Week 1: Ratios and Rates (Math Book, Chapter 1) · PDF fileSummer Math Assignment End of Grade 6 1 Week 1: Ratios and Rates (Math Book, Chapter 1) For questions 1 and 2, write each

Summer Math Assignment End of Grade 6

1

Week 1: Ratios and Rates (Math Book, Chapter 1)

For questions 1 and 2, write each ratio as a fraction in simplest form. Then explain its meaning.

1.

cats to dogs

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

2. There are 16 girls and 20 boys in the school band. What is the ratio of girls to boys?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

For questions 3 and 4, write each rate as a unit rate.

3. $8 for 2 pounds of rice = __________________________________________________________

4. 240 miles in 6 hours = ____________________________________________________________

5. Chin bought 12 pounds of apples for $6. Use the ratio table to find the cost of buying 3 pounds

of apples.

Pounds of Apples 12 3 Price of Apples $6 ______


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6. The table shows the amount of money that Dawson earned for watching his neighbor’s cat.

Graph the ordered pairs (number of days, amount earned). Then describe the pattern in the

graph.

Amount Earned ($) 0 7 14 21 Number of Days 0 1 2 3

7. Markus received dollar bills from his grandfather for one week. On the first day he received $1;

on the second day he received $2, on the third day he received $4, and on the fourth day he

received $8. If this continues, how much money will Markus have by the end of the week?

Show your work in the box below.

1 2 3 4 5 6

Number of Days

42

35

28

21

14

7

Am

ou

nt

Earn

ed (

$)


3

8. The table shows the animals at a petting zoo. What is the ratio of goats to the total number of

animals in simplest form?

Animals at a Petting Zoo Chickens 2 Deer 4 Donkey 3 Goats 6

______________________________________________________________________________

9. A manatee surfaced for air 3 times in 60 seconds. How many seconds went by before the

manatee surfaced the first time if it held its breath for the same rate? Show or explain how you

know.

10. Rashida bought 3 tickets to a concert for $75. At this rate, how much would 5 tickets cost. Use

the ratio table below to scale back and scale up.

Number of Tickets 3 5 Money Spent ($) 75 ______


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Week 2: Computing with Decimals (Math Book, Chapter 3)

1. 25.4 ● 5.1

2. 5.87 ● 0.15


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3. The dance committee has 1,036 flowers. The want to divide them evenly among 28

centerpieces. How many flowers will be in each centerpiece? Show your work in the space

below.

4. Bananas cost $0.54 per pound and grapes cost $1.28 per pound. Leanne bought 2.6 pounds

of bananas and 3.1 pounds of grapes. How much did Leanne pay for the bananas and

grapes she bought? Show your work in the space below.


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5. A cat can jump five times as high as it is tall. How high can a cat jump if it 16.4 centimeters

tall?

6. 32.79 ÷ 0.3

7. 516.15 ÷ 2.5


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8. On Saturday, Hattie biked 3.2 hours at a speed of 12.5 miles per hour. On Sunday, she biked

2.5 hours at a speed of 14.3 miles per hour. How much farther did she bike on Saturday

than on Sunday? Show how you know.

9. There are 632 students going on a school-wide field trip. Each bus can carry 48 students.

How many buses should the school reserve for students? Show your work. Then explain

your reasoning.

___________________________________________________________________________

___________________________________________________________________________

10. A ball rolls 5.24 feet each second. How many feet will the ball roll in 1.8 seconds?


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Week 3: Multiplying and Dividing Fractions (Math Book, Chapter 4)

1.

● 28

2.

● 1

3. What is the area of a room that is 3

yards long by 3

yards wide?

(Reminder: A = l ● w)


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4. ÷

5. 4 ÷ 1

6. A box contains 1

pounds of pasta. How many ounces of pasta are

in the box? (Reminder: 16 ounces = 1 pound)


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7. Mia is making costumes for a play. Each costume needs 3

yards of

fabric. If Mia is making 6 costumes, how much fabric does she need?

8. Lyndsay has 3 gallons of paint. She plans on using 1

gallons in

each room she paints. How many rooms will she be able to paint?

Show or explain how you know.

9. Phillip rides his scooter to school in 6 minutes. It takes Joey 4

times as long to get to school. How long does it take Joey to get

school?


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Week 4: Integers and the Coordinate Plane (Math Book, Chapter 5)

For questions 1 and 2, write an integer for each situation.

1. Jake lost 14 pounds. ________________________

2. The temperature rose 7 degrees this morning. ________________________

3. Graph/plot the following set of integers on a number line: {2, -4, 5, -3, 0}

4. |-46| __________________

5. |-6| - |2 + 3| __________________

6. Order the following set of integers from least to greatest: {16, -24, 9, -30, 25}

___________________________________________________________________

7. Graph/plot the following set of rational numbers on a number line: { -

,

, 1

, -1

}


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y

O

x

8. Use the grid below to answer the following questions:

a. Graph Y(1.5, -2) on the coordinate grid to the right.

b. Graph H(-4,-2.5) on the coordinate grid to the right.

c. Graph P(-4.5, -1.5) on the coordinate grid to the right. Then graph its reflection across the y-axis.

d. Graph Q(0,-2.5) on the coordinate grid to the right. Then graph its reflection across the x-axis.

9. Graph and label each point on the coordinate plane.

a. L(–2, 0) b. M(5, 2)

c. N(–4, –3) d. P(1, –1)

10. In which quadrant would each of the following order pairs be found?

a. (-4, 3) _________________________________________

b. (8, 7) _________________________________________

c. (-6, -10) _________________________________________

d. (2.5, -1) _________________________________________


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Week 5: Expressions (Math Book, Chapter 6)

1. Write an expression with exponents for the following:

9 ● 9 ● 9 ● 9 = __________

For questions 2 and 3, evaluate the expression using the order of operations.

2. 24 – 6 ÷ 2 ● 2 +7 3. 15 - 2 + (8 ÷ 2) – (9 ÷ 3)2

For questions 4 and 5, evaluate each expression if m = 3 and n = 7.

4. 4m – 5 5. n2 – 2m

For questions 5-6, write each phrase as an algebraic expression.

6. the product four and a number f 7. the quotient of a number w and five

____________________________________ ___________________________________


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8. Molly is 7 inches shorter than her older brother, Mike.

a) Write an algebraic expression that represents Molly’s age. ____________________

b) If Mike is 49 inches tall, how tall is Molly? __________________________________

9. Use the Distributive Property to write an equivalent expression for the following:

6(x +4) = _________________________________

10. Use the Distributive Property by finding a common factor to write the factored form of

the following:

20x + 35y = ________________________________


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Week 6: Equations & Inequalities (Math Book, Chapters 7 & 8)

For questions 1 and 2, identify the solution of each equation or inequality from the list

given. Show your work by substituting the values in place of the variable.

1. 23 = 30 – g; 6, 7, 8 2. 8p ≥ 40; 4, 5, 6

3. In a game, Halley has 35 cards. This is 12 more cards than Felix. Write and solve an

addition equation to find the number of cards Felix has.

4. Families can purchase a children’s ticket to the movies at a discounted price. Children

who are 10 years old or younger qualify for a children’s ticket. Write an inequality that

represents the age, a, that children must be to qualify for a children’s ticket.

Inequality: _______________________________________________________________


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5. At a local greenhouse, plants are half off their original price. The sale price of a potted

plant is $5.50. Write and solve an equation that represents that original price of the

potted plant.

6. Solve. Show your work.

42 = 6f

7. Solve. Show your work.

8. An exterminator charges $80 to visit a home and $35 to spray each room. If the total

bill was $395, how many rooms were sprayed? Write an algebraic equation that

represents this situation. Then solve it.

9. Tina noticed that she had taken notes on 25 pages of her notebook. Ninety-five pages

were still blank. Write and solve a subtraction equation to find the total number of

pages in the notebook.


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Week 7: Functions (Math Book, Chapter 8)

Complete the function tables below.

1. 2.

Use words and symbols to describe the value of each term as a function of its position. Then find the

value of the tenth term in the sequence.

3. 4.

Words: _________________________________ Words: _________________________________

Symbols: _______________________________ Symbols: _______________________________

10th term: ______________________________ 10th term: ______________________________

Write an equation to represent each function in the tables below.

5. 6.

Input (x) 2x – 1 Output (y)

7

5

4

Input (x) x + 9 Output (y)

12

15

17

Position 1 2 3 4 n

Value of Term 6 12 18 24

Position 1 2 3 4 n

Value of Term 10 11 12 13

Input, x 0 1 2 3 4

Output, y 7 8 9 10 11

Input, x 2 4 6 8 10

Output, y 5 9 13 17 21


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7. The school library is buying new books that cost $9 each. a. Write an equation to find t, the total cost in dollars for any number of books b. b. Make a function table to show the relationship between the number of books b and the total cost t. c. Graph the ordered pairs from your table. In a sentence, analyze the graph.

Books (b) Total Cost (t)


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Week 8: Area, Surface Area, & Volume (Math Book, Chapters 9 & 10)

Find the area of the figures below.

1. 2.

3. 4.

Find the volume of the figures below.

5. 6.

1.5 ft

.5 ft

3 ft

6 in

4 in

3 in


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Find the surface area of the figures below.

7.

.

8. Find the surface area of a rectangular

prism that is 3 feet by 4 feet by 6 feet.

9.

Documents

Week 1: Ratios and Rates (Math Book, Chapter 1) · PDF fileSummer Math Assignment End of Grade 6 1 Week 1: Ratios and Rates (Math Book, Chapter 1) For questions 1 and 2, write each