Math€¦ · ©Curriculum Associates, LLC Copying is not permitted. Lesson 17 Equivalent Expressions 185 Name: Lesson 17 Properties of Operations Study the example showing how to

For families who need academic support, please call 504-349-8999

Monday-Thursday • 8:00 am–8:00 pmFriday • 8:00 am–4:00 pm

Available for families who have questions about either the online learning resources or printed learning packets.

6th GradeMath

#JPSchoolsLove

Show us your

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)

1

2

3

4

©Curriculum Associates, LLC Copying is not permitted. 15

Name:

Lesson 2 Understand Unit Rate

Reason and Write

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

Example

Mom’s muffin recipe uses 10 ounces of berries for 2 dozen muffins Grandma’s muffin recipe uses 12 ounces of berries for 3 dozen muffins Which recipe has more berries per dozen muffins? How many ounces of berries would you need to make 60 muffins of this recipe? (1 dozen 5 12 muffins)

Show your work. Use ratios, unit rates, models, and words to explain your thinking

In Mom’s recipe, the ratio of berries (ounces) to muffins (dozens) is 10 : 2. There are 5 ounces of berries per 1 dozen muffins. So the unit rate is 5.

Berries(ounces)

Mom’s Recipe

Mu�ns(dozen)

50 10 15 3020 25

6543210

In Grandma’s recipe, the ratio of berries (ounces) to muffins (dozens) is 12 : 3. There are 4 ounces of berries per 1 dozen muffins. So the unit rate is 4.

Berries(ounces)

Grandma’s Recipe

Mu�ns(dozen)

40 8 12 2416 20

6543210

The unit rate of 5 is greater than the unit rate of 4, so Mom’s recipe has more berries per dozen.

60 muffins 5 5 dozen muffins, so I would need 5 3 5 or 25 ounces of berries for 5 dozen muffins of Mom’s recipe.

Lesson 2

Where does the example . . . • answer both parts

of the problem?• use words to

explain?• use numbers to

explain?• use models to

explain?• give details?

5

©Curriculum Associates, LLC Copying is not permitted.16 Lesson 2 Understand Unit Rate

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

You buy 3 tickets for $48 total for the jazz concert on Friday night Your friend buys 2 tickets for $36 total for the jazz concert on Saturday night Your brother collected $96 from his friends to buy 6 tickets Which night can they go to the concert? Did they buy the less expensive tickets? Explain

Show your work. Use ratios, unit rates, models, and words to explain your thinking Where does the

example . . . • answer both parts

of the problem?• use words to

explain?• use numbers to

explain?• use models to

explain?• give details?

6

6.RP The Escalator, Assessment

Variation

Task

Ty took the escalator to the second floor. The escalator is 12 meters long, and he rode

the escalator for 30 seconds. Which statements are true? Select all that apply.

a. He traveled 2 meters every 5 seconds.

b. Every 10 seconds he traveled 4 meters.

c. He traveled 2.5 meters per second.

d. He traveled 0.4 meters per second.

e. Every 25 seconds, he traveled 7 meters.

6.RP The Escalator, Assessment Variation Typeset May 4, 2016 at 22:54:39. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1

Illustrative Mathematics

7

8

9

10

11

12

13

©Curriculum Associates, LLC Copying is not permitted. 37Lesson 4 Solve Problems with Unit Rate

Name: Lesson 4

Solve Problems with Unit Rate

Solve the problems.

3 The price of 6 pretzels is $5 10 Simon and Sofia bought 8 pretzels and shared the cost equally How much did each person pay?

A $0 85 C $6 80

B $3 40 D $20 40

Jacob chose C as the correct answer How did he get that answer?

2 A carpenter uses 65 shelves to make 13 bookcases She uses the same number of shelves for each bookcase Are 32 shelves enough to build 6 more bookcases?

Show your work.

Solution:

1 The double number line shows the relationship between the number of minutes and the number of pages that a printer prints How many pages does the

printer print in 4 1 ·· 2 minutes?

200 40 60 80 100

543210

Pages

Minutes

A 80 pages B 85 pages C 90 pages D 100 pages

Where is 4 1 · 2 minuteslocated on the number line?

What is the unit rate?

One calculation is not enough to solve this problem.

14

©Curriculum Associates, LLC Copying is not permitted.38 Lesson 4 Solve Problems with Unit Rate

6 At Teen Tops, a package of 5 T-shirts costs $38. At Bargain City, a package of 4 T-shirts costs $34. Which statement is the most accurate?

A Bargain City is the better buy because it sells T-shirts at $8.50 per T-shirt.

B Teen Tops is the better buy because the package has more T-shirts.

C Bargain City is the better buy because $34 is less than $38.

D Teen Tops is the better buy because it sells T-shirts at $7.60 per T-shirt.

Solve.

4 Michael drove 350 miles in 7 hours at a constant speed. Tell whether each statement is True or False.

a. The unit rate for miles to hours is 50. u True u False

b. Michael drove 250 miles in 4 hours. u True u False

c. To find the number of miles Michael drove in 3 hours, multiply 3 by 50. u True u False

d. To find the number of hours it took Michael to drive 300 miles, divide 300 by 50. u True u False

5 Jorge says there are 198 inches in 5.5 yards. Is he correct? Explain your answer.

Show your work.

Solution:

Do you know the unit rate for inches per foot? Do you know the unit rate for feet per yard?

Finding unit prices will help you choose the correct answer.

How can you find a unit rate?

15

16

17

18

19

6.RP Perfect Purple Paint I

Task

Jessica gets her favorite shade of purple paint by mixing 2 cups of blue paint with 3

cups of red paint. How many cups of blue and red paint does Jessica need to make 20

cups of her favorite purple paint?

6.RP Perfect Purple Paint I Typeset May 4, 2016 at 23:34:49. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1


20

21

22

23

24

25

26

27

6.NS Jumping Flea

Task

A flea is jumping around on the number line.

a. If he starts at 1 and jumps 3 units to the right, then where is he on the number line?

How far away from zero is he?

b. If he starts at 1 and jumps 3 units to the left, then where is he on the number line?

How far away from zero is he?

c. If the flea starts at 0 and jumps 5 units away, where might he have landed?

d. If the flea jumps 2 units and lands at zero, where might he have started?

e. The absolute value of a number is the distance it is from zero. The absolute value of

the flea’s location is 4 and he is to the left of zero. Where is he on the number line?

6.NS Jumping Flea Typeset May 4, 2016 at 22:02:15. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

1


28

29

30

31

32

6.NS Integers on the Number

Line 1

Task

a. Find and label the numbers and on the number line.

b. For each of the following, state whether the inequality is true or false. Use the

number line diagram to help explain your answers.

i.

ii.

iii.

iv.

6.NS Integers on the Number Line 1 Typeset May 4, 2016 at 22:01:57. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

−3 −5

−3 > −5

−5 > −3

−5 < −3

−3 < −5

1


33

©Curriculum Associates, LLC Copying is not permitted. 185Lesson 17 Equivalent Expressions

Name: Lesson 17

Properties of Operations

Study the example showing how to use properties of operations to write equivalent expressions with variables. Then solve problems 1–9.

1 What does b represent in the expressions?

2 What does 2b 1 5b represent?

3 Does the expression 2b 1 5b have like terms? Explain

4 What is the common factor of each term in the expression 2b 1 5b?

5 Explain how to use the distributive property to create an expression that is equivalent to 2b 1 5b

Example

Sam bought 2 granola bars and Hayley bought 5 granola bars Each granola bar was the same price

Write an expression for the total price of the granola bars Then simplify the expression to create an equivalent expression Use the model to help you

bbHayley

bbSam

b bb

2b 1 5b 5 b(2 1 5) 5 7b

34

©Curriculum Associates, LLC Copying is not permitted.186 Lesson 17 Equivalent Expressions

Solve.

Use the situation below to solve problems 6–7.

Larry bought 12 containers of pasta salad for a school picnic Each container held the same number of ounces of salad Students finished the pasta salad in 8 of the containers

6 Let p equal the number of ounces of pasta salad in one container Write an expression with two terms to represent how many ounces of pasta salad are left

7 Simplify the expression you wrote in problem 6 to create an equivalent expression Use the distributive property

8 A soccer coach bought 16 medium T-shirts and 9 large T-shirts Each T-shirt was the same price Onaje and Paula tried to write equivalent expressions to represent the total price of the T-shirts The expressions they wrote are shown below

Onaje: 16t 1 9t 5 t(16 1 9) 5 25t Paula: 16t 1 9t 5 16 1 9 1 2t 5 25 1 2t

Whose expression is correct? Why is the other expression incorrect?

9 Adem writes 18y to simplify an expression with three like terms

a. What could the expression be?

b. Simplify the expression you wrote for part (a) to check your answer

35


Name: Lesson 17

Properties and Equivalent Expressions

Study the example showing how to use properties of operations to write equivalent expressions with variables. Then solve problems 1–9.

1 Explain how the model shows 4(5 1 x)

2 Simplify the expression in the example

3 What are the factors in the expression 4(5 1 x)?

4 Show how to use the distributive property to simplify 4(5 1 x)

5 Are the expressions (5 1 5 1 5 1 5) 1 (x 1 x 1 x 1 x) and 4(5 1 x) equivalent? If so, write another expression that is equivalent to both of them If not, explain why not

Example

Four students are buying tickets to a play The tickets cost $5 each plus a service fee The expression 4(5 1 x) represents the total cost Write an expression that is equivalent to 4(5 1 x)

You can use math tiles to model 4(5 1 x)

From the math tiles, you can see that the expression 4(5 1 x) 5 (5 1 5 1 5 1 5) 1 (x 1 x 1 x 1 x)

1 1 111

1 1 111

1 1 111

1 1 1

x

x

x

x11

36


Solve.

6 Use the distributive property to find two expressions that are equivalent to 7(3x 2 4)

7 A rectangular play area is 8 yards long The expression 56 1 8x represents the area of the play area in square yards What expression represents the width of the play area in yards? Draw a picture to model the problem

Show your work.

Solution:

8 Use the distributive property to write two expressions that are equivalent to 12 1 30x Describe the steps you follow to find the expressions

9 Are 9(4 2 x) and 36 2 9x equivalent expressions? Explain how you know

37


Name: Lesson 17

Determine Whether Expressions Are Equivalent

Study the example problem showing how to determine whether expressions are equivalent. Then solve problems 1–7.

1 Are the terms 2s and 3s2 like terms? Explain

2 Explain how the tiles show that 2s 1 3s2 is not equivalent to 5s

3 Use substitution to prove that 2s 1 3s2 is not equivalent to 5s

4 Use the distributive property to write an expression that is equivalent to 2s 1 3s2

Example

Is 2s 1 3s2 equivalent to 5s?

Use math tiles to model 2s 1 3s2 and 5s

s s

2s 5s3s2

s s s s ss2 s2 s2

The expression 2s 1 3s2 is not equivalent to 5s

38


Solve.

5 Look at the expressions s2 1 2s2 and 3s2

a. Draw math tiles to model s2 1 2s2 and 3s2 Does your model show that they are equivalent expressions? Explain

b. Use substitution to check your answer in part (a)

6 Use the terms 4, 12a, 6, 2a, and 24 to make equivalent expressions Use each term only once Use substitution to prove that the expressions are equivalent

Show your work.

Solution:

7 Bethany says that 3x 1 6 1 x and 3(x 1 2) are equivalent expressions She used substitution to support her answer Explain what Bethany did wrong

Let x 5 2

3x 1 6 1 x 5 3(2) 1 6 5 6 1 6 5 12

3(x 1 2) 5 3(2 1 2) 5 3(4) 5 12

12 5 12

39


Name: Lesson 17

Equivalent Expressions

Solve the problems.

2 The picture shows the dimensions of a vegetable garden and a flower garden

6 ft

7 ftVegetable garden

Flower garden x ft

Which expression represents the combined area of the gardens in square feet? Select all that apply

A 42 1 6x

B (6 • 7) 1 (6 • x)

C 13 1 6 1 x

D 6(7 1 x)

William chose C as a correct answer How did he get that answer?

1 Are 5n 1 9 1 n and 3(2n 1 9) equivalent expressions? Use substitution to check your answer

Show your work.

Solution:

What value will you substitute for to check your answer?

How do you find the area of a rectangle?

40


5 Which expression is equivalent to 6 1 7n 1 4 1 8n? Select all that apply

A 13n 1 12n

B 5(3n 1 2)

C 5(3n 1 10)

D 15n 1 10

Solve.

3 Look at the expression 1 ·· 2 (c 1 8) Tell whether each statement about the expression is True or False.

a. 1 ·· 2 (c 1 8) and c 1 8 ····· 2 are

equivalent expressions u True u False

b. 1 ·· 2 (c 1 8) and 1 ·· 2 c 1 4 are

equivalent expressions u True u False

c. The only terms in 1 ·· 2 (c 1 8)

are c and 8 u True u False

d. You can multiply c and 8

by 1 ·· 2 in 1 ·· 2 (c 1 8) to find

an equivalent expression u True u False

4 The expressions a(8x 1 7) and 4x 1 3 5 are equivalent What is the value of a?

Show your work.

Solution:

Look at the expressions. Do you have to distribute a to find its value?

How can you use the distributive property to find equivalent expressions?

How do you know that expressions are equivalent?

41

6.EE Equivalent Expressions

Task

Which of the following expressions are equivalent? Why? If an expression has no match,

write 2 equivalent expressions to match it.

a.

b.

c.

d.

e.

6.EE Equivalent Expressions Typeset May 4, 2016 at 22:18:17. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

2(x + 4)

8 + 2x

2x + 4

3(x + 4) − (4 + x)

x + 4

1


42

6.EE Make Use of Structure

Task

Think about what these equations mean, and find their solutions. Write a sentence

explaining how you know your solution is correct.

a.

b.

c.

d.

e.

f.

g.

h.

6.EE Make Use of Structure Typeset May 4, 2016 at 23:44:49. Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

x + 6 = 10

1000 − y = 400

100 = m + 99

0.99 = 1 − t

3a = 300

p = 81

2

10 = 0.1w

1 = 50b

1


43

44

45

46

47

48

49

50

Documents

Math€¦ · ©Curriculum Associates, LLC Copying is not permitted. Lesson 17 Equivalent Expressions 185 Name: Lesson 17 Properties of Operations Study the example showing how to