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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 1 Module 3

**Bridges in Mathematics Grade 5 Student Book Unit 1 Module 3 Session 1 Answer Key**

**Pricing Brad’s Baseballs**

Brad is taking inventory of the balls in the storeroom and deciding how to price them to sell. Solve each problem and write an expression or equation to represent it.

Question 1.

There is a box of 100 miscellaneous balls that Brad wants to sell.

a. What are one or two possible sets of dimensions for the box?

Answer:

10 × 10 × 1 or 5 × 10 × 2

Explanation:

Given that,

There is a box of 100 miscellaneous balls that Brad wants to sell.

one or two possible sets of dimensions for the box are 10 × 10 × 1 or 5 × 10 × 2

b. What is the total price for the box of balls if Brad charges $20 per ball?

Answer:

$2,000

Explanation:

Given that,

There is a box of 100 miscellaneous balls.

Cost of one ball is $20

100 × $20 = $2,000

c. What if he charges $19 per ball?

Answer:

$1,900

Explanation:

Given that,

There is a box of 100 miscellaneous balls.

if he charges $19 per ball,

100 × $19 = $1900

d. What if he charges $21 per ball?

Answer:

$2,100

Explanation:

Given that,

if he charges $21 per ball,

There is a box of 100 miscellaneous balls.

100 × $21 = $2,100

Question 2.

Brad noticed there are actually only 99 balls in the box.

a. What is the total price if Brad charges $20 per ball?

Answer:

$2,000

Explanation:

Given that,

There is a box of 99 balls.

Cost of one ball is $20.

99 × $20 = $1,980

b. What if he charges $19 per ball?

Answer:

$1,900

Explanation:

Given that,

There is a box of 99 balls.

if he charges $19 per ball,

99 × $19 = $1,881

c. What if he charges $21 per ball?

Answer:

$2,100

Explanation:

Given that,

There is a box of 99 miscellaneous balls.

if he charges $21 per ball?,

99 × $21 = $2,079

Question 3.

Brad keeps championship balls on a rack, as shown in the picture of Brad’s Baseball Storeroom.

a. How many balls are on the championship rack?

Answer:

36 balls.

Explanation:

b. Write an expression to represent how you could quickly find the number of balls on the championship rack without counting every one.

Answer:

(4 × 5) + (4 × 4) = 36 balls as shown in the Championship base ball rack.

Explanation:

With reference to the above figure,

an expression to represent how you could quickly find the number of balls on the championship rack without counting every one is (4 × 5) + (4 × 4)

20 + 16 = 36

c. What is the total price if Brad charges $25 per championship ball?

Answer:

$900

Explanation:

Given that,

There are 36 base balls in the championship rack.

Cost of one ball is $25.

36 × $25 = $900

Question 4.

Brad has a box of 72 bargain baseballs.

a. What is the total price for all the bargain baseballs if each ball is $10?

Answer:

$720

Explanation:

Given that,

Cost of one ball is $10.

then the total price for all the bargain baseballs is,

72 × $10 = $720

b. What is the total price for the bargain baseballs if each ball is $9?

Answer:

$648

Explanation:

Given that,

cost of each ball is $9,

then the total price for all the bargain baseballs

72 × $9 = $648

c. If Brad charges $792 for the whole box, how much is each ball?

Answer:

Each ball is $11

Explanation:

Given that,

If Brad charges $792 for the whole box.

Brad has a box of 72 bargain baseballs.

cost of each ball is $792 ÷ 72 = $11

d. If Brad charges $648 for the whole box, how much is that for each ball?

Answer:

Each ball is $9

Explanation:

Given that,

Brad has a box of 72 bargain baseballs.

If Brad charges $648 for the whole box,

cost of each ball is $648 ÷ 72 = $9

Question 5.

**CHALLENGE** There is a box of Blue Bombers that contains 72 baseballs. What are the dimensions of all of the possible boxes that contain 72 baseballs? Which one do you think is pictured in the storeroom?

Answer:

Base of 18 length by 2 width and 2 of height.

18 × 2 × 2

Explanation:

72÷ 4

18 × 2 × 2

base of 18 length by 2 width and 2 of height.

18 × 2 × 2

18 × 4 = 72

**Lily’s Lacrosse Team**

Lily is the manager of her school’s lacrosse team. Help Lily keep track of the team’s equipment. Show your work using numbers, sketches, or words.

Question 1.

Lily brought this box of lacrosse balls to practice on Monday.

a. How many lacrosse balls does the box hold if one lacrosse ball fits in a 1 unit × 1 unit × 1 unit space?

Answer:

728 balls in the box hold lacrosse ball fits in a 1 unit × 1 unit × 1 unit space.

Explanation:

Given that,

if one lacrosse ball fits in a 1 unit × 1 unit × 1 unit space.

13 × 8 × 7 = 728

728 balls in the box hold,

b. How much cardboard does it take to make the box?

Answer:

502 units.

Explanation:

Given that,

lacrosse ball fits in a 1 unit × 1 unit × 1 unit space.

(104 + 91 + 56) × 2 = 251 × 2 = 502 units.

Question 2.

Lily needs to buy 110 new lacrosse balls for the team. The balls come in sets of 22.

a. How many sets of lacrosse balls should Lily buy?

Answer:

5 sets.

Explanation:

Given that,

Lily needs to buy 110 new lacrosse balls for the team.

The balls come in sets of 22.

5 × 22 = 110 balls.

b. If one set of 22 lacrosse balls costs $20, how much will 110 lacrosse balls cost?

Answer:

$100

Explanation:

If one set of 22 lacrosse balls costs $20, how much will 110 lacrosse balls cost.

5 sets × $20 = $100

Question 3.

Is each equation true or false?

a. 98 × 34 = (100 × 34) – (1 × 34) ______

b. 46 × 28 = 23 × 56 ________

Answer:

False.

Explanation:

Given that,

a. 98 × 34 = (100 × 34) – (1 × 34) ______

98 × 34 = 3,332

(100 × 34) – (1 × 34) = (3400) – (34)

3,332 ≠ 3,366

b. 46 × 28 = 23 × 56

46 × 28 = 1,288

23 × 56 = 1,288

1,288 = 1,288

**Bridges in Mathematics Grade 5 Student Book Unit 1 Module 3 Session 2 Answer Key**

**Sam’s Sewing Supplies**

Question 1.

Sam needs more thread for a sewing project. One spool of thread costs 72 cents. Fill out the ratio table below to find out how much 12 spools of thread cost.

a. How much do 12 spools of thread cost?

Answer:

864 cents.

Explanation:

Given that,

One spool of thread costs 72 cents.

72 × 2 = 144

72 × 10 = 720

72 x 12 = 864

71 × 24 = 1728

b. How would you figure out how much 24 spools of thread cost?

Answer:

1,728 cents.

Explanation:

72 × 2 = 144

72 × 10 = 720

72 x 12 = 864

71 × 24 = 1728

c. Write an expression with parentheses to show how you would figure out how much 24 spools of thread cost.

Answer:

72 x 24 = 1,728 cents.

Explanation:

1 spool = 72 cents

24 spools = 72 x 24

72 x 24 = 1,728 cents

Question 2.

Sam saw a sign advertising thread on sale. The sign said, “Thread Sale! 12 spools for 840 cents, 15 spools for 900 cents, and 18 spools for 990 cents.” Which is the best deal? Why? Show your thinking.

Answer:

18 spools for 990 cents is the best deal.

Explanation:

12 spools for 840 cents, 15 spools for 900 cents, and 18 spools for 990 cents.

18 spools for 990 cents is the best deal as marked in the green box.

Question 3.

Write an expression for the calculation.

**ex** To find 18 times 35, I double 35 and halve 18:

(35 × 2) × \(\frac{1}{2}\) × (18) or (35 × 2) × (18 ÷ 2)

a. To find 38 times 14, I multiply 30 times 14 and 8 times 14 and add the two products together.

Answer:

532

Explanation:

Given that,

To find 38 times 14, I multiply 30 times 14 and 8 times 14 and add the two products together.

38 times 14:

(30 × 14) + (8 × 14)

= 420 + 112

= 532

**Bridges in Mathematics Grade 5 Student Book Unit 1 Module 3 Session 3 Answer Key**

**Charlie’s Chocolates**

Charlie is filling boxes with handmade chocolates. She starts with the following boxes.

Question 1.

Charlie fills a box with 5 layers. Each layer has 3 rows of 5 chocolates.

a. Write an expression that shows how many chocolates are in the box.

Answer:

3 × 5 × 5

Explanation:

Given that,

Charlie fills a box with 5 layers.

Each layer has 3 rows of 5 chocolates.

An expression that shows chocolates is 3 × 5 × 5

b. Write an equation shows how many chocolates are in the box.

Answer:

3 × 5 × 5 = 75 chocolates.

Explanation:

Given that,

Charlie fills a box with 5 layers.

Each layer has 3 rows of 5 chocolates.

3 × 5 × 5 = 75 chocolates.

c. Charlie’s brother dropped his baseball on the box and broke 6 chocolates, which had to be removed. Write an expression that shows how many chocolates are in the box now.

Answer:

X – 6

3 × 5 × 5 = 75 – 6

Explanation:

Given that,

A box with 5 layers.

Each layer has 3 rows of 5 chocolates = 75 chocolates.

Charlie’s brother dropped his baseball on the box and broke 6 chocolates.

d. Write an equation that shows how many chocolates are in the box now.

Answer:

69

Explanation:

Given that,

A box with 5 layers.

Each layer has 3 rows of 5 chocolates = 75 chocolates.

Charlie’s brother dropped his baseball on the box and broke 6 chocolates.

3 × 5 × 5 = 75 – 6 = 69 chocolates.

Question 2.

Charlie fills 2 more boxes with chocolates. These boxes have 7 layers of chocolates with 12 chocolates in each layer. Then, Charlie puts both boxes together in a larger box.

a. Write an expression that shows how many chocolates are in the larger box.

Answer:

12 × 7 × 2

Explanation:

Charlie fills 2 more boxes with chocolates.

7 layers of chocolates with 12 chocolates in each layer.

12 × 7 × 2

b. Write an equation that shows how many chocolates are in the larger box.

Answer:

12 × 7 × 2 = 168 chocolates.

Explanation:

Given that,

Charlie fills 2 more boxes with chocolates.

7 layers of chocolates with 12 chocolates in each layer.

12 × 7 × 2

84 × 2 = 168 chocolates.

**Bridges in Mathematics Grade 5 Student Book Unit 1 Module 3 Session 4 Answer Key**

**Work Place Instructions 1C Beat the Calculator**

Each pair of players needs:

- a set of Beat the Calculator Cards to share
- scratch paper and pencil (optional)
- 1 calculator to share

Some calculators will not work for this game. Check the calculator you want to use by entering 1 + 3 × 2 = . If the answer shown is 7, that calculator will work for this game. If the answer shown is 8, you’ll need to find a different calculator.

One player shuffles the cards and places the deck face-down. Players decide which of them will start with the calculator, and they decide on the number of rounds they will play.

The player with the calculator turns over a card so both players can see it.

The player with the calculator enters the problem exactly as it is written on the card. If the calculator doesn’t have parentheses, the player just enters all the other parts of the problem.

At the same time, the other player evaluates the expression using an efficient strategy, either mentally or with paper and pencil. The player who gets the correct answer first keeps the card.

Players compare answers and share strategies for evaluating the expression.

Players switch roles and draw again. (The player who didn’t have the calculator has it now.)

The game continues for an agreed-upon number of rounds. The player with the most cards at the end wins.

**Game Variations**

A. Players write their own problems on cards, mix them up, and then choose from those problems.

B. Instead of racing the calculator, students race each other to find the answer mentally, and check the answer to be sure it’s correct using a calculator if necessary.

C. Players play cooperatively by drawing a card and discussing their preferred mental strategy.

D. Players spread the cards face-down on the table. Each student chooses a different card at the same time and then races to see who gets the correct answer first.

**Expressions & Equations**

Question 1.

Write a numerical expression that includes grouping symbols for each:

a. To find 8 × 17, I double and halve.

Answer:

(8 × 2) × (17 ÷ 2)

Explanation:

Given, to find 8 × 17, I double and halve.

multiply and divide by 2

(8 × 17) × 2/2

(8 × 2) × (17 ÷ 2)

we double 8 and half 17

b. To find 36 × 19, I find 36 times 20 and remove 1 group of 36.

Answer:

(36 × 20) – 36

Explanation:

Given,

To find 36 × 19, I find 36 times 20 and remove 1 group of 36.

36 × 19

19 can be written as 20 – 1

36 × (20 – 1)

(36 × 20) – (36 × 1)

(36 × 20) – 36

c. To find the volume of a box that has a 19 by 22 base and 27 layers, I multiply the area of the base times the height.

Answer:

(19 × 22) × 27

Explanation:

Given that,

To find the volume of a box that has a 19 by 22 base and 27 layers,

I multiply the area of the base times the height.

area of base = 19 × 22

height = 27

Question 2.

Write an equation for each:

a. To find 7 times 32, I double and halve.

Answer:

(7 × 2) × (32 ÷ 2)

Explanation:

Given that,

To find 7 times 32, I double and halve.

multiply and divide by 2

(7 × 32) × 2/2

(7 × 2) × (32 ÷ 2)

we double 7 and half 32

b. To find 26 times 13, I multiply 20 times 13 and add it to 6 times 13.

Answer:

(13 × 20) + (13 x 6)

Explanation:

Given that,

To find 26 times 13, I multiply 20 times 13 and add it to 6 times 13.

13 × 26 we can write 26 as 20 +6

13 × (20 + 6)

(13 × 20) + (13 × 6)

c. To find 98 times 54, I multiply 100 times 54 and subtract 2 times 54.

Answer:

(54 × 100) – (54 × 2)

Explanation:

Given that,

To find 98 times 54, I multiply 100 times 54 and subtract 2 times 54.

54 × 98 we can write 98 as 100 – 2

54 × (100 – 2)

(54 × 100) – (54 × 2)

Question 3.

Show your work for each problem.

a. Xavier counted 38 balls in one layer of a box. The box has 17 layers. How many balls can the box hold?

Answer:

38 × 17

Explanation:

Given that,

Xavier 38 balls in one layer of a box.

The box has 17 layers.

so total number of balls are 38 × 17

b. A box holds 448 balls. Each layer has 28 balls. How many layers does the box have?

Answer:

448 ÷ 28

Explanation:

Given that,

A box holds 448 balls.

Each layer has 28 balls.

So, each layer has 448 ÷ 28