g., temperature above/below zero, elevation above/below sealevel, credits/debits, positive/negative electric charge); use positive and negative numbers torepresent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6. Understand a rational number as a point on the number line. Extend number line diagrams andcoordinate axes familiar from previous grades to represent points on the line and in the planewith negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on thenumber line; recognize that the opposite of the opposite of a number is the number itself,e.g., −(−3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of thecoordinate plane; recognize that when two ordered pairs differ only by signs, the locationsof the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical numberline diagram; find and position pairs of integers and other rational numbers on a coordinateplane.

7. Understand ordering and absolute value of rational numbers.

a. Interpret statements of inequality as statements about the relative position of two numberson a number line diagram. For example, interpret −3 > −7 as a statement that −3 islocated to the right of −7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-worldcontexts. For example, write −3◦C > −7◦C to express the fact that −3◦C is warmer than−7◦C.

2

c. Understand the absolute value of a rational number as its distance from 0 on the numberline; interpret absolute value as magnitude for a positive or negative quantity in a real-worldsituation. For example, for an account balance of −30 dollars, write | − 30| = 30 todescribe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For example,recognize that an account balance less than −30 dollars represents a debt greater than 30dollars.

8. Solve real-world and mathematical problems by graphing points in all four quadrants of thecoordinate plane. Include use of coordinates and absolute value to find distances betweenpoints with the same first coordinate or the same second coordinate.

Expressions and Equations 6.EE

Apply and extend previous understandings of arithmetic to algebraic expressions.

1. Write and evaluate numerical expressions involving whole-number exponents.

2. Write, read, and evaluate expressions in which letters stand for numbers.a. Write expressions that record operations with numbers and with letters standing for

numbers. For example, express the calculation “Subtract y from 5” as 5− y.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor,quotient, coefficient); view one or more parts of an expression as a single entity. Forexample, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as botha single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that arisefrom formulas used in real-world problems. Perform arithmetic operations, includingthose involving whole number exponents, in the conventional order when there are noparentheses to specify a particular order (Order of Operations). For example, use theformulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides oflength s = 1/2.

3. Apply the properties of operations to generate equivalent expressions. For example, applythe distributive property to the expression 3(2 + x) to produce the equivalent expression6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalentexpression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalentexpression 3y.

4. Identify when two expressions are equivalent (i.e., when the two expressions name the samenumber regardless of which value is substituted into them). For example, the expressionsy + y + y and 3y are equivalent because they name the same number regardless of whichnumber y stands for.

3

Reason about and solve one-variable equations and inequalities.

5. Understand solving an equation or inequality as a process of answering a question: whichvalues from a specified set, if any, make the equation or inequality true? Use substitution todetermine whether a given number in a specified set makes an equation or inequality true.

6. Use variables to represent numbers and write expressions when solving a real-world ormathematical problem; understand that a variable can represent an unknown number, or,depending on the purpose at hand, any number in a specified set.

7. Solve real-world and mathematical problems by writing and solving equations of the formx+ p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

8. Write an inequality of the form x > c or x < c to represent a constraint or condition ina real-world or mathematical problem. Recognize that inequalities of the form x > c orx < c have infinitely many solutions; represent solutions of such inequalities on number linediagrams.

Represent and analyze quantitative relationships between dependent and independent vari-ables.

9. Use variables to represent two quantities in a real-world problem that change in relationship toone another; write an equation to express one quantity, thought of as the dependent variable,in terms of the other quantity, thought of as the independent variable. Analyze the relationshipbetween the dependent and independent variables using graphs and tables, and relate theseto the equation. For example, in a problem involving motion at constant speed, list andgraph ordered pairs of distances and times, and write the equation d = 65t to represent therelationship between distance and time.

Geometry 6.G

Solve real-world and mathematical problems involving area, surface area, and volume.

1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons bycomposing into rectangles or decomposing into triangles and other shapes; apply thesetechniques in the context of solving real-world and mathematical problems.

2. Find the volume of a right rectangular prism with fractional edge lengths by packing it withunit cubes of the appropriate unit fraction edge lengths, and show that the volume is the sameas would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwhand V = bh to find volumes of right rectangular prisms with fractional edge lengths in thecontext of solving real-world and mathematical problems.

3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinatesto find the length of a side joining points with the same first coordinate or the same secondcoordinate. Apply these techniques in the context of solving real-world and mathematicalproblems.

4

4. Represent three-dimensional figures using nets made up of rectangles and triangles, and usethe nets to find the surface area of these figures. Apply these techniques in the context ofsolving real-world and mathematical problems.

Statistics and Probability 6.SP

Develop understanding of statistical variability.

1. Recognize a statistical question as one that anticipates variability in the data related to thequestion and accounts for it in the answers. For example, “How old am I?” is not a statisticalquestion, but “How old are the students in my school?” is a statistical question because oneanticipates variability in students’ ages.

2. Understand that a set of data collected to answer a statistical question has a distribution whichcan be described by its center, spread, and overall shape.

3. Recognize that a measure of center for a numerical data set summarizes all of its values witha single number, while a measure of variation describes how its values vary with a singlenumber.

Summarize and describe distributions.

4. Display numerical data in plots on a number line, including dot plots, histograms, and boxplots.

5. Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was measuredand its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and variability (interquartilerange and/or mean absolute deviation), as well as describing any overall pattern and anystriking deviations from the overall pattern with reference to the context in which the datawere gathered.

d. Relating the choice of measures of center and variability to the shape of the datadistribution and the context in which the data were gathered.

5

Chart of Standards

ChapterStandard Number6.RP.1 66.RP.2 66.RP.3 66.NS.1 16.NS.2 36.NS.3 26.NS.4 16.NS.5 36.NS.6 4, 56.NS.7 3, 46.NS.8 56.EE.1 76.EE.2 86.EE.3 76.EE.4 86.EE.5 96.EE.6 8, 96.EE.7 96.EE.8 96.EE.9 106.G.1 116.G.2 126.G.3 56.G.4 126.SP.1 136.SP.2 136.SP.3 136.SP.4 146.SP.5 13, 14

6

Chapter 1 FractionsPage 2 Common Factors1. {1, 2, 4, 8, 16, 32}2. {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}3. {1, 3, 9, 27}4. {1, 3, 5, 9, 15, 45}5. {1, 2, 3, 4, 6, 12}6. {1, 2, 3, 4, 6, 9, 12, 18, 36}

7. 16: 1, 2, 4, 8, 16 20: 1, 2, 4, 5, 10, 20 common factors: 1, 2, 48. 45: 1, 3, 5, 9, 15, 45 25: 1, 5, 25 common factors: 1, 59. 9: 1, 3, 9 20: 1, 2, 4, 5, 10, 20 common factor: 1

10. 18: 1, 2, 3, 6, 9, 18 30: 1, 2, 3, 5, 6, 10, 15, 30 common factors: 1, 2, 3, 611. 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 54: 1, 2, 3, 6, 9, 18, 27, 54 common factors: 1, 2, 3, 6, 9, 1812. 18: 1, 2, 3, 6, 9, 18 21: 1, 3, 7, 21 common factors: 1, 3

The answers for questions 13–20 are just one of the possible answers.

13. 3(3 + 5) = (3× 3) + (3× 5)14. 2(10 + 3) = (2× 10) + (2× 3)15. 5(5 + 7) = (5× 5) + (5× 7)16. 4(3 + 5) = (4× 3) + (4× 5)

17. 9(4 + 6) = (9× 4) + (9× 6)18. 7(2 + 3) = (7× 2) + (7× 3)19. 8(2 + 1) = (8× 2) + (8× 1)20. 10(3 + 10) = (10× 3) + (10× 10)

Page 3 Greatest Common Factor

8 1, 2, 4, 820 1, 2, 4, 5, 10, 2016 1, 2, 4, 8, 1640 1, 2, 4, 5, 8, 10, 20, 4012 1, 2, 3, 4, 6, 1232 1, 2, 4, 8, 16, 32

1. 4

2. 83. 2

4. 3

5. 5

6. 4

7. 9

8. 10

9. 7

10. 8

11. By making a list of all the factors of each number, finding all the common factors, then findingthe greatest number of the common factors.

Page 4 Least Common Multiple

1. 30

2. 483. 36

4. 21

5. 24

6. 24

7. 28

8. 18

9. 30

10. 42

11. 36

12. 35

13. 90

14. 24

15. 36

16. 45

17. 15

18. 44

7

Page 5 Simplifying Improper Fractions

1. 235

2. 323

3. 4

4. 116

5. 316

6. 227

7. 158

8. 145

9. 713

10. 314

11. 712

12. 249

13. 189

14. 338

15. 447

16. 112

17. 134

18. 2 110

19. 712

20. 1225

21. 11

22. 312

23. 656

24. 1012

Page 6 Changing Mixed Numbers to Improper Fractions

1.7

2

2.23

8

3.29

3

4.23

5

5.29

4

6.69

8

7.9

7

8.22

9

9.31

5

10.37

7

11.18

5

12.75

8

13.54

5

14.33

10

15.29

7

16.17

6

17.52

7

18.61

9

19.37

5

20.13

7

21.4

1

22.10

1

23.3

1

24.2

1

25.15

1

26.5

1

27.6

1

28.11

1

29.8

1

30.16

1

Page 7 Multiplying Fractions

1.12

35

2.3

20

3.2

21

4.2

9

5.4

45

6.3

40

7.1

6

8.1

4

9.1

36

10.1

4

11.1

3

12.1

4

13.1

4

14.1

14

15.1

9

16.2

3

17.3

4

18.1

3

19.1

14

20.1

3

21.1

6

Page 8 Multiplying Mixed NumbersStudents should show their work.

1. 2358

2. 2415

3. 82332

4. 7

5. 112

6. 252532

7. 111116

8. 4125

9. 2614

10. 916

11. 13357

12. 7 112

13. 7 127

14. 7537

15. 112764

8

Page 9 Reciprocals

1. 51

2. 32

3. 85

4. 72

5. 193

6. 134

7. 38

8. 175

9. 112

10. 2115

11. 1124

12. 1918

13. 53

14. 3319

15. 74

16. 175

17. 127124

18. 92

19. 411358

20. 10091

21. 118

22. 120

23. 19

24. 1143

Page 10 Dividing Fractions and Mixed NumbersStudents should show their work.

1. 2 815

2. 512

3. 523

4. 31

5. 119

6. 8 511

7. 102126

8. 227

9. 112

10. 159

11. 4 112

12. 535

13. 11936

14. 427

15. 2465

16. 4 211

17. 2025

18. 612

19. 6 815

20. 22027

21. 22152

22. 1438

23. 217

24. 23

Page 11 Fraction Word Problems

1. 214

jars

2. 113

3. 312

ft

4. 732

m

5. 116

6. 732

7. 514

yd

8. 38

9. 1124

9

Page 12 Going Deeper into FractionsStudents should show their work.

1.Ingredient Amount for 61

2Recipes

Brown Sugar 478

cup

White Sugar 413

cup

Vanilla 934

tsp.

Flour 1614

cups

2. 12

gal

3. 14

4. Part 1: 918

ftPart 2: 18, 250 ft

5. 25 60 100Ingredient Meals Meals Meals

Chicken 5 lb 12 lb 20 lb

Noodles 318

lb 712

lb 1212

lb

Cheese 212

lb 6 lb 10 lb

Tomatoes 614

lb 15 lb 25 lb

6. 110

lb

Chapter 1 ReviewPage 13Students should show their work for problems 5–10.

1. 12

2. 120

3. 13

4. 112

5. 2656

6. 33338

7. 21013

8. 225

9. 2 110

10. 416

11. 85

12. 3

13. 75

14. 199

15. 52

16. 8574

17. 9

18. 3

19. 2

20. 8

21. 75

22. 16

23. 42

24. 223

25. 912

26. 334

27. 11

28. 338

29. 267

30. 635

31. 216

32. 72

33. 263

34. 234

35. 365

36. 316

37. 116

Chapter 1 TestPages 14–15

1. C

2. A3. B

4. A

5. C

6. C

7. B

8. D

9. D

10. C

11. A

12. B

13. D

14. C

15. A

10

Chapter 2 DecimalsPage 17 Changing Fractions to Decimals

1. 0.8

2. 0.6

3. 0.5

4. 0.5

5. 0.1

6. 0.625

7. 0.83

8. 0.16

9. 0.6

10. 0.7

11. 0.36

12. 0.1

13. 0.7

14. 0.9

15. 0.25

16. 0.375

17. 0.1875

18. 0.75

19. 0.8

20. 0.416

Page 17 Changing Mixed Numbers to Decimals

1. 5.6

2. 8.45

3. 15.6

4. 13.6

5. 30.3

6. 3.5

7. 1.875

8. 4.09

9. 6.8

10. 13.5

11. 12.8

12. 11.625

13. 7.25

14. 12.3

15. 1.625

16. 2.75

17. 10.1

18. 20.4

19. 4.9

20. 5.36

Page 18 Changing Decimals to Fractions

1.11

20

2.3

5

3.3

25

4.9

10

5.3

4

6.41

50

7.3

10

8.21

50

9.71

100

10.7

50

11.14

25

12.6

25

13.7

20

14.24

25

15.1

8

16.3

8

Page 18 Changing Decimals to Mixed Numbers

1. 718

2. 9912

3. 2 13100

4. 5 110

5. 161920

6. 358

7. 42150

8. 152125

9. 6 710

10. 451740

11. 1545

12. 8 425

13. 13 910

14. 321320

15. 1714

16. 94150

Page 19 Adding Decimals

1. 12.05

2. 9.705

3. 22.612

4. $13.39

5. $14.15

6. 22.355

7. 12.537

8. 20.864

9. $22.65

10. $69.58

11. 15.357

12. 23.624

13. 55.423

14. $21.13

15. $34.10

16. 18.13

17. 18.6084

18. 291.652

19. $107.34

20. $18.96

21. 12.3754

11

Page 20 Subtracting Decimals

1. 0.55

2. 13.827

3. $38.62

4. $213.79

5. $1.01

6. 49.447

7. 398.645

8. $30.10

9. $110.66

10. $21.53

11. 5.64

12. 10.57

13. 3.027

14. $13.74

15. $7.05

16. 9.469

17. 379.43

18. $6.87

19. 101.421

20. 4.045

21. 9.185

Page 21 Multiplying Decimals

1. 53.2

2. 50.562

3. 36.036

4. 15.36

5. 100.76

6. 31.95

7. 0.01716

8. 28.016

9. 217.58

10. 0.6622

11. 2.867

12. 2.041

13. 8.2

14. 2.7927

15. 3.861

16. 1.794

Page 22 Dividing Decimals

1. 52

2. 879

3. $65.00

4. $23.00

5. 14.2

6. 7300

7. $167.00

8. $20.00

9. 85.6

10. 145.8

11. 1010

12. 21.25

13. 60

14. 50

15. 4.25

16. $670.00

Page 23 Decimal Word Problems

1. $11. 20

2. $18. 753. $9. 99

4. $2. 45

5. $645. 33

6. $26. 24

7. 1211

8. 25.38

9. $896.05

10. $62.11

11. $1.26

12. 10

Page 24 Going Deeper into DecimalsStudents should show their work.

1. Part 1: 41.5bucketsPart 2: 18.5 buckets

2. Part 1: 2, 565 lbPart 2: 2, 137.5 lbPart 3: 3, 847.5 lb

3. Part 1: $38.62Part 2: $19.31Part 3: $12.87

4. $1, 382

Chapter 2 ReviewPage 25

1. 25.2

2. 33.6

3. 57

4. 0.9

5. 1.53

6. 0.148

7. 45

8. 40

9. 0.3

10. 1120

11. 2125

12. 825

13. 738

14. 935

15. 1314

16. 5.12

17. 0.07

18. 10.5

19. 14.1

20. 0.4

21. 21.42

22. 4.3

23. 27

24. 36

25. Spent: $73.92, Saved: $49.28, Gave: $24.64

12


1. A

2. C3. B

4. B

5. B

6. D

7. D

8. A

9. A

10. C

11. D

12. A

13. A

14. C

15. D

16. B

Chapter 3 Rational NumbersPages 29–30 Integers

1. +25

2. −103. −16◦4. +72

5. >

6. >

7. <

8. <

9. <

10.−34, −6, 0, 78, 8911.−54, −6, 7, 14, 45

12. 2, 3, 4, 5

13. 4, 5, 6, 7, 9

14. 3, 4, 5, 8, 11

15. Thunder

16.−4, −2, 3, 7, 8

Page 31 Opposites

1. −42. 18

3. − 611

4. 57

5. 23.05

6. −11.117. 5◦

8. $12.25, 17.25

9. 7 or +7

10.−21

Page 32 Integer Word Problems

1. 734 pennies

2. 2 dozen3. −13◦4. −18 spaces

5. 85 ft

6. 80◦F

7. 50◦C

8. 1, 260 feet

9. 64, 826 feet

10. $36.25

Page 33 Dividing Multi-Digit Numbers

1. 768

2. 2, 000

3. 2, 159

4. 16

5. 28, 415

6. 183

7. 6, 855

8. 9, 140

9. 274

10. 1, 144

11. 683

12. 3, 219

13. 347, 281

14. 1, 123

15. 951

16. 334

17. 7, 821

18. 4, 714

19. 564

20. 642

21. 2, 839

13

Page 34 Dividing Multi-Digit Numbers

1. 375 R4

2. 51, 620 R22

3. 1, 774 R21

4. 24, 140 R10

5. 637 R4

6. 607, 350 R5

7. 415 R7

8. 65, 222 R9

9. 190 R21

10. 2, 011 R8

11. 43 R8

12. 227 R12

13. 5, 555 R9

14. 25 R750

15. 5, 506 R200

16. 212 R46

17. 31, 447 R9

18. 119 R39

19. 4, 271 R10

20. 9, 625 R7

21. 114, 254 R25

Page 35 Going Deeper into Rational NumbersStudents should show their work.

1. No; short 1, 500 2. $90.60 3. 557 cases6 bags & 12 ozleft over

4. Part 1: 85◦ FPart 2: 3◦Part 3: 37◦


1. −6712. 52.4

3. −16◦4. −4

7

5. 23◦

6. 23

7. −17, −8, −7, −78

8. −97, −5, −34, −1

2

9. −444, −44, −4, −14

10.− 710

, −35, −2

5, − 2

10

11. Kyle, Mark, Marta

12. blackbird, squirrel,Alexandra, beehive, dove

13. 4

14. 5, 353 R6

15. 1, 293

16. 902

17. 613, 375 R3

18. Part 1: 39◦ FPart 2: 29◦Part 3: 3◦


1. B

2. B

3. A

4. B

5. C

6. A

7. B

8. B

9. D

10. C

11. C

12. B

13. B

14. A

15. D

16. C

Chapter 4 Introduction to GraphingPage 40 Graphing Fractional Values

1. A = 38, B = 7

8, C = 11

2, D = 21

4

2. E = −45, F = −2

5, G = 3

10, H = 7

10

3. I = −825, J = −73

5, K = −64

5, L = −51

5

4. M = 213, N = 32

3, P = 41

3, Q = 52

3

5. R = 1513, S = 161

2, T = 171

6, U = 172

3

6. V = −157, W = −4

7, X = 1

7, Y = 6

7

14

Page 42 Recognizing Improper Fractions and Decimals on a Number Line

1.−2 D C A B−1 0 1 2 3

2.−3 F G H E−2 −1 0 1 2

3. G

4. H

5. B

6. A

7. C

8. I

9. D

10. E

11. K

12. N

13. M

14. P

15. L

16. J

17. Q

18. S

Page 43 Plotting Points on a Vertical Number Line

1. −512

2. −43. −34. −2

5. 0

6. 1

7. 212

8. 4

9. 1134

10. 1014

11. 814

12. 7

13. 514

14. 434

15. 2

16. 34

17. 29

18. 20

19. 17

20. 9

21. 2

22.−723.−1424.−26

25.−25

26.−127.−13

5

28.−235

29.−330.−33

5

31.−532.−54

5

Page 44 Real-World Number Line Problems

1. −150 2. −125 3. −75 4. −300 5. −250 6. 250 7. 100

Page 45 Absolute Value

1. 9

2. −53. 25

4. −125. −646. 2

7. −38. 1

9. 4

10. 9

11. 8

12. 18

13. 6

14. 7

15. 2

Page 46 Absolute Value Word Problems

1. |$30.00|2. |20◦|

3. |1, 000|4. |$470, 000, 000|

5. |6, 700|6. |32◦|

7. |$12, 200|8. |23|

Page 47 Comparing Rational Numbers

1. >

2. <

3. <

4. <

5. >

6. <

7. <

8. >

9. >

10. >

11. >

12. >

13. <

14. <

15. <

16. >

17. >

18. <

15

Page 48 Comparing Rational Numbers

1. > 2. < 3. = 4. > 5. < 6. < 7. > 8. =

Page 50 Ordering Rational Numbers

1.

2.

3.

4.

5.

6.

7.

8.

Page 51 Ordering Rational Numbers

1. −19,−8,−4,−2

2. −5,−3,−12,−1

4

3. −88,−21,−13,−7

4. −37,− 3

14,−1

7,− 1

14

5. −221,−109,−81,−17

6. −39,−38,−89,−2

3

7. −15,−10,− 910,−2

5

8. −41,−14,−4,−1

9. −8,−4,−38,−1

4

10.−300,−30,−3,−13

11.−2526,−12

13,− 3

26,− 1

13

12.−111,−11,−2,−113.−6,−5,−1

5,−1

6

14.−888,−88,−18,−815.−33,−13,−3,−1

3

Page 52 Rational Number Word Problems

1. They still need to make 185, 000 airplanekits.

2. Marian walked a total of 2.4 miles roundtrip.

3. Lyle ascended and descended the hill a totalof 530 feet.

4. Alex took 5 weeks to pay back his aunt.

5. Robert has 11.25 feet of rope left.

6. The students liked English best, then math,then history.

7. Scott has 13

of the pages left to read.

8. Jason ate the most, then Mr. O’Reilly, Mrs.O’Reilly, and Abby. 1

6of the pizza remains.

16

Page 53 Going Deeper into GraphingStudents should show work.

1. − |13| = −13

2. − |−8| = −8

3. |−15| = 15

4. |6| = 6

5. −0.5 > −0.6

6. −0.03 < −0.02

7. − 115

> − 116

8. 115

> 116

9. B

10. G

11. F

12. D

Chapter 4 ReviewPages 54–55

1. 2

2. −183. 2

4. −245. −58

6. 4

7. −78. 4

9. 3

10. 17

11. 12

12. 29

13. 8

14. 8

15. 7

16. 32 ft

17. 252 lb

18. 37 mph

19. 15 lb

20. 54

21. 356

22.4 5 5 63

5

23.−3 1

2−4 −3 −2 −1 0

24.7.26 7 8 9 10

25.−2.3−3 −2 −1

26. 3.18, 3.8, 8.13, 8.3

27. 13, 38, 58, 34

28. −7.7,−7,−1.7,−0.7

29. 113, 11

2, 21

2, 31

3

30. 3.75

31. 3.25

32. 2.5

33. 2

34. 1.25

35. 0.75

36. 0.25

37. D, students should show work

38. E, students should show work


1. A

2. C

3. C

4. A

5. D

6. B

7. A

8. A

9. A

10. B

11. A

12. D

13. B

14. C

15. D

16. B

17. C

17

Chapter 5 The Coordinate SystemPage 59 Cartesian Coordinate System

0−1−2−3−4−5 1 2 3 4 5

1

2

3

4

A

P

E

J

M

H

Q L

C

I

D

K

O

R

N

F

B

G

5

−1

−2

−3

−4

−5

Page 60 Ordered Pairs

1. (−3, 4), II

2. (−4, 5), II

3. (−5, 6), II

4. (−5,−5), III

5. (5, 1), I

6. (−5, 2), II

7. (4, 6), I

8. (−2,−4), III

9. (−2,−2), III

10. (6, 6), I

11. (5,−2), IV

12. (2, 2), I

13. (3,−4), IV

14. (2,−6), IV

15. (1, 4), I

16. (−5,−3), III

17. (−6,−4), III

18. (3,−2), IV

19. (6,−5), IV

20. (−3,−2), III

Page 61 Ordered Pairs

1. (0, 3)

2. (−4, 0)3. (0,−6)4. (5, 0)

5. (−6, 0)6. (0, 1)

7. (0, 5)

8. (0, 6)

9. (3, 0)

10. (0,−3)11. (0,−2)12. (−3, 0)

18

Page 63 Finding Opposites on a Coordinate Plane

1. (−4,−5)2. (−1,−2)

3. (−2, 0)4. (−3, 3)

5. (2,−5)6. (2, 0)

7. (2,−2)8. (3,−1)

9. (0, 3)

10. (−4, 4)

Page 65 Finding Distance Between Points

1. 14 units

2. 15 units

3. 5 units

4. 4 units

5. 10 units

6. 5 units

7. 2 units

8. 7 units

9. 6 units

10. 10 units

11. 10 units

Page 67 Plotting Coordinates on a Map1. G2

2. E53. 4

4. 5

5. southeast

6. H3

7. 70 yards

8. north

9. A7

10. south

Page 69 Drawing Geometric Figures on a Coordinate Plane1. A = (−1,−1)2. B = (−2, 4)3. C = (2, 2)

4. D = (2, 0)

5. E = (−6, 2)6. F = (−3, 2)

7. G = (−3,−4)8. H = (−6,−4)9. I = (3,−5)

10. J = (5,−1)11. K = (6,−7)

Page 71 Solving Problems Using Geometric Figures on a Coordinate Plane

1. 3 units

2. 4 units

3. 4 units

4. 5 units

5. 7 units

6. 3 units

7. 7 units

8. 3 units

9. 3 units

10. 2 units

Page 72 Going Deeper into the Coordinate System1.

2.

3.

4.

5.

6.

19


1. A = (−2, 2), II

2. B = (2, 1), I

3. C = (−3,−3), III

4. D = (2,−2), IV

5. see graph to the right




1 2

7.G

8.H

6.F

5.E

x

y

3 40

−1

−2

−3

−4

1

2

3

4

−1−2−3−4

9. (1, 4)

10. (2, 3)

11. (−3, 3)

12. 5 units

13. 3 units

14. 5 units

15. (F, 1)

16. 2 miles W,6 miles N

17. (A, 3)

18. (2, 6)

19. (2, 2)

20. (6, 6)

21. (6, 2)

22. 2 units

23. 5 units

24.


1. B 2. A 3. D 4. C 5. C 6. D 7. B 8. A 9. C

Chapter 6 Ratios, Unit Rates, and PercentsPage 77 Ratios

1.1

22.2

33.3

44.1

45.2

16.4

17.1

38.2

1

Page 78 Ratio Problems

1.117

3012.11

33.42

2654.1

35.$2.00

3

20

Page 79 Using Graphs to Solve Ratio Problems

1.1

42.2

33.3

24.3

85.4

36.5

47.14

158.12

1

Page 80 Equivalent Ratios

1.3

52. 1 : 2 3.

1

84. 2 : 3

5.2 : 3

40 : 60

4

6

12

18

6.1 : 5

30 : 150

5

25

6

30

7.3 : 4

21 : 28

30

40

18

24

8.2 : 7

22 : 77

8

28

4

14

9.3 : 8

9 : 24

33

88

18

48

10. 6 cups 11. Language Arts : SocialStudies

12. 225

Page 81 Modeling Ratios

1. 2. 3. 4.

5. C 6. A 7. D 8. B


1. 2. 3. 4.

21


Double TapeRatio Equation Number Line Diagram

1. 1 : 2 y = 2xLemons =

Pints of Water =

2. 3 : 5 3y = 5xRed Beads =

Yellow Beads =

3. 5 : 6 5y = 6xMiles =

Minutes =

4. 1 : 5 y = 5x Onions =

Potatoes =

5. 2 : 3 2y = 3xNails:

Feet of Wood:

Page 85 Unit Rate

1. 50 mph

2. 2 min/problems

3. 13 min/mile

4. 120

5. 45

6. 55 mph

7. 212

min

8. 14

min

Page 86 More Unit Rates

1. 624 2. $500.00 3. 5, 000 4. $1, 050 5. 27.5 6. 48

22

Page 88 Percents

Percent Fraction Decimal1. 15% 3

200.15

2. 39% 39100

0.39

3. 25% 14

0.25

4. 35% 720

0.35

5. 99% 991000

0.99

6. 33% 33100

0.33

7. 58% 2950

0.58

8. 18% 950

0.18

9. 29% 29100

0.29

10. 67% 67100

0.67

11.

12.

13.

14.

Page 89 Finding the Whole in a Percent Problem

1. 40

2. 120

3. 150

4. 75

5. $180

6. 200

7. 75

8. 25

Page 90 Going Deeper into Ratios, Unit Rates, and Percents

1. Part 1: 105211

Part 2: $3.49Part 3: 3 ring binders

2. Part 1: Ms. WarrickPart 2: Mrs. TaylorPart 3: 17

16

3. Part 1: 31

Part 2: 25%Part 3: 45 gallons

23


1. 23

2. 12

3. 12

4. 35

5. 1427

6. 137

7. 54

8. 60 mph

9. 3 miles

10. 5

11.1 : 7

10 : 70

3

21

5

35

12.2 : 11

6 : 33

12

66

4

22

13.3 : 5

60 : 100

6

10

15

25

Double TapeRatio Equation Number Line Diagram

14. 1 : 2 y = 2x Cups of Sugar =

Cups of Flour =

15. 1 : 3 y = 3xBlack Cars =

All Cars =

Percent Fraction Decimal16. 10% 1

100.1

17. 40% 25

0.4

18. 20% 15

0.2

19. 75% 34

0.7520. 4021. 20


1. C

2. A

3. D

4. A

5. D

6. C

7. B

8. B

9. C

10. A

11. C

12. A

13. D

14. B

15. C

16. B

24

Chapter 7 Exponents and Arithmetic PropertiesPage 96 Understanding Exponents

1. 74

2. 102

3. 123

4. 44

5. 93

6. 252

7. 153

8. 55

9. 24

10. 142

11. 35

12. 113

13.−51214. 144

15. 20

16. 625

17. 1

18. 256

19. 100

20. 243

21. 10,000

22. 1

23. 64

24. 54

25. 32

26. 42 or 24

27. 33

28. 62

29. 23

30. 25

31. 103

32. 53

33. 92 or 34

34. 82, 43,or 26

35. 72

36. 112

Page 97 Evaluate Expressions and Exponents

1. 11

2. 49

3. 200

4. 8

5. 93

6. 4

7. 87

8. 27

9. 8

10. 15

11. 3

12. 214

13. 192

14. 63

15. 112

16. 8

17. 22

18. 136

19. 16

20. 7

21. 46

22. 76

23. 83

24. 44

Page 98 Basic Properties of Rational Numbers

1. 3

2. 13. 5

4. 2

5. 7

6. 9

7. 7

8. 6

9. 8

10. 4

11. 6

12. 5

13. 2

14. 8

15. 3

16. 1

Page 99 Matching Expressions Using Properties

1. F

2. J

3. A

4. I

5. B

6. N

7. C

8. M

9. D

10. G

11. H

12. K

13. E

14. L

Page 101 Order of Operations

1. 23

2. 253

3. 5

4. −1

5. 9

6. 60

7. 10

8. 48

9. 9

10. 54

11. 5

12. 13

13. 12

14. 51

15. 16

16. 9

17. 42

18.−719. 23

20. 51

25

Page 102 Order of Operations

1. 19

2. 13. 15

4. −38

5. 12

6. 4

7. 5

8. 13

9. 6

10. 11517

11.−1412. 15

8

13. 1 813

14. 1314

15. 56

Page 103 More Order of Operations

1. ×,+,−2. +,×,−

3. −,×,÷,−4. ÷,×,−

5. −,×,−6. ÷,×,+

7. +,×,÷,×8. −,×,÷,+

Page 104 Going Deeper into Exponents and Arithmetic Properties

Matherines1. correct 6. correct2. 68 7. 1933. correct 8. 4

114. 0 9. correct5. correct 10. correct

Math-Task-Tics1. 36

556. correct

2. correct 7. correct3. correct 8. correct4. 2

39. correct

5. 177 10. correct

Who won?Math-Task-Tics


1. 83

2. 323. 143

4. −85. 25

6. 16

7. 16

8. 1

9. 144

10. 9211. 62

12. 7213. 15

14. 50

15. 27

16. Commutative Property of Addition

17. Associative Property of Addition

18. Distributive Property

19. Identity Property of Multiplication

20. C

21. A

22. D

23. B

24. 14

25. 41

26. 4

27. 12

28. 12

29. 45

Chapter 7 TestPage 106

1. B

2. C

3. D

4. B

5. A

6. B

7. D

8. C

9. B

10. A

11. B

12. D

Introduction to AlgebraPage 108 Algebra Vocabulary

1. algebra

2. expression(s)3. term(s)

4. base

5. exponent

6. equation(s)

7. equality

8. inequality

9. variable(s)

10. coefficient

26

Page 109 Substituting Numbers for Variables

1. 10

2. 11

3. 3

4. 16

5. 50

6. 10

7. 21

8. 7

9. 41

10. 7

11. 63

12. 14

13. 26

14. 20

15. 2

16. 2

17. 14

18. 80

19. 21

20. 60

21. 3

22. 38

23. 35

24. 111

Page 110 Substituting Numbers in Formulas

1. 27 in3

2. 24 in23. 336 in3

4. 600 cm2

5. 250 cm2

6. 480 in27. 429 in3

Pages 111–112 Understanding Algebra Word Problems

1. A

2. E

3. D

4. C

5. B

6. E

7. B

8. A

9. x+ 5

10. x− 811. x− 3112. x− 1813. 8x

14. 8x3

15. 9− x

16. 0.8x

17.x

4

18.x

2+ 7

19. 2b

20. 3y

21. 10− n

22. 3 + p

23. 4m

24. y − 2025. 5x

26. n+ 4

27. t− 628. 18÷ x

Page 113 Parts of an Expression

1. difference of 2 terms

2. sum of 2 terms

3. product of 2 terms

4. quotient of 2 terms

5. sum of 2 terms


7. difference of 2 terms


9. product of 2 factors and sum of 2 terms

10. sum of 2 terms


12. sum of 2 terms, 1 term is the product of 2terms

13. product of 2 terms and the sum of 2 terms

14. sum of 2 terms, 1 term is the product of 2terms



27

Page 114 Equivalent Expressions

1. E 2. C 3. G 4. A 5. I 6. B 7. H 8. D 9. F

Page 115 Going Deeper into Algebra1. 37 chores

2.Piece Number for Each Square Number for Whole QuiltGray Square with Flower 4 384White Square with Flower 1 96White Rectangle 4 384White square 4 384Gray Square 4 384

3. MATH IS AWESOME! NO ONE WILL KNOW WHAT WE ARE TEXTING! (SHARE)


1. coefficient

2. constant

3. variable

4. exponent

5. base

6. 6

7. 4

8. 4

9. 212

10. 213

11. x = 6− 212. x = 4($13)

13. x =60

15

14. 600 in3

15. 294 cm2

16. sum of 2 terms

17. sum of 2 terms1 terms is theproductof 2 terms


19. C

20. A

21. D

22. B

Chapter 8 TestPage 117

1. A

2. B3. C

4. D

5. D

6. C

7. D

8. A

9. C

10. A

Chapter 9 Solving Equations and InequalitiesPage 119 Solving One-Step Equations with Addition and Subtraction

1. p = 6

2. k = 83

3. m = 54

4. z = 13

5. f = 11

6. q = 42

7. r = 9

8. w = 50

9. a = 136

10. p = 13

11. b = 19

12. t = 48

13. z = 54

14. z = 40

15. n = 39

16. s = 39

17. m = 0

18. y = 69

19. y = 22

20. x = 146

28

Page 120 Solving One-Step Equations with Multiplication and Division

1. m = 9

2. k = 9

3. y = 332

4. t = 20

5. m = 16

6. x = 55

7. q = 60

8. m = 4

9. a = 4

10. b = 3

11. x = 41

12. x = 8

13. h = 120

14. b = 334

15. z = 45

16. n = 12

17. k = 16

18. x = 2

19. w = 100

20. x = 45

Page 121 Solving Two-Step Equations

1. s = 2

2. c = 1

3. x = 4

4. y = 40

5. x = 2

6. k = 3

7. r = 4

8. p = 40

9. n = 1

10. x = 9

11. y = 14

12. s = 8

13. y = 1

14. x = 1

15. x = 3

16. y = 60

17. w = 1

18. w = 9

19. x = 14

20. w = 640

Page 122 Combining Like Terms

1. 3x+ 3

2. 5k + 2

3. 19 + 9y

4. 5n− 55. 11x− 136. m+ 1

7. 5w − 58. 12x− 369. 9 + 2x

10. 7− 6y

11. 11x+ 6

12. 38 + 3x

13. 14x− 714. 6x+ 7

15. 16s− 716. 5n+ 14

17. 1 + 3x

18. 6x− 319. 106q + 11

20. 25x− 18

21. 19x

22. 3y + 8

23. 13− 2x24. 10a− 1625. 12w + 3

26. 8x

27. 10w − 1528. 30− 12t29. 12− 3x30. 11b+ 12

31. 3h− 332. 2k + 10

33. 15a− 534. 9c− 535. 3d− 336. 3h+ 9

37. 8x+ 7

38. 4z + 5

39. 12 + 2y

40. 12p− 4

Page 123 Solving Two-Step Equations by Combining Like Terms

1. x = 4

2. x = 9

3. x = 4

4. x = 10

5. x = 2

6. x = 3

7. x = 7

8. x = 11

9. x = 9

10. x = 5

11. x = 5

12. x = 3

13. x = 5

14. x = 2

15. x = 2

16. x = 6

17. x = 1

18. x = 20

19. x = 5

20. x = 5

29

Page 124 Solving Algebra Word Problems

1. $18.75

2. $6.39

3. 48

4. 42

5. 216

6. 144

7. 252

8. 504, 000

Page 125 Solving Algebra Word Problems

1. $1.19 + $0.30j = $2.99, j = 6

2. $155.00 + $15g = $335, g = 12

3. 2p− 3 = 45, p = 24

4. $24− $12 = 2t, t = $65. 1

4m = 11, m = 44

6. $250− ($10× 5) = 8(5c), c = $5

Page 127 Graphing Inequalities

1.8

2.5

3.

4.7

5.41

6.

7.10

8.4

9.53

10.

11. x ≥ 012. x ≤ 7 or x ≥ 913. 2 ≤ x ≤ 414. x < 8

15. 2 ≤ x < 6

16. x ≤ 417. x < 2

18. x > 6

Page 128 Solving Inequalities by Addition and Subtraction

1. x > 2

2. x < 15

3. x ≤ 3

4. x ≥ 7

5. x > 2

6. x ≤ 9

7. x > 3

8. x ≤ 5

9. x ≥ 1

10. x > 10

11. x < 4

12. x > 4

30

13. x > 6

14. x > 32

15. x ≤ 11

16. x ≥ 0

17. x < 20

18. x < 10

19. x ≤ 8

20. x ≥ 27

Page 129 Solving Inequalities by Multiplication and Division

1. x > 2020

2. x ≤ 1212

3. x > 4

4. x ≤ 11

5. x > 10

6. x ≤ 7

7. x ≤ 8

8. x > 32

9. x ≤ 66

10. x > 88

11. x ≥ 27

12. x < 3

13. x ≤ 4040

14. x ≤ 33

15. x < 20

16. x > 6

Page 130 Inequality Word Problems

1. 2x+ 50 < 230

2. 2g + 3 ≤ 313. 2w − 8 ≥ 188

4. 12s < $85, 000

or $85, 000 > 12s

5. x− 23 > 86

6. x < 20

7. m+ j < 25

8. n ≥ 2a

9. b < 4c

10. t > 94

Page 131 Going Deeper into Solving Equations and Inequalities

1. x = 2

2. x = 3

3. x > 8

4. x = 11

5. x < 4

6. x = 5

7. x = 11

8. x > 8

9. x > 2

10. x = 2

11. x < 4

12. x = 2

31


1. x = 15

2. k = 45

3. w = 34

4. r = 535

5. x = 64

6. x = 5

7. y = 68

8. x = 104

9. r = 5

10. x = 27

11. x = 5

12. y = 52

13. x = 2

14. r = 25

15. x = 1

16.

17.6

18.

19.4

20. x ≥ 3

21. 5 ≤ x < 9

22. x > 10

23. x > 6

624. x ≤ 3

25. x ≥ 9

926. x ≥ 2

27. $9

28. $7.16

29. $2.49 + $4.29x = $15.36, x = 3

30. $54.00 + $6.50x = $119.00, x = 10

31. x+ (x+ 23) < 190

32. g + (g + 5) ≤ 27


1. C

2. A

3. C

4. C

5. A

6. C

7. C

8. B

9. C

10. D

11. A

12. D

13. B

14. C

15. B

16. D

32

Chapter 10 Introduction to Graphing EquationsPage 136 Graphing Linear Equations (top of page)

1.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

2.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

3.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

4.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

5.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

6.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

33

Page 136 Graphing Linear Equations (bottom of page)

1.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

2.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

3.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

4.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

5.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

6.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

7.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

8.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

9.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

34

Page 138 Independent and Dependent Variables

Independent DependentEquation Variable Variable

1. d = 12× t t (time) d (miles traveled)2. y = 1

2x x (days) y (food eaten)

3. y = 8x x (hours) y (miles traveled)4. y = x

10× 25 x (pages) y (minutes)

5. d = t× 37 t (time) d (miles traveled)6. y = 3

4x y (dozens of muffins) y (amount of sugar)

7. y = 4x x (number of sides of birdhouse) y (number of nails)8. 7 = 6x x (number of rows) none

Pages 139–140 Finding Values of Variables in Tables

1.y =

x

10× 22

x y

200 440

220 484

240 528

260 572

2.y =

x

3× 5

x y

9 15

12 20

15 25

18 30

3.y = (x× 50)× $2x y

6 $600

10 $1, 000

15 $1, 500

20 $2, 000

4.y =

x

0.2× 3

x y

0.6 9

0.8 12

1.0 15

1.2 18

5.y =

x

3× 1.5

x y

15 7.5

18 9

21 10.5

24 12

6.y =

x

34

x y

510 15

680 20

1, 020 30

1, 360 40

35

Page 142 Understanding Slope

1. slope = 1

0−1

2

−2−3

1

3

−1−4 1

4

2 3 4

5

6

7

x

y

(2, 3)

(4, 5)

rise = 1run = 1

2. slope = 2

0−1

2

−2−3

1

3

−1−4 1

4

2 3 4

5

6

7

x

y

(1, 3)

(2, 5)rise = 2

run = 1

3. slope = −15

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

(4, 1)

( 1, 2)−

rise = 1

run = 5

4. slope = 0

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

(1, 2)−

(4, 2)−rise = 0

5. slope is undefined

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

(3, 4)

(3, 0)

run = 0

6. slope = −32

0−1

3

−2−3

2

1

4

−4 1

5

2 3 4

6

7

8

x

y

( 1, 8)−

(3, 2)

rise = 3−

run = 2

7. slope = −12

3

2 3

2

10

1

−1−1 4

4

5 6 7

5

6

7

x

y

(2, 4)

(4, 3)rise = 1−

run = 2

8. slope = −3

0−1

1

−2−3

2

−1

−2

−4 1

3

2 3 4

4

5

6

x

y

(1, 5)

(2, 2)

rise = 3−

run = 1

9. slope = 1

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

(3, 4)

(1, 2)

rise = 1

run = 1

10. slope is undefined

0−1

1

−2−3

2

−1

−2

−4 1

3

2 3 4

4

5

6

x

y(3, 6)

(3, 2)

run = 0

11. slope = 0

x0 2−1

1 3

−2

−3

−4

−1 4

1

5 6 7

2

3

4

y

(6, 2)−(3, 2)−

rise = 0

12. slope = 1

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

(3, 4)

(1, 2)

rise = 1run = 1

36

13. slope = −1

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

( 4, 3)−

( 2, 1)−

rise = 1−

run = 1

14. slope = 3

0 1−1

2−1

−2

−3

−4

−2 3

1

4 5 6

2

3

4

x

y

(5, 2)

(4, 1)

rise = 3

run = 1

15. slope = −73

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

rise = 7−

run = 3

16. slope = 6

0−1

1

−2−3

2

−1

−2

−4 1

3

2 3 4

4

5

6

x

y

( , )−2 1

(3, 5)

rise = 6

run = 1

Page 144 Graphing Linear Data

1.

0 1

5

2 3 4 5

10

15

20

25

Circ

umfe

renc

e

Diameter

2. circumference = about 9.5 inches

3. about 1 inch

4. slope = 3.14

5. The slope of circumference over diametergives the value of π.

6.

0 1

5

2 3 4 5

10

15

20

25

Perim

eter

Length of Side

7. Perimeter = 16 inches

8. slope = 4

37

9.

0 1

10

2 3 4 5

20

30

40

50

Oun

ces

Pounds

60

70

10. 2.5 pounds

11. The slope represents ounces per pound.

12. pounds

13. ounces

14.

0 1

5

2 3 4 5

10

15

20

25

Day

s

Weeks15. about 17.5 days

16. weeks

17. days


1.x y1 12 23 34 4

2.x y1 22 43 6

3.x y−1 20 01 −22 −4

38

Independent DependantEquation Variable Variable

4. y = 3.5x x (number of hours) y (miles traveled)5. y = 3

4x x (days) y (amount of food eaten)

6. d = t× 37 t (hours) d (miles traveled)

7.

0−1−1

−2−3

−2

−3

−4

−4 1

1

2 3 4

2

3

4

x

y

8. −12

9. y = 125x+ 75

10. y = 50x+ 120

11.y =

x

10× 18

x y

180 324

230 414

260 468

310 558

12.y =

x

0.5× 14

x y

1.0 28

1.5 42

2.0 56

2.5 70

13. 14

14. 14

15. 1


1. C

2. C

3. A

4. D

5. B

6. C

7. C

8. C

9. A

10. D

39

Chapter 11 Plane GeometryPage 150 Types of Shapes

1. triangle

2. trapezoid

3. pentagon

4. octagon

5. rectangle

6. hexagon

7. parallelogram

8. decagon

9. square

10. heptagon

11. nonagon

12. rhombus

Page 151 Area of Squares and Rectangles

1. 7.84 m2

2. 150 cm 2

3. 600 cm2

4. 1250 yd2

5. 144 in2

6. 18 ft2

7. 169 ft2

8. 3.96 m2

9. 2000 yd2

10. 625 m2

Page 152 Area of Triangles

1.

4 in

3 in

2.

3 in

5 in

3.

2.5 in

2.5 in

Base Height Area4. 6 m 27 m 81 m2

5. 12 ft 12 ft 72 ft26. 10 cm 12 cm 60 cm2

7. 15 in 12 in 90 in28. 14 yd 7 yd 49 yd29. 5 in 12 in 30 in2

10. 10 ft 18 ft 90 ft2

40

Page 153 Area of Parallelograms

1.

6 ft

20 ft2.

10 m

12 m

3.

4 in

8 in4. 50 ft2

5. 36 in2

6. 144 ft2

7. 169 cm2

8. 5.33 cm2

9. 72 m2

10. 69.92 mm2

Page 154 Area of Trapezoids

1. 5

9

8

2. 10

6

12

3. 6

7

9

Bases Height Area4. 6 m, 4 m 10 m 50 m2

5. 2 ft, 6 ft 12 ft 48 ft26. 10 cm, 5 cm 8 cm 60 cm2

7. 3 in, 5 in 12 in 48 in28. 2 yd, 3 yd 6 yd 15 yd29. 5 in, 5 in 6 in 30 in2

10. 10 ft, 4 ft 8 ft 56 ft2

Page 156 Area of Other Polygons

1. 432 m2

2. 74 ft23. 30 cm2

4. 122 in25. 150 ft2

6. 32 ft27. 4,800 in2

8. 240 ft2

Page 157 Area Word Problems

1. 4.5 ft2

2. 28 ft23. 209 ft2

4. 18 ft25. 200 ft2

6. 13.75 ft27. 22, 050 ft2

8. 183 ft29. 200 ft2

10. 128 ft2

41


1. A = s2

2. A = lw

3. A = 12bh

4. A = bh

5. A = 12h(a+ b)

6. pentagon

7. parallelogram

8. octagon

9. trapezoid

10. hexagon

11. 24 cm2

12. 60 cm2

13. 116 cm2

14. 110 cm2

15. 64 in2

16. 33 in2

17. 11, 000 ft2

18. 66 in2

19. 50 cm2


1. B

2. C

3. C

4. B

5. C

6. D

7. B

8. B

9. D

10. A

11. C

12. C

13. A

14. A

Chapter 12 Solid GeometryPage 162 Types of Three-Dimensional Figures

1. rectangularpyramid

2. cone

3. triangular prism

4. triangular pyramid

5. rectangular prism

6. cylinder

7. square pyramid

Page 163 Understanding Volume

1. 30 units3 2. 36 units3 3. 24 units3 4. 54 units3

Page 164 Volume of Rectangular Prisms

1. 48 ft3

2. 2, 160 mm3

3. 768.75 in3

4. 576 m3

5. 42 ft3

6. 4, 536 in3

7. 800.8 cm3

8. 96 cm3

9. 110 m3

Page 165 Volume of Cubes

1. 15.625 cm3

2. 512 cm3

3. 1, 728 cm3

4. 421.875 in3

5. 27 cm3

6. 7.9 in

7. 64 in3

8. 216 ft3

9. 1, 728 in3

42

Page 167 Nets of Solid Objects

1. cube

2. square pyramid

3. triangular prism


5. rectangular prism

6. rectangular pyramid

Page 168 Using Nets to Find Surface Area

1. 54 in2 2. 139 cm2 3. 518 ft2

Pages 170 Surface Area of Cubes and Rectangular Prisms

1. 96 ft2

2. 602 cm2

3. 120 m2

4. 486 mm2

5. 192 ft2

6. 320 cm2

7. 720 in2

8. 126 ft29. 24 m2

10. 278 cm2

Page 171 Surface Area of Triangular Prisms

1. 156 cm2 2. 4240 in2 3. 1248 in2 4. 8640 cm2

Page 172 Surface Area of Pyramids

1. 16 ft2

2. 180 mm2

3. 400 m2

4. 176 cm2

5. 33 m2

6. 261 in2

7. 88 m2

8. 125 in2

9. 147 ft2

Page 173 Solid Geometry Word Problems

1. SA = 550, 000 yd3

2. V = 5, 184 in3

3. SA = 250 cm2

4. SA = 756 cm2

5. SA = 24 ft2, V = 8 ft3

6. SA = 1, 350 in2

7. Floor: SA = 195 ft2Walls: SA = 504 ft2Ceiling: SA = 195 ft2

8. V = 64 in3

9. V = 1, 440 in3

Page 174 Going Deeper into Solid Geometry

1. SA = 274 ft2V = 222 ft3

2. SA = 504 cm2

V = 592 cm33. SA = 154 in2V = 90 in3

4. SA = 62 cm2

V = 29 cm2

43


1. V = 125 in3SA = 150 in2

2. V = 38, 400 in3

3. V = 365 in3

4. SA = 34 ft2

5. cube

6. triangular prism

7. cone


9. 2

10. 12

11. cone

12. cube

13. triangular prism

14. square pyramid


16. cylinder

17. V = 70 in3SA = 118 in2

18. SA = 106 cm2

19. SA = 88 in2V = 44 in3

20. SA = 126 cm2

V = 74 cm3


1. B 2. C 3. B 4. C 5. C 6. A 7. D 8. D 9. B 10. A

Chapter 13 StatisticsPage 179 Range

1. 63

2. 513. 67

4. 67

5. 50

6. 80

7. 7

8. 50

9. $10.11

10. 180

Page 180 Mean

1. 80

2. 10.2

3. 7

4. 4

5. 6

6. 75

7. 75

8. 4.5

9. 505.5

10. $55

11. about 63

12. 12 calls

13. $12/hr

14. 1.8 RBIs

15. 61 mph

Page 181 Median

1. 10

2. 32

3. 90

4. 65

5. 34

6. 6

7. 3

8. 31

9. 13

10. 234

11. 15

12. 5

13. 12

14. 36

15. 350

16. $510

17. 5.8

18. 7

19. 182

20. 1

44

Page 183 Variability

1. We can see by both the mean absolute deviation and the interquartile range that set 1 has awider range of ages.





Page 184 Questions About DataIf answer is no, student is to write a statistical question. Answers may vary.

1. yes

2. no

3. yes

4. yes

5. no

6. yes

7. no

8. yes

9. no

10. yes

11. What are the weights of kittens seen on May 21st in Dr. Kim’s veterinary clinic?

12. What are Oliver’s math test scores?

Page 185 Describing a Data Set

1. Mean: 3, Range: 6Conclusion: The mean is half the size of the range.

2. Mean: 20, Range: 70Conclusion: The mean is on the lower end of the range.

3. Mean: 8, Range: 8Conclusion: The mean is equal to the range.

4. Mean: 5.5, Range: 9Conclusion: The mean is a little more than half of the range.

45

Chapter 13 ReviewPage 1861.Data Mean Median Range98, 65, 78, 88, 89, 92, 80 84.3 88 3390, 55, 75, 60, 80, 90 75 77.5 3520, 22, 28, 30 25 25 1015, 20, 25, 30, 35 25 25 202, 6, 10, 14, 18 10 10 16

2. 242

3. Turkey

4. Meatloaf

5. 104

6. Based on the mean absolute deviation and interquartile range, there is a wider range of ages inClinic 2.

7. Based on the mean absolute deviation and interquartile range, there is a wider range of ages inClinic 2.

8. yes

9. no

10. yes

11. yes


1. C

2. D3. B

4. B

5. A

6. A

7. B

8. D

9. C

10. C

11. B

12. B

Chapter 14 Data AnalysisPage 190 Tally Charts and Frequency Tables

1. 2.

46

Page 191 Histograms1.

2.

Pages 192–193 Dot Plots

1. more

2. April & May

3. yes

4. November

5. Spring

6. July & September

7. January, March, & August

8. 29

9. true

10. February

11. 2,500

12. false

47

Page 194 Stem-and-Leaf Plots

1. Stem Leaf1 6, 6, 8, 92 3, 4, 5, 6, 6, 83 5, 64 2

2. Stem Leaf1 2, 3, 4, 8, 92 0, 1, 2, 2, 4, 43 2, 24 4

3. Stem Leaf2 0, 0, 0, 5, 5, 53 0, 0, 0, 0, 0, 04 0, 5, 5, 5, 5, 5, 556 0

4. Stem Leaf6 07 6, 6, 8, 88 0, 2, 2, 2, 2, 6, 6, 8, 89 2, 4, 4, 6, 810 0

Page 195 Box Plots

1. Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme Range10 19 35 45 59 49



Page 196 Matching Statistical Measures to Plots

1. false

2. true

3. 12

4. 20 minutes

5. 75 minutes

6. week 4

7. true

8. 15 dozen

9. false

10. V

11. G

12. D

13. D

14. G

15. V

48

Page Going Deeper into Data Analysis

1. Amy is 8.

2. John is 24.

3. Arliss is 48.

4. Charla is 2.

5. Melissa is 30.

6. James is 59.

7. Sally is 41.

8. Alan is 3.

9. Cesar is 8.

10. Henry is 14.

11. Marie is 39.

12. Joan is 52.

13. Noah is 17.

14. Franklin is 1.

15. Michael is 10.

16. Erin is 5.

17. Larry is 45.

18. Krista is 14.

19. Paul is 3.

20. Jake is 57.

21. Andrew is 4.

22. Celia is 21.

23. Sharika is 33.

24. Christopher is 46.

25. Christina is 46.

26. Olivia is 30.

27. Hannah is 11.

28. Ethan is 7.

29. Madison is 25.

30. Joseph is 28.

31. Anthony is 59.

32. Shawn is 35.

33. Betty is 42.

34. Abigail is 13.

35. Matthew is 37.

36. Luke is 45.

37. Peter is 47.

Ages of the O’Malley FamilyStem Leaf0 1, 2, 3, 3, 4, 5, 7, 8, 81 0, 1, 3, 4, 4, 72 1, 4, 5, 83 0, 0, 3, 5, 7, 94 1, 2, 5, 5, 6, 6, 7, 85 2, 7, 9, 9

49


1. 48

2. 4

3. 10

4. Games 2 & 3

5. Games 1 & 4

6. 2

7. 6

8. 12

9. 19

10. 26

11. 24

12.

76543210

2467

101265

Numberof Pets Frequency

13. Histogram: Pets per Student

Number of StudentsNum

ber o

f Pet

s Pe

r Stu

dent

0 1 2 3 4 5 6 7 8 9 10 11 12 13

76543210

14. January & April

15. true

16. $15

17. 78, 88, 89, 89, 92, 95,100

18. Math

19. English


1. C 2. B 3. C 4. D 5. D 6. C 7. A 8. D 9. A

Chapter 15 How to Answer Constructed-Response QuestionsChapter 15 ReviewPages 204–2051. Good Answer:A 4.5 yearsClosest dog: SydneyB Erin owns Bella.C 7x = 47.6D 6.8 years old; Dawn owns Pogo.

50

Better Answer:

AMean age: 4.5 yearsClosest dog: Sydney (4.6 years)

BMedian age: 3.5 years (Bella). Erin owns Bella.

C Expressed algebraically: 7x = 47.6

D Solve for x: x = 6.8 years oldDawn owns Pogo.

Best Answer:

A Add all the ages together, then divide by the total number of dogs.(0.7 + 1.1 + 14 + 3.5 + 4.6 + 6.8 + 1.1)÷ 7 = 4.5Mean age: 4.5 yearsClosest dog: Sydney (4.6 years)

B Order the ages from least to greatest. The median is the middle age.0.7, 1.1, 1.1, 3.5, 4.6, 6.8, 14Median age: 3.5 years (Bella). Erin owns Bella.

CMultiply 7 by the age in human years to find the "doggie year."Expressed algebraically: 7x = 47.6

D Solve for x by dividing both sides by 7: x = 6.8 years oldDawn owns Pogo.

2. Good Answer:

A 6× 8; 8× 10B 80 sq. units

C The units must be feet.

Better Answer:

AMattress: 6× 8Sheets: 8× 10B 8× 10 = 80 sq. units

C The units must be feet. Meters/yards would be too big.

Best Answer:

AMattress: 6× 8 (or 8× 6).Sheets: 8× 10 (or 10× 8)BMultiply the length (8) by the width (10). 8× 10 = 80 sq. units

C The units must be feet. Meters/yards would be too big, cm/inches would be too small.

51

Teaching Activities (DOK 4)

Ratios and Proportional Relationships 6.RP• Encourage the students to organize their information by creating tables when solving proportions.http://www.homeschoolmath.net/teaching/proportions.php

Dollars 3.30Pounds 1 2 3 4 5

• Give students recent sales ad from the newspaper. Have them create their own ratio problems forother classmates to solve and then plot values on a coordinate plane.

The Number System 6.NS• Have students research climate temperatures around the world, making sure to include positiveand negative temperature. These can then be graphed on a coordinate plane.• Have students balance a checkbook registry to see how positive and negative numbers worktogether to describe quantity.

Expressions and Equations 6.EE• Write algebraic expressions on index cards. Ex: The value of 3x2 when x = 3. Have studentsdraw a card at random and solve. Switch with a partner to check work.• Have students create their own algebraic expressions for other students to solve.• Dishes for a Penny Lesson Plan - http://www.uen.org/Lessonplan/preview?LPid=5462

Geometry 6.G• Online geoboard – great for the students to create polygonshttp://nlvm.usu.edu/en/nav/frames_asid_282_g_3_t_3.html?open=activities• Allow students to use graph paper when creating polygons• Use square color tiles and interlocking cubes to find patterns in perimeter, area, and volume.http://www.uen.org/Lessonplan/preview?LPid=15427

Statistics and Probability 6.SP• Have students collect, summarize, and describe numerical data among their classmates such asnumber of steps walked in a day, birth month, or heart rate.• Students can display the numerical data they collect through plots on a number line. They cancompare their plots with other classmates.

52

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ANSWER KEY & ACTIVITIES COMMON CORE GPS