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7th GradeMath

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Book 1

6th-8th GRADE DAILY ROUTINE

TTiimmee AAccttiivviittyy EExxaammpplleess

66--88 8:00a Wake-Up and

Prepare for the Day

• Get dressed, brush teeth, eat breakfast

9:00a Morning Exercise

• Exercises o Walking o Jumping Jacks o Push-Ups o Sit-Ups o Running in place o High Knees o Kick Backs o Sports

NNOOTTEE:: Always stretch before and after physical activity

10:00a Academic Time: Reading Skills

• Online: o Plato (ELA)

• Packet o Reading (one lesson a day)

11:00a Play Time Outside (if weather permits) 12:00p Lunch and Break

• Eat lunch and take a break • Video game or TV time • Rest

2:00p Academic Time: Math Skills

• Online: o Plato (Math)

• Packet o Math (one lesson a day)

3:00p Academic Learning/Creative Time

• Puzzles • Flash Cards • Board Games • Crafts • Bake or Cook (with adult)

4:00p Academic Time: Reading for Fun

• Independent reading o Talk with others about the book

5:00p Academic Time: Science and Social Studies

• Online o Plato (Science and Social Studies)

Para familias que necesitan apoyo académico, por favor llamar al 504-349-8999 De lunes a jueves • 8:00 am – 8: 00 pm Viernes • 8:00 am – 4: 00 pm Disponible para familias que tienen preguntas ya sea sobre los recursos de aprendizaje en línea o los paquetes de aprendizaje impresos.

Tiempo Actividad Detalles 8:00a Despierta y Prepárate para el día • Vístete, cepíllate los dientes, desayuna

9:00a Ejercicio Mañanero

NOTE: Siempre hay que estirarse antes y después de cualquier actividad física.

• Ejercicios o Caminar o Saltos de tijeras o Lagartijas o Abdominales o Correr en el mismo lugar o Rodillas altas o Patadas hacia atrás o Deportes

10:00a Tiempo Académico:

Habilidades de Lectura • En Línea:

o Plato (ELA) • Paquete:

o Leer(una lección al día) 11:00a Tiempo para jugar Afuera(si el clima lo permite) 12:00p Almuerzo y Descanso • Almorzar y tomar un descanso

• Este es tiempo para jugar videos y ver televisión

• Descansar 2:00p Tiempo Académico:

Habilidades de Matemáticas • En Línea:

o Plato (Matemática) • Paquete

o Matemática (una lección al día)

3:00p Aprendizaje Académico/Tiempo Creativo • Rompecabezas • Tarjetas Flash • Juegos de Mesa • Artesanías • Hornear o Cocinar( con un adulto)

4:00p Tiempo Académico: Leyendo por Diversión

• Lectura Independiente o Habla con otros acerca de

lo que leíste 5:00p Tiempo Académico:

Ciencias y Estudios Sociales • En Línea

o PLato(Ciencia y Estudios Sociales)

7.NS Distances on the Number

Line 2

Task

On the number line above, the numbers and are the same distance from . What is

? Explain how you know.

7.NS Distances on the Number Line 2 Typeset May 4, 2016 at 22:03:32. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

a b 0

a + b

1

Illustrative Mathematics

3

©Curriculum Associates, LLC Copying is not permitted. 21Lesson 3 Add and Subtract Positive and Negative Integers

Name: Lesson 3

Addition Methods for Integers

Study the example problem showing how to add positive and negative integers. Then solve problems 1–7.

1 Complete this model to represent the problem

score at the end 1

5

of first round

2 Write an addition equation using numbers to represent the verbal equation in problem 1

3 Amy said she would have solved this problem differently She saw that she was looking for the difference between the score in the second round, 3, and the score in the first round, 25, so she wrote the expression 3 2 (25) Does her method work? Explain

Example

At the end of the first round of a game, Luis has a score of 25 points At the end of the second round, he has a score of 3 points How many points did he score during the second round?

You can use a number line to help you understand the problem

212223242526 0 1 2 3 4

18 End at 3.Start at 25.

The number line shows that Luis scored 8 points during the second round

4

©Curriculum Associates, LLC Copying is not permitted.22 Lesson 3 Add and Subtract Positive and Negative Integers

Solve.

4 The temperature in Indianapolis was 24°F at 7:00 am The temperature rose 3°F by noon What was the temperature at noon? Use a number line to find the answer

5 Aiden had saved $22 before he earned $25 mowing a lawn He then spent $32 on a suitcase How much money does he have now? Explain how you found your answer

6 Omar has a score of 12 in a bean-bag toss game On his next turn he gets 28 points Use the bar model to write an addition sentence that shows Omar’s score now

12

8?

7 Gina works in a clothing store At noon, she has $125 in the cash register James gives her $60 for a sweater, and she gives him $7 change Hana then gives her $40 for a blouse and receives $3 change Use a series of addition equations to find out how much money Gina has in her cash register at the end of these sales

Show your work.

Solution:

5


Name: Lesson 3

Subtraction Methods for Integers

Study the example showing how to subtract positive and negative integers. Then solve problems 1–4.

1 Use a number line to find the team score for Round 3

Round 3 team score:

Example

Two friends are playing a game with a spinner that has positive and negative numbers on it Each player takes turns spinning the spinner The table shows the results of the first 4 rounds

Round 1 Round 2 Round 3 Round 4

Player 1 2 25 25 8

Player 2 12 210 2 24

Team Score

The team score at the end of each round is found by subtracting Player 2’s score from Player 1’s score

For Round 1: Subtracting 12 from 2 is the same as adding 212 Start at 2 and move left 12 units to arrive at 210

212223242526272829210211 0 1 2 3 4 5 6 7

212

For Round 2: Subtracting 210 is the same as adding 10 Start at 25 and move right 10 units to arrive at 5

212223242526272829210211 0 1 2 3 4 5 6 7

110

6


Solve.

2 Refer to the table from the previous page

Round 1 Round 2 Round 3 Round 4

Player 1 2 25 25 8

Player 2 12 210 2 24

Team Score

On which round did the team get the highest score? Explain your answer

3 Anita recorded the daily high and low temperatures as 13°F and 23°F, respectively

a. Write the difference in temperatures, in °F, as a subtraction equation Then write the difference in temperatures as an addition equation

b. Give an example of a positive temperature and a negative temperature that have a difference of 5°F

4 Consider the following problems

a. Write a subtraction equation that involves one negative integer but results in a positive difference Does the other integer have to be positive? Explain your answer

b. Write a subtraction problem involving two positive integers with a negative difference Explain the relationship between the two integers that must exist for the difference to be negative

7


Name:

2 Lamont keeps track of his math grades by recording them in a table He wants to keep an average of 90, so he also lists the amount that each grade is above or below 90

a. Complete the table

Test 1 2 3 4 5 6

Grade 83 94 79 96

Above/Below 90 27 4 7 23

b. Use the numbers in the Above/Below 90 row to find out whether Lamont’s average is above or below 90

Show your work.

Solution:

c. What grade does Lamont need to get on the next test to have an average of exactly 90? Explain your answer

Add and Subtract Positive and Negative Integers

Solve the problems.

1 The element bromine turns into a liquid at 27°C, and it turns into a gas at 59°C From the temperature at which bromine becomes a liquid, by how many degrees must the temperature change for it to turn into a gas?

A 266°C C 52°C

B 252°C D 66°C

Johnathan chose C as his answer How did he get that answer?

You may want to group the positive numbers and the negative numbers.

Should you add or subtract?

Lesson 3

8


5 A duck is sitting on a ledge that is 11 feet above the surface of a pond The duck dives 27 feet straight down to get food at the bottom of the pond Which expression represents the position of the bottom of the pond, in feet, relative to its surface level?

A 27 1 11 C 11 2 (227)

B 27 1 (211) D 11 1 (227)

6 Which of the following are negative integers? Select all that are correct

A the sum of two positive integers

B the sum of two negative integers

C the difference of a positive integer and an integer that is greater than it

D the difference of a negative integer and an integer that is greater than it but that is not its opposite

Solve.

3 Which expressions are equivalent to 29? Select all that are correct

A 8 2 8 1 9

B 3 2 (26) 1 (218)

C 21 1 7 2 (23)

D 4 2 5 2 8

4 Tell whether each equation is True or False

a. 24 1 (27) 5 11 u True u False

b. 5 1 (24) 5 25 1 4 u True u False

c. 210 1 7 5 7 2 10 u True u False

d. 14 1 (23) 5 10 1 1 u True u False

What should be your first step?

What does a negative value mean in this situation?

Recall how to write a subtraction problem as an addition problem.

You may want to draw a number line and try sample numbers.

9

7.NS Differences of Integers

Task

Ojos del Salado is the highest mountain in Chile, with a peak at about 6900 meters

above sea level. The Atacama Trench, just off the coast of Peru and Chile, is about 8100

meters below sea level (at its lowest point).

a. What is the difference in elevations between Mount Ojos del Salado and the

Atacama Trench?

b. Is the elevation halfway between the peak of Mount Ojos del Salado and the

Atacama Trench above sea level or below sea level? Explain without calculating the

exact value.

c. What elevation is halfway between the peak of Mount Ojos del Salado and the

Atacama Trench?

7.NS Differences of Integers Typeset May 4, 2016 at 23:32:08. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1


11

©Curriculum Associates, LLC Copying is not permitted. 61

Name:

Lesson 7 Add and Subtract Rational Numbers

Lesson 7

Add Negative Fractions

Study the example problem showing how to add negative fractions. Then solve problems 126.

1 Use a common denominator to find 21 1 ·· 4 1 1 2 3 ·· 8 2

2 Use a common denominator to find 2 2 ·· 3 1 1 2 4 ·· 5 2 Show your work.

Solution:

Example

Willie is making cookies From a bag of sugar, he removed

1 1 ·· 4 cups for the cookie dough and 3 ·· 8 cup to sprinkle on top

What number represents the total change in the amount of

sugar in the bag?

You can use a number line to solve this problem

02122 2 48

2 38

21 48

21 14

The model shows that the total change in the amount of

sugar in the bag is 21 5 ·· 8 cups

You can also use an equation to find the solution

Change in sugar 1

Change in sugar 5

Overall for dough for sprinkles change

21 1 ·· 4 1 1 2 3 ·· 8 2 5 21 5 ·· 8

12

©Curriculum Associates, LLC Copying is not permitted.62 Lesson 7 Add and Subtract Rational Numbers

3 Serena is building a bookcase She cuts two pieces of

wood from one board One piece is 1 7 ·· 8 feet long and

another is 3 1 ·· 2 feet long What is the total change in the

length of the original board?

Show your work.

Solution:

4 In an experiment, the temperature of a solution is 2 7 ·· 8 °F

The temperature drops 1 1 ·· 2 °F What is the temperature

after the drop?

Show your work.

Solution:

5 The sum of two negative fractions with different

denominators is 2 7 ·· 10 What are two possible fractions?

Show your work.

Solution:

6 Find the sum

a. 22 1 ·· 10 1 1 24 4 ·· 5 2

b. 23 5 ·· 6 1 1 21 7 ·· 12 2

Solve.

13

©Curriculum Associates, LLC Copying is not permitted. 63Lesson 7 Add and Subtract Rational Numbers

Name: Lesson 7

Add and Subtract Rational Numbers

Study the example problem showing how to add and subtract rational numbers. Then solve problems 127.

1 Write an addition equation to represent the situation

2 Find 25 1 ·· 4 1 3 1 ·· 2 Explain how you found your answer

3 Elaine says that when you add two rational numbers, the sign depends on how many negative numbers you have Do you agree with Elaine? Explain your answer

Example

On a test, wrong answers are worth 25 25 points and right answers are worth 3 5 points So far, Marshall has one right answer and one wrong answer What is Marshall’s current score?

You can solve this problem using a number line

212223242526 0 1

Lost 5.25 points

Gained 3.50 points

The number line model shows that Marshall’s current score is 21 75

14

©Curriculum Associates, LLC Copying is not permitted.64 Lesson 7 Add and Subtract Rational Numbers

Solve.

4 A gardener cuts a plant down by 1 5 ·· 8 inches The plant

then grows 9 1 ·· 4 more inches What is the total change in

the height of the plant? Explain

Show your work.

Solution:

5 Solve each problem

a. What is 24 3 2 (26 8)?

b. What is 1 3 ·· 5 1 1 22 7 ·· 10 2 ?

6 You are playing a game You lose 4 8 points, lose another 7 6 points, and then win 2 5 points What is the overall change in your score?

Show your work.

Solution:

7 Find the number that makes the equation true

2 7 ·· 10 1 ? 5 22 9 ·· 20

Show your work.

Solution:

15

7.NS Comparing Freezing Points

Task

Ocean water freezes at about . Fresh water freezes at . Antifreeze, a liquid

used in the radiators of cars, freezes at .

Imagine that the temperature has dropped to the freezing point for ocean water. How

many degrees more must the temperature drop for the antifreeze to turn solid?

7.NS Comparing Freezing Points Typeset May 4, 2016 at 22:03:38. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

−2 C1

2

∘C0

∘

− C64∘

1


16

©Curriculum Associates, LLC Copying is not permitted. 99Lesson 10 Understand Proportional Relationships

Name: Lesson 10

Identify Proportional Relationships

Study the example showing one way to test whether a relationship is proportional. Then solve problems 1–7.

1 Explain how you can tell whether a group of ratios represents a proportional relationship

2 Look at the ratios for Company A in the example What is the constant of proportionality and what does it mean?

3 Write an equation to represent the relationship between the number of mugs and cost for Company A Use c for cost and m for the number of mugs

4 Complete the table to show a proportional relationship Write the constant of proportionality

Number of Yoga Classes 2 4 6 8

Cost ($) 60

constant of proportionality:

Example

The tables show the prices for ordering photo mugs from two different companies You can use the information to write ratios showing the relationship between the cost and the corresponding number of mugs

Company A Company B

Number of Mugs 5 10 25 50 Number of Mugs 5 10 25 50

Cost ($) 15 30 75 150 Cost ($) 20 35 80 155

15 ·· 5 5 3 30 ·· 10 5 3 75 ·· 25 5 3 150 ·· 50 5 3 20 ·· 5 5 4 35 ·· 10 5 3 5 80 ·· 25 5 3 2 155 ·· 50 5 3 1

These ratios are all equivalent These ratios are not all equivalent This relationship is proportional This relationship is not proportional

Vocabularyconstant of proportionality

another term for the unit

rate in a proportional

relationship

17

©Curriculum Associates, LLC Copying is not permitted.100 Lesson 10 Understand Proportional Relationships

Solve.

5 Plot a point for some of the ordered pairs from the example problem shown at the right Model the relationships by drawing a line from the y-axis through each point Explain how the graphs show which relationship is proportional and which is not proportional

6 Determine whether each equation below does or does not represent a proportional relationship Support your answer using either a table or a graph

Equation A: y 5 x

Equation B: y 5 x 1 2

7 Zahra has paper rectangles of different sizes Every rectangle is 5 centimeters longer than it is wide Is there a proportional relationship between the lengths and widths of these rectangles? Explain

Company A: (5, 15), (10, 30), (25, 75)Company B: (5, 20), (10, 35), (25, 80)

Co

st (

$)

Number of Mugs10 20 30O

x

y

20

10

40

60

70

80

30

50

18

©Curriculum Associates, LLC Copying is not permitted. 101Lesson 10 Understand Proportional Relationships

Name:

Example

Describe a relationship involving some product or service and its cost that is NOT proportional Explain how you know that it is not a proportional relationship

Show your work. Use tables, graphs, words, and numbers to explain your answer

Best Bike Rentals rents bikes by the day. The longer you rent the bike, the better their rate is. The table shows the cost of renting a bike for up to 7 days. The ratios of cost to days in this table are not equivalent because the relationship is not proportional.

Number of Days 1 2 3 4 5 6 7

Cost ($) 60 100 130 150 170 180 190

For example, 60 ··· 1 5 60, 100 ···· 2 5 50, and 130 ···· 3 5 43 1 ·· 3 . These

three ratios are not equivalent. The rate of dollars per day is less the longer you keep the bike.

I can also plot the ordered pairs from the table on a coordinate grid.

The points cannot be connected with a straight line that goes through the origin. This is another way to show that the relationship is not proportional.

Lesson 10

Reason and Write

Study the example. Underline two parts that you think make it a particularly good answer and a helpful example.

Where does the example . . . • answer both parts

of the problem?• use a table or graph

to explain?• use numbers to

explain?• use words to

explain?• give details?

Co

st ($

)

Number of Days2 4 61 3 5 7O

x

y

40

20

80

120

140

160

180

60

100

19

©Curriculum Associates, LLC Copying is not permitted.102 Lesson 10 Understand Proportional Relationships

Solve the problem. Use what you learned from the model.

Describe a relationship involving some product or service and its cost that IS proportional Explain why it is a proportional relationship, and identify the constant of proportionality

Show your work. Use tables, graphs, words, and numbers to explain your answer Did you . . .

• answer both parts of the problem?

• use a table or graph to explain?

• use numbers to explain?

• use words to explain?

• give details?

20

©Curriculum Associates, LLC Copying is not permitted. 107Lesson 11 Equations for Proportional Relationships

Name: Lesson 11

Write Equations for Proportional Relationships

Study the example showing how to identify a proportional relationship. Then solve problems 1–9.

1 Graph the relationship between the money earned and the number of lawns and connect the points How does the graph tell you that the relationship is proportional?

2 What does the ratio 5 ·· 1 represent in terms of the example?

3 How can you use the graph to find the constant of proportionality? What is the constant of proportionality?

4 Use the constant of proportionality to write an equation that represents the amount of money earned, y, for mowing x lawns

5 If you know the constant of proportionality, m, for two proportional quantities, x and y, what equation can you write to describe the relationship?

Example

The table shows the relationship between the money that Leo earns and the number of lawns that he mows Is the relationship proportional?

Number of Lawns 2 4 5 8

Money Earned ($) 10 20 25 40

The ratios of the money earned to the number of lawns all

simplify to 5 ·· 1 , or 5, so the relationship is proportional

Mon

ey E

arne

d ($

)

Number of Lawns2 4 6 8 91 3 5 7O

x

y

10

5

20

30

35

40

45

15

25

21

©Curriculum Associates, LLC Copying is not permitted.108 Lesson 11 Equations for Proportional Relationships

Solve.

6 Nila uses the equation c 5 8h to figure out the total amount c she should charge a customer if she babysits for h hours Find the constant of proportionality and explain what it means

7 Use the information in problem 6 to solve this problem Nila decides to increase the rate she charges customers by $2 per hour What equation should she now use to determine how much to charge her customers? Explain

8 The table shows the cost of several bunches of bananas What equation can be used to represent the cost c of a bunch that weighs p pounds?

Show your work.

Solution:

9 The graph shows the relationship between the distance that Dustin can drive his car and the amount of gas needed for that distance Explain how Dustin can use the graph to predict the number of gallons of gas he will need for a trip of 120 miles Then find the amount of gas he will need

Show your work.

Solution:

Number of Pounds

2 5 3 5 4 4 5

Cost ($) 1 05 1 47 1 68 1 89

Dis

tan

ce (m

i)

Gas (gal)1 20.5 1.5O

g

d

10

5

20

30

35

40

45

15

25

22

7.RP Buying Coffee

Task

Coffee costs $18.96 for 3 pounds.

a. What is the cost for one pound of coffee?

b. At this store, the price for a pound of coffee is the same no matter how many

pounds you buy. Let be the number of pounds of coffee and be the total cost of

pounds. Draw a graph of the relationship between the number of pounds of coffee

and the total cost.

c. Where can you see the cost per pound of coffee in the graph? What is it?

7.RP Buying Coffee Typeset May 4, 2016 at 21:51:36. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

x y x

1


23

Grid paper is provided on page 26 & 27.

Grid paper is provided on page 26 & 27.

7.RP Tax and Tip

Task

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and

that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the

pre-tax amount. How much should you leave for the waiter? How much will the total

bill be, including tax and tip? Show work to support your answers.

7.RP Tax and Tip Typeset May 4, 2016 at 21:51:48. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1


7.RP Finding a 10% increase

Task

5,000 people visited a book fair in the first week. The number of visitors increased by

10% in the second week. How many people visited the book fair in the second week?

7.RP Finding a 10% increase Typeset May 4, 2016 at 21:53:46. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1


35

©Curriculum Associates, LLC Copying is not permitted. 151Lesson 15 Writing Linear Expressions

Name: Writing Linear Expressions

Lesson 15

Prerequisite: Identify Equivalent Expressions

Study the example problem showing how to write equivalent linear expressions. Then solve problems 1–8.

1 Why did Paolo add 3(x 1 2) to itself and subtract 8?

2 What is the meaning of each part of Carla’s expression?

3 How do you know that Paolo’s and Carla’s expressions are equivalent?

Example

Mia babysits some children after school. For each child, she charges x 1 2 dollars per hour. One day she cared for 2 children for 3 hours each. She paid $4 per child for materials for activities. Two students wrote expressions for the amount of money Mia earned. Are their expressions equivalent?

Paolo wrote the expression 3(x 1 2) 1 3(x 1 2) 2 8. Carla wrote the expression (3x 1 6) 2 4 1 (3x 1 6) 2 4.

Simplify the expressions to see whether they are equivalent.

Paolo’s Expression Carla’s Expression

3(x 1 2) 1 3(x 1 2) 2 8 (3x 1 6) 2 4 1 (3x 1 6) 2 4 5 3x 1 6 1 3x 1 6 2 8 5 3x 1 3x 1 6 1 6 2 4 2 4 5 6x 1 4 5 6x 1 4

The expressions are equivalent.

Vocabularyequivalent expressions

expressions that have

the same value for every

value of the variable.

2(x 1 1) and 2 1 2x

are equivalent

expressions.

1

36

©Curriculum Associates, LLC Copying is not permitted.152 Lesson 15 Writing Linear Expressions

Solve.

4 Is the expression 3 1 x 1 1 1 ·· 2 2 2 3 equivalent to 3x 1 1 1 ·· 2 ?

Explain.

5 Is 2 1 ·· 2 n 1 1 1 ·· 2 n 1 3 2 n equivalent to 3? Explain.

6 Brady said that the expression 2.6x 2 (1.3x 2 4.5) is equivalent to 1.3x 2 4.5. Is he correct? If not, explain his error.

7 Faye says that the perimeter of the rectangle shown is 2x 1 (x 1 10) 1 2x 1 (x 1 10). Khai says that the perimeter is 2(2x) 1 2(x 1 10). Jesse says that the perimeter is 4x 1 20. Who is correct? Explain.

Show your work.

Solution:

8 If a, b, and c are constants, is a(x 2 b) 2 c 5 ax 2 (ab 1 c)? Explain.

2x2x

x 1 10

x 1 10

37

©Curriculum Associates, LLC Copying is not permitted. 153Lesson 15 Writing Linear Expressions

Name: Lesson 15

1 Did Ari and Cal walk the same distance? Explain.

2 In the expression for Cal’s distance, why is (2x 1 1) multiplied by 2?

3 Cindy wrote the expression 2x 1 2x 1 x 1 1 1 1 2 4 to represent Ari’s distance. Is her expression correct? Explain.

4 Did Ben walk the same distance as the other two boys? Use an expression to explain your answer.

Example

The distance from Ari’s house, A, to Ben’s house, B, is equal to the distance from Ari’s house to Cal’s house, C. One day the boys all met at Ari’s house, and then they went to Ben’s house and from there to Cal’s house. Then Ari and Ben went home. Ari and Cal each wrote expressions for the distance they walked.

Ari’s travel distance 5 (2x 1 1) 1 (x 2 4) 1 (2x 1 1)

Cal’s travel distance 5 2(2x 1 1) 1 (x 2 4)

2x 1 1 2x 1 1

x 2 4

A

B C

Writing Equivalent Expressions

Study the example showing different ways to write an expression for a problem. Then solve problems 1–7.

38

©Curriculum Associates, LLC Copying is not permitted.154 Lesson 15 Writing Linear Expressions

Solve.

5 The perimeter of a square is given as 8x 1 20. Write two different expressions for the perimeter. Use factoring to write one of the expressions.

6 The length of a rectangle is 4 times its width. Write three different expressions to describe its perimeter. Explain how you wrote each expression.

7 Each of the two congruent sides of an isosceles triangle has length 2x 2 1.5, and the third side has length x 1 3. Label the sides of the triangle. Then write two equivalent expressions for its perimeter.

Show your work.

Solution:

4w

ww

4w

39

7.EE Writing Expressions

Task

Write an expression for the sequence of operations.

a. Add 3 to , subtract the result from 1, then double what you have.

b. Add 3 to , double what you have, then subtract 1 from the result.

7.EE Writing Expressions Typeset May 4, 2016 at 22:18:11. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

x

x

1


40

©Curriculum Associates, LLC Copying is not permitted. 163Lesson 16 Solve Problems with Equations

Name: Lesson 16

Solve Two-Step Problems with Fractions

Study the example showing how to solve two-step problems that involve fractions. Then solve problems 1–8.

1 In the example, explain how the term 9 ·· 4 x was obtained

in the expression for the perimeter

2 To find the value of x in the equation 9 ·· 4 x 1 2 5 20, you

first get the term with x by itself on one side of the equation How can you do that? What equation do you then have?

3 How can you find the value of x in the equation you wrote for problem 2? What is the value of x?

4 Find the length of each side of the triangle Check that the perimeter is equal to 20 inches

Show your work.

Solution:

Example

The perimeter of the triangle shown is 20 inches Write an expression for the perimeter Then write an equation that you can use to find the length of each side

Perimeter: (x 2 4) 1 (x 1 1) 1 1 1 ·· 4 x 1 5 2 = 9 ·· 4 x + 2

Equation: 9 ·· 4 x + 2 5 20

x 2 4 x 1 1

x 1 514

41

©Curriculum Associates, LLC Copying is not permitted.164 Lesson 16 Solve Problems with Equations

Solve.

5 Solve the equation 2 ·· 5 x 2 1 5 9 Complete each step of

the solution and check your solution

2 ·· 5 x 2 1 5 9

2 ·· 5 x 2 1 5 9

2 ·· 5 x 5

2 ·· 5 x 5

x 5

Check:

6 Paco says that the solution to 2 ·· 5 x 2 1 5 9 is x 5 4

Do you agree? Explain

7 The width of a rectangle is two-thirds of the length The perimeter of the rectangle is 15 centimeters What is the length, ℓ, of the rectangle? Explain

8 You buy 1 1 ·· 4 yards of fabric and an $8 clothing pattern

Your total cost with a 6% sales tax added is $18 55 What is the cost per yard of the fabric?

Show your work.

Solution:

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©Curriculum Associates, LLC Copying is not permitted. 165Lesson 16 Solve Problems with Equations

Name: Lesson 16

Solve Multi-Step Problems with Decimals

Study the example showing how to solve multi-step problems that involve decimals. Then solve problems 1–9.

1 What does n represent in the problem?

2 What does 27 75n represent? Explain

3 How much did Olga pay for the tickets without the handling fee? Explain how you know

4 When solving the equation 27 75n 1 5 50 5 144 25, what can you do to get 27 75n by itself on one side of the equation? What is the result?

5 How can you solve the simplified equation that you wrote in problem 3? Solve the equation

Example

Olga buys tickets to a concert She pays $27 75 for each ticket plus a handling fee of $5 50 for the order The total cost is $144 25 How many tickets, n, did Olga buy?

You can use an equation to solve the problem

Cost of tickets 1 Handling fee 5 Total cost

27 75n 1 5 50 5 144 25

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©Curriculum Associates, LLC Copying is not permitted.166 Lesson 16 Solve Problems with Equations

Solve.

6 Solve the equation 18 2 1 1 5x 5 37 7

a. How can you get 1 5x by itself on one side of the equation? Do this first step to start to solve the equation

b. How could you use the result of part (a) to find the value of x?

7 Solve the equation 0 04x 2 3 82 5 0 68

Show your work.

Solution:

8 Solve the equation 8 5 2 1 2x 5 6 7

Show your work.

Solution:

9 Nita simplified the equation in problem 8 to 1 8 5 1 2x How did she get that? Is this a valid way to solve the equation? Explain

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7.EE Fishing Adventures 2

Task

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each

boat can only carry 1200 pounds of people and gear for safety reasons. Assume the

average weight of a person is 150 pounds. Each group will require 200 lbs of gear for

the boat plus 10 lbs of gear for each person.

a. Create an inequality describing the restrictions on the number of people possible in

a rented boat. Graph the solution set.

b. Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5

people. Group 3 has 8 people. Which of the groups, if any, can safely rent a boat? What

is the maximum number of people that may rent a boat?

7.EE Fishing Adventures 2 Typeset May 4, 2016 at 22:26:25. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

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Math - Jefferson Parish Public Schools · 8:00a Wake-Up and Prepare for the Day • Get dressed,...

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