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Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 1 Module 3
Bridges in Mathematics Grade 5 Home Connections Unit 1 Module 3 Session 1 Answer Key
Piper’s Ping-Pong Team
Piper is the captain of her school’s ping-pong team. Help Piper keep track of the team’s equipment. Show your work using numbers, labeled sketches, or words.
Question 1.
Piper brought this box of ping-pong balls to practice on Tuesday.
a. How many ping-pong balls does the box hold if one ping-pong ball fits in a 1 unit × 1 unit × 1 unit space?
Answer:
l = 12
b = 9
h = 5
Volume of the rectangular prism = lbh
V = 12 × 9 × 5 = 540 cu. units
b. How much cardboard does it take to make the box?
Answer:
Surface area of the rectangular prism = 2(lb + bh + lh)
lh = 12 × 5 = 60
bh = 9 × 5 = 45
lb = 12 × 9 = 108
2(60 + 45 + 108) = 426 square units
Question 2.
Piper needs to buy 320 new ping-pong balls for the team. Ping-pong balls come in sets of 16.
a. How many sets of ping-pong balls should Piper buy?
Answer:
Given,
Piper needs to buy 320 new ping-pong balls for the team.
Ping-pong balls come in sets of 16.
320 ÷ 16 = 20 sets
b. If one set of 16 ping-pong balls costs $8, how much will 320 ping-pong balls cost?
Answer:
20 × 8 = $160
Thus 320 ping-pong balls cost $160.
Question 3.
Piper saw a large box of ping-pong balls with 48 balls in each layer.
a. If the box has 5 layers, how many balls can the box hold?
Answer:
Piper saw a large box of ping-pong balls with 48 balls in each layer.
The box has 5 layers.
48 × 5 = 240
(48 × 10) ÷ 2 = 480 ÷ 2 = 240 ping-pong balls.
b. If the box has 15 layers, how many balls can the box hold?
Answer:
480 + 240 = 720 ping-pong balls
Question 4.
Is the equation true or false?
a. 27 × 15 = (20 × 15) – (7 × 15) ________
Answer:
27 × 15 = (20 × 15) – (7 × 15)
27 × 15 = 405
(20 × 15) – (7 × 15) = 300 – 105 = 195
The equation is false.
b. 45 × 18 = (40 × 10) + (40 × 8) + (5 × 10) + (5 × 8) ________
Answer:
45 × 18 = (40 × 10) + (40 × 8) + (5 × 10) + (5 × 8)
45 × 18 = 810
(40 × 10) + (40 × 8) + (5 × 10) + (5 × 8) = 400 + 320 + 50 + 40 = 810
The equation is true.
c. 99 × 31 = (100 × 31) – (1 × 31) ______
Answer:
99 × 31 = (100 × 31) – (1 × 31)
99 × 31 = 3069
(100 × 31) – (1 × 31) = 3100 – 31 = 3069
The equation is true.
d. 64 × 15 = 32 × 30 ________
Answer:
64 × 15 = 32 × 30
64 × 15 = 960
32 × 30 = 960
The equation is true.
Question 5.
Write an expression for each item below.
ex To find 12 times 17, I multiply 10 times 17 and 2 times 17 and add the two products together. (10 × 17) + (2 × 17)
a. To find 79 times 24, I multiply 80 times 24 and take off one group of 24.
Answer:
79 times 24, I multiply 80 times 24 and take off one group of 24.
79 × 24 = 1896
(80 × 24) – 24 = 1920 – 24 = 1896
b. To find 12 times 13, I double 13 and halve 12 and then multiply.
Answer:
12 × 13 = 156
26 × 6 = 156
(13 × 2) × (12 ÷ 2) = 156
c. CHALLENGE To find 1,188 divided by 12, I think about 1,200 divided by 12— that’s 100 groups of 12. 1,188 has 1 fewer group of 12.
Answer:
(1188 ÷ 12) = 99
(1200 ÷ 12) – 12 = 100 – 12 = 88
Bridges in Mathematics Grade 5 Home Connections Unit 1 Module 3 Session 3 Answer Key
Student Strategies
Question 1.
Juliana loves multiplying by 8 because she can double-double-double.
a. Write an expression to show how Juliana would solve 8 × 23.
Answer:
Juliana would solve 8 × 23.
(2 × 2 × 2) × 23 = 184
b. What is 8 × 23?
Answer:
8 × 23 = 184
c. Write an expression that shows a different way to solve 8 × 23.
Answer:
(4 × 2) × 23 = 8 × 23 = 184
Question 2.
Kevin was asked to add 6 and 9 then multiply by 17. Which expression shows Kevin’s problem?
a. 6 + 9 × 17
Answer:
Kevin was asked to add 6 and 9 then multiply by 17.
6 + 9 × 17 = 159
b. (6 + 9) × 17
Answer:
(6 + 9) × 17
= 15 × 17
= 255
c. 6 + (9 × 17)
Answer:
6 + (9 × 17)
6 + 153 = 159
b. (6 + 9) × 17 is the correct expression.
ex Elizabeth needed to multiply 7 and 8 and then subtract 13. Write an expression to show the problem. Then, solve the problem and write an equation.
a. Expression
(7 × 8) – 13
Answer:
Elizabeth needed to multiply 7 and 8 and then subtract 13.
(7 × 8) – 13
b. Equation
(7 × 8) – 13 = 43
Answer:
56 – 13 = 43
Question 3.
Kaden divided 96 by 12 and then multiplied by 6. Write an expression to show the problem. Then, solve the problem and write an equation.
a. Expression:
Answer:
Kaden divided 96 by 12 and then multiplied by 6.
(96 ÷ 12) × 6
b. Equation:
Answer:
(96 ÷ 12) × 6 = 8 × 6 = 48
Evaluate the following expressions.
Question 4.
81 – (9 × 7)
Answer:
81 – (9 × 7)
81 – 63 = 18
Question 5.
(54 – 6) × 8
Answer:
(54 – 6) × 8
48 × 8 = 384
How many 1 × 1 × 1 cubes are in the following rectangular prisms? For each problem, write an expression and evaluate it to find the number of cubes.
Question 6.
Expression: __________ Number of cubes: _____
Answer:
l = 5
w = 4
h = 8
Volume = lbh
V = 5 × 4 × 8
V = 160 cu. units
Thus there are 160 cubes.
Question 7.
Expression: __________ Number of cubes: _____
Answer:
l = 7
b = 6
h = 3
V = 7 × 6 × 3
V = 126 cu. units
Thus there are 126 cubes.
Question 8.
CHALLENGE Chloe is sorting items at a thrift store. She finds a box of tiny blocks that has 1,344 written on the outside. She can see that each layer in the box has 64 blocks.
a. How many layers of blocks are there?
Answer:
Given,
Chloe is sorting items at a thrift store. She finds a box of tiny blocks that has 1,344 written on the outside.
She can see that each layer in the box has 64 blocks.
1344/64 = 21
Thus there are 21 layers of blocks.
b. What is another way Chloe could arrange the 1,344 blocks to fit in a different box?
Answer:
64 × (20 + 1) = 64 × 20 + 64 × 1 = 1344.