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## Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 1 Module 4

**Bridges in Mathematics Grade 5 Home Connections Unit 1 Module 4 Session 1 Answer Key**

**More Expressions & Equations**

Question 1.

Write a numerical expression that includes grouping symbols.

a. To find 73 × 9, I find 73 times 10 and remove 1 group of 73.

Answer:

73 × 9 = 657

(73 × 10) – (1 × 73) = 730 – 73 = 657

b. To find the volume of a box that has an 18 by 25 base and 12 layers, I multiply the area of the base times the height.

Answer:

Volume = lbh

V = 18 × 25 × 12

V = 5400 cu. units

Question 2.

Write and solve an equation to represent each situation.

a. To find 23 times 8, I double and halve.

Answer:

23 × 8 = 184

23 × 16 = 368

23 × (16 ÷ 2) = 23 × 8 = 184

b. To find 24 times 17, I multiply 20 times 17 and add it to 4 times 17.

Answer:

24 × 17 = 408

I multiply 20 times 17 and add it to 4 times 17

20 × 17 = 340

4 × 17 = 68

340 + 68 = 408

Question 3.

True or False?

a. 12 × 17 = 6 × 34 ______

Answer:

12 × 17 = 204

34 × 6 = 204

204 = 204

The statement is true.

b. 99 × 75 = (100 × 75) – 1 ______

Answer:

99 × 75 = (100 × 75) – 1

99 × 75 = 7425

100 × 75 = 7500

7500 – 1 = 7499

7425 ≠ 7499

The statement is false.

c. To find the volume of a box, I can multiply the length times the width. _______

Answer:

The equation for volume is V = length x width x height, so simply multiply all three sides together to get your volume.

Question 4.

Evaluate each expression (solve each problem).

a. (7 × 8) × 9

Answer:

(7 × 8) × 9

56 × 9 = 504

b. 2 (5 × 5) + 3 (4 × 4)

Answer:

2 (5 × 5) + 3 (4 × 4)

2(25) + 3(16)

= 50 + 48

= 98

c. (100 × 67) – (1 × 67)

Answer:

(100 × 67) – (1 × 67)

6700 – 67 = 6633

d. (98 × 47) + (2 × 47)

Answer:

(98 × 47) + (2 × 47)

= 4606 + 94

= 4700

Question 5.

How many 1 × 1 × 1 cubes are in the following rectangular prisms? Write and solve equations to show.

a. Equation for number of cubes:

Answer:

l = 7

b = 3

h = 4

V = lbh

V = 7 × 3 × 4

b. Equation for number of cubes:

Answer:

V = 4 × 5 × 6

V = 20 × 6

V = 120 cu. units

Question 6.

A box holds 125 balls. Each layer has 25 balls. How many layers does the box have? Show your work.

Answer:

Given,

A box holds 125 balls. Each layer has 25 balls.

125/25 = 5 layers

Thus the box has 5 layers.

Question 7.

**CHALLENGE** A box holds 425 balls. Each layer has 17 balls. How many layers does the box have? Show your work.

Answer:

Given,

A box holds 425 balls. Each layer has 17 balls.

425/17 = 25 layers

Thus the box has 25 layers.

**Bridges in Mathematics Grade 5 Home Connections Unit 1 Module 4 Session 3 Answer Key**

**Expressions, Equations & Stories**

Question 1.

Write an expression with parentheses for each statement below.

a. I multiplied 7 times 8 and then I added 9. ___________

Answer:

I multiplied 7 times 8 and then I added 9.

(7 × 8) + 9

56 + 9 = 65

b. I multiplied 3 times 12 and then multiplied the product of 3 times 12 by 5.

Answer:

I multiplied 3 times 12 and then multiplied the product of 3 times 12 by 5.

3 × 12 = 36

36 × 5 = 180

c. I subtracted 14 from 30 and then I multiplied the difference by 6.

Answer:

I subtracted 14 from 30 and then I multiplied the difference by 6.

Question 2.

Emir loves multiplying by 99 because he can use an over strategy.

a. Write an expression to show how Emir would solve 99 × 76.

Answer:

(100 – 1) × 76

(100 × 76) – (1 × 76)

= 7600 – 76

= 7524

b. What is 99 × 76?

Answer:

99

×76

7524

c. Show a different way to solve 99 × 76.

Answer:

Another way to solve 99 × 76 is

99(76) = 7524

99 • 76 = 7524

Question 3.

Erica likes to multiply by 25 because she can use the double-half strategy.

a. Write an expression to show how Erica would solve 25 × 28.

Answer:

25 × 28 = 700

50 × (28 ÷ 2) = 50 × 14 = 700

b. What is 25 × 28? _________

Answer:

28

×25

700

c. Show a different way to solve 25 × 28.

Answer:

(20 × 28) + (5 × 28)

= 560 + 140

= 700

Question 4.

Evaluate each expression.

a. (25 × 10) × 10 =

Answer:

(25 × 10) × 10

250 × 10 = 2500

b. 4 (4 × 4) + 3 (3 × 3) =

Answer:

4 (4 × 4) + 3 (3 × 3)

4(16) + 3(9)

64 + 27

= 91

c. (100 × 89) – (1 × 89) =

Answer:

(100 × 89) – (1 × 89)

8900 – 89

= 8811

Question 5.

For each problem below:

- Use numbers, words, or labeled sketches to solve the problem. Show all your work.
- Figure out the best way to handle the remainder, if there is one, for that situation.
- Write an equation to show each problem and the answer, labeled with the correct units.

a. Thirty-eight fifth graders at Vernon Elementary are going on the field trip to the art museum. They are riding in vans that each hold 9 students. How many vans will they need for everyone to get to the art museum?

Equation _______________

Answer:

Given,

Thirty-eight fifth graders at Vernon Elementary are going on the field trip to the art museum. They are riding in vans that each hold 9 students.

38/9 = 4.2 vans

Thus the number of vans they will need for everyone to get to the art museum is 5.

b. When Alex and Marcus went to the store with their mom, she said they could split the change evenly. The total cost of their groceries was $57.32. She gave the cashier three $20 bills. How much money did Alex and Marcus each get?

Equation ___________

Answer:

Given,

When Alex and Marcus went to the store with their mom, she said they could split the change evenly.

The total cost of their groceries was $57.32. She gave the cashier three $20 bills.

3(20) – 57.32

60 – 57.32

= $2.68

c. **CHALLENGE** On Friday afternoon, Maya realizes that she has put off her reading for too long and that she needs to finish her book by Monday. The book is 265 pages long. She is on page 127. How many pages will she need to read each night to finish the book before school on Monday morning?

Equation _________________

Answer:

Given,

On Friday afternoon, Maya realizes that she has put off her reading for too long and that she needs to finish her book by Monday.

The book is 265 pages long. She is on page 127.

265 – 127 = 138

138/3 = 46 pages per day

**Bridges in Mathematics Grade 5 Home Connections Unit 1 Module 4 Session 5 Answer Key**

**Agree or Disagree?**

Choose 5 of the 6 problems on this page and the next. For each one you choose, write whether you agree or disagree. Then explain your thinking using numbers, words, and/or labeled sketches.

**Do you agree or disagree? Explain your thinking.**

Question 1.

The 5th graders set up 20 rows of chairs with 25 chairs in each row for the assembly. Mrs. Lord asked if they’d set up enough chairs for all 552 students. Kamil said he could skip-count to find out how many chairs there were in all, and then they’d know if they had enough.

Answer:

Given,

The 5th graders set up 20 rows of chairs with 25 chairs in each row for the assembly.

20 × 25 = 500

Mrs. Lord asked if they’d set up enough chairs for all 552 students.

552 – 500 = 52

Kamil is correct.

Question 2.

The track at the high school is 400 meters. After she ran 6 times around the track, Isuko said she’d gone more than 2 kilometers.

Answer:

Given,

The track at the high school is 400 meters.

After she ran 6 times around the track, Isuko said she’d gone more than 2 kilometers.

400 × 6 = 2400 m

2.4 km > 2 km

She had gone more than 2 kilometers.

Question 3.

Mr. Madison needs 175 granola bars for the 5th grade field trip. The bars come in boxes of 10. He’ll need to buy 17 boxes to have enough.

Answer:

Given,

Mr. Madison needs 175 granola bars for the 5th grade field trip.

The bars come in boxes of 10. He’ll need to buy 17 boxes to have enough.

17 × 10 = 170

170 <175

I disagree. He would only have 170 bars from 17 boxes, so he had 5 bars short.

Question 4.

To multiply 247 × 4, you can do these smaller problems and add them together:

200 × 4

4 × 4

7 × 4

Answer:

247 × 4 = 988

(200 × 4) + (40 × 4) + (7 × 4) = 800 + 160 + 28 = 988

Question 5.

There are 46 kids in the After-School Club. Today they’re going to the pool at the Community Center. If each minivan can take 6 kids, they’ll need 8 minivans for all the kids.

Answer:

Given,

There are 46 kids in the After-School Club. Today they’re going to the pool at the Community Center. If each minivan can take 6 kids, they’ll need 8 minivans for all the kids.

6 × 8 = 48

48 > 46

You have to have enough buses for each person, and none of them are walking and so you will need 8 minivans.

Question 6.

**CHALLENGE** Brad wants to package his baseballs in sets of 100. Bethany says the box that will take the least amount of cardboard for 100 baseballs is one with a base of 2 × 5 and a height of 10.

Answer:

Brad wants to package his baseballs in sets of 100.

Bethany says the box that will take the least amount of cardboard for 100 baseballs is one with a base of 2 × 5 and a height of 10.

2 × 5 × 10 box will have area.

2(2 × 5 + 10 + 2 × 5) = 2(10 + 100 + 10) = 160 sq. units

4 × 5 × 5

2(4 × 5 + 5 × (4 + 5)) = 130 sq. units

Since baseballs can be close-packed, the box may be able to be made smaller than the above-suggested dimensions might indicate.