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Bridges in Mathematics Grade 5 Student Book Answer Key Unit 4 Module 2
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 2 Session 1 Answer Key
Work Place Instructions 4B Multiplication Battle
Each pair of players needs:
- 1 4B Multiplication Battle Record Sheet
- 1 deck of Number Cards (remove the 0s, 1s, and wild cards)
- 1 more/less die
- pencils
1. Players work together to remove the 0s, 1s, and wild cards from the deck and set them aside. Then they shuffle the remaining cards and place them in a stack, face-down, between them.
2. Each player draws a card from the stack. The player with the higher number goes first.
3. Players should place the cards they just drew at the bottom of the stack for use during the game.
4. Player 1 rolls the more/less die to see whether more or less is the goal, and then circles the word on the record sheet.
5. Player 1 draws three cards from the top of the stack, records the numbers on the record sheet, and thinks about the best order for multiplying these three numbers.
It may help to move the cards around.
6. Player 1 writes an expression to show the order to multiply the numbers.
The two numbers that will be multiplied first are written in parentheses, with the third number outside the parentheses.
7. Player 1 multiplies the first two numbers inside the parentheses and write the product, along with the third number, on the next line.
8. Player 1 finds and records the product, using the work space to do any figuring if necessary.
If Player 2 does not agree with the answer, Player 1 must record his thinking in the work space to prove that he is correct (or make corrections jibe is not).
Pablo I can just do this one ¡n my head. That’s why I multiplied the 6 × 4 first, because any number times 10 is really easy.
9. The Last Draw Option: If a player is not happy with his total, he can choose to d raw one more card from the top of the stack and then multiply or divide the total by that number.
He can do the work in his head if he likes, but if Player 2 does not agree with the answer, Player 1 must record his thinking in the work space to prove that he is correct (or make corrections if he is not).
10. Player 2 takes a turn drawing three cards, finding the product, and exercising the Last Draw Option if she chooses to do so.
11. Players compare their totals and circle the winner.
The lower total wins if players rolled “less” at the start of the round. The higher total wins if they rolled “more” at the start of the round.
12. Players begin a new round. Best out of three rounds wins the game.
Game Variations
A. Start with a whole deck. Remove the 0s, 7s, 8s, 9s, and wild cards so you’re playing the game with 1s, 2s, 3s, 4s, 5s, 6s, and 10s.
B. Eliminate the Last Draw Option for fewer steps and less computation.
C. Leave the deck set up as instructed in the first step on the previous page, but put the wild cards back in and shuffle the deck thoroughly. If a player draws a wild card, she can assign it any value between 11 and 20, even if she draws it for the Last Draw Option. She must write the assigned value on one of the lines, just as if she had drawn that number from the stack of cards.
Answer:
Find the Product
Question 1.
Complete the box challenges.
a.
Answer:
8 × 0.25 = 2
8 + 0.25 = 8.25
So, the missing number in the box is 8.25
b.
Answer:
6/0.25 = 24
0.25 × 24 = 6
0.25 + 24 = 24.25
So, the missing number in the box is 24.25
c.
Answer:
1.50/0.75 = 2
0.75 + 2 = 2.75
So, the missing number in the box is 2.75
d.
Answer:
3/0.75 = 4
4 + 0.75 = 4.75
So, the missing number in the box is 4.75
Question 2.
Find the product.
a. \(\frac{1}{5}\) of 20 = _______________
Answer:
\(\frac{1}{5}\) of 20
\(\frac{1}{5}\) × 20 = 4
b. \(\frac{1}{3}\) of 18 = _______________
Answer:
\(\frac{1}{3}\) of 18
\(\frac{1}{3}\) × 18 = 6
c. \(\frac{4}{5}\) of 20 = _______________
Answer:
\(\frac{4}{5}\) of 20
\(\frac{4}{5}\) × 20
= 4 × 4
= 16
d. \(\frac{2}{3}\) of 18 = _______________
Answer:
\(\frac{2}{3}\) of 18
\(\frac{2}{3}\) × 18
= 2 × 6
= 12
e. \(\frac{1}{6}\) of 30 = _______________
Answer:
\(\frac{1}{6}\) of 30
\(\frac{1}{6}\) × 30
= 1 × 5
= 5
f. \(\frac{1}{15}\) of 60 = _______________
Answer:
\(\frac{1}{15}\) of 60
\(\frac{1}{15}\) × 60
= 1 × 4
= 4
g. \(\frac{5}{6}\) of 30 = _______________
Answer:
\(\frac{5}{6}\) of 30
\(\frac{5}{6}\) × 30
= 5 × 5
= 25
h. \(\frac{2}{15}\) of 60 = _______________
Answer:
\(\frac{2}{15}\) of 60
\(\frac{2}{15}\) × 60
= 2 × 4
= 8
Question 3.
Brooke and Kaden each sold 15 boxes of cookies for $2.25 per box. How much money did they collect together? Show your work.
Answer:
Given,
Brooke and Kaden each sold 15 boxes of cookies for $2.25 per box.
15 × $2.25 = $33.75
Thus they collect $33.75 in all.
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 2 Session 2 Answer Key
Callie’s Soccer Cleats
Callie is still trying to make money to buy some soccer cleats. She decided to make some charts to help her choose what to do.
Question 1.
She could make beaded bracelets. They cost $2.25 each to make. Fill in the table to show how much it would cost to make different numbers of beaded bracelets.
Answer:
Given,
She could make beaded bracelets.
They cost $2.25 each to make.
2.25 × 1 = $2.25
2.25 × 2 = $4.50
2.25 × 4 = $9
2.25 × 5 = $11.25
2.25 × 8 = $18
2.25 × 9 = $20.25
2.25 × 10 = $22.5
2.25 × 19 = $42.75
2.25 × 20 = $45
Question 2.
Callie can sell the beaded bracelets for $3.50 each. Fill in the table to show how much money Callie could make by selling different numbers of beaded bracelets.
Answer:
Given,
Callie can sell the beaded bracelets for $3.50 each.
3.50 × 1 = $3.50
3.50 × 2 = $7
3.50 × 4 = $14
3.50 × 5 = $17.5
3.50 × 8 = $28
3.50 × 9 = $31.5
3.50 × 10 = $35
3.50 × 19 = $66.5
3.50 × 20 = $70
Question 3.
She could also make woven bracelets. They cost $1.20 each to make. Fill in the table to show how much it would cost to make different numbers of woven bracelets.
Answer:
Given,
She could also make woven bracelets.
They cost $1.20 each to make.
$1.20 × 1 = $1.20
$1.20 × 5 = $6
$1.20 × 9 = $10.8
$1.20 × 10 = $12
$1.20 × 15 = $18
$1.20 × 49 = $58.8
$1.20 × 50 = $60
$1.20 × 99 = $118.8
$1.20 × 100 = $120
Question 4.
The woven bracelets sell for $1.50. Fill in the table to show how much money Callie could make by selling different numbers of woven bracelets.
Answer:
Given,
The woven bracelets sell for $1.50.
$1.50 × 1 = $1.50
$1.50 × 5 = $7.5
$1.50 × 9 = $13.5
$1.50 × 10 = $15
$1.50 × 15 = $22.5
$1.50 × 49 = $73.5
$1.50 × 50 = $75
$1.50 × 99 = $148.5
$1.50 × 100 = $150
Question 5.
Which kind of bracelet do you think Callie should make? Why?
Answer: Callie Should make woven bracelet.
Multiplication Battle
When you play Multiplication Battle, you get to draw 3 cards and multiply the numbers on those cards in any order you want. Part of the idea is to put them in an order that makes it easy to get the answer. For example, if you got the cards 7, 8, and 5, you might decide to multiply them in this order: (7 × 8) × 5 because 7 × 8 is 56, and you can multiply 56 by 10 and then cut the product in half because 5 is half of 10.
Question 1.
Dana and Tyler were playing Multiplication Battle. Dana went first, and got the cards 5, 8, and 6.
a. Dana said she solved the problem by finding the product of 8 and 5, and then multiplying that by 6. Write an expression to show her thinking.
Answer:
Given,
Dana and Tyler were playing Multiplication Battle. Dana went first, and got the cards 5, 8, and 6.
(5 × 8) × 6
= 40 × 6
= 240
b. What is the product of 6, 8, and 5? Show your work. (You can put the numbers in a different order if you want; you don’t have to use Dana’s idea.)
Answer:
(6 × 8) × 5
= 48 × 5
= 240
Question 2.
Tyler went next and got 4, 7, and 5.
a. Tyler said he solved the problem by finding the product of 7 and 5, and then doubling it twice. Write an expression to show his thinking.
Answer:
Given,
Tyler went next and got 4, 7, and 5.
(7 × 5) × 4
= 35 × 4
= 140
b. What is the product of 4, 7, and 5? (You can put the numbers in a different order if you want; you don’t have to use Tyler’s idea.)
Answer:
(4 × 7) × 5
= 28 × 5
= 140
Question 3.
If you were playing Multiplication Battle and got the cards 6, 7, and 9, what order would you use to make the problem easy to solve? Write an expression to show, and then solve the problem.
Answer:
(6 × 7) × 9
= 42 × 9
= 378
Question 4.
Round 13,674.947 to the nearest:
Answer:
13,674.947 to the nearest ten is 13,675
13,674.947 to the nearest one 13,670.
13,674.947 to the nearest tenth is 13,674.95
13,674.947 to the nearest hundredth is 13,674. 9
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 2 Session 3 Answer Key
More Planning for Callie
As Callie was planning how to raise money, she wondered about making other numbers of bracelets and cake pops.
Question 1.
Beaded bracelets cost $2.25 each to make. How much would it cost to make 61 beaded bracelets? Use the ratio table below to record your strategy.
Note You don’t need to use all the boxes on this table or any of the others below; just use what you need and leave the rest.
It would cost ______________ to make 61 beaded bracelets.
Answer:
Given,
Beaded bracelets cost $2.25 each to make.
$2.25 × 1 = $2.25
$2.25 × 2 = $4.5
$2.25 × 5 = $11.25
$2.25 × 10 = $22.5
$2.25 × 15 = $33.75
$2.25 × 20 = $45
$2.25 × 50 = $112.5
$2.25 × 60 = $135
$2.25 × 61 = $137.25
It would cost $137.25 to make 61 beaded bracelets.
Question 2.
Beaded bracelets sell for $3.50 each. How much money would Callie bring in if she sold 42 beaded bracelets? Use the ratio table below to record your strategy.
42 beaded bracelets would sell for a total of _____________.
Answer:
Given,
Beaded bracelets sell for $3.50 each.
$3.50 × 1 = $3.50
$3.50 × 2 = $7
$3.50 × 5 = $17.5
$3.50 × 10 = $35
$3.50 × 20 = $70
$3.50 × 30 = $105
$3.50 × 40 = $140
$3.50 × 41 = $143.5
$3.50 × 42 = $147
42 beaded bracelets would sell for a total of $147.
Question 3.
Woven bracelets cost $1.20 each to make. How much would it cost to make 22 woven bracelets? Use the ratio table below to record your strategy.
It would cost ______________ to make 22 woven bracelets.
Answer:
Given,
Woven bracelets cost $1.20 each to make.
$1.20 × 1 = $1.20
$1.20 × 2 = $2.40
$1.20 × 3 = $3.60
$1.20 × 5 = $6
$1.20 × 10 = $12
$1.20 × 15 = $18
$1.20 × 20 = $24
$1.20 × 21 = $25.2
$1.20 × 22 = $26.4
It would cost $26.4 to make 22 woven bracelets.
Question 4.
Woven bracelets sell for $1.50 each. How much money would Callie bring in if she sold 55 woven bracelets? Use the information on the ratio table below, and write in your own to solve the problem.
55 woven bracelets would sell for a total of ________________.
Answer:
Given,
Woven bracelets sell for $1.50 each.
$1.50 × 1 = $1.50
$1.50 × 2 = $3.00
$1.50 × 4 = $6.00
$1.50 × 10 = $15
$1.50 × 5 = $7.5
$1.50 × 45 = $67.50
$1.50 × 50 = $75
$1.50 × 51 = $76.5
$1.50 × 55 = $82.5
55 woven bracelets would sell for a total of $82.5
Question 5.
Callie spilled frosting on several of her tables. Fill in all the spots that are covered. Use the information to answer the questions.
a. Callie was figuring the cost to make cake pops at $1.25 each and found how many cake pops she could make if she had $67.50.
How many cake pops can she make for $67.50?
Answer:
Given,
Callie was figuring the cost to make cake pops at $1.25 each
$1.25 × 1 = $1.25
$1.25 × 2 = $2.50
$1.25 × 4 = $5
$1.25 × 40 = $50
$1.25 × 10 = $12.50
67.50/1.25 = 54
$1.25 × 54 = $67.50
b. Callie made a different table to figure out how many cake pops she could make if she had $95.00.
How many cake pops can she make for $95.00?
Answer:
$1.25 × 20 = $25
$12.50/$1.25 = $10
$1.25 × 5 = $6.25
$1.25 × 50 = $62.5
$1.25 × 25 = $31.25
$1.25 × 75 = $93.75
$95/$1.25 = 76
c. One of Callie’s tables was for beaded bracelets.
How many beaded bracelets can she make for $101.25?
Answer:
$4.50/$2.25 = 2
$2.25 × 4 = $9
$2.25 × 40 = $90
$22.50/$2.25 = 10
$2.25 × 5 = $11.25
$101.25/$2.25 = 45
d. The last table showed woven bracelets.
How many woven bracelets can she make for $67.50?
Answer:
$3/$1.50 = 2
$6/$1.50 = 4
$1.50 × 10 = $15
$1.50 × 5 = $7.5
$67.50/$1.50 = 45
Question 6.
CHALLENGE If Callie wants to make a profit of $100 or more selling bracelets, how many of each type do you think she should make? Explain your thinking.
Answer:
Callie wants to make a profit of $100
$100/$1.25 = 80
With or Without
Callie’s friend Vanessa also wants to raise money and decided to sell homemade frozen yogurt to her friends and neighbors.
Question 1.
Vanessa will sell vanilla yogurt for $2.50 a cup. Fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt.
Note: You don’t need to use all the boxes in this table or those below. Just use as many as you need and leave the rest.
Vanessa will make _____________ if she sells 19 cups of vanilla yogurt.
Answer:
Given,
Vanessa will sell vanilla yogurt for $2.50 a cup.
$2.50 × 1 = $2.50
$2.50 × 2 = $5
$2.50 × 3 = $7.5
$2.50 × 5 = $11.25
$2.50 × 10 = $25
$2.50 × 15 = $37.5
$2.50 × 19 = $47.5
Vanessa will make $47.5 if she sells 19 cups of vanilla yogurt.
Question 2.
Vanessa will sell vanilla yogurt in waffle cones for $2.75 each. Fill in the table to show how much money Vanessa will make if she sells 21 cones of vanilla yogurt.
Vanessa will make _______________ if she sells 21 cones of vanilla yogurt.
Answer:
Given,
Vanessa will sell vanilla yogurt in waffle cones for $2.75 each.
$2.75 × 1 = $2.75
$2.75 × 2 = $5.50
$2.75 × 5 = $13.75
$2.75 × 10 = $27.50
$2.75 × 15 = $41.25
$2.75 × 20 = $55
$2.75 × 21 = $57.75
Vanessa will make $57.75 if she sells 21 cones of vanilla yogurt.
Question 3.
Vanessa will also offer a variety of toppings for her yogurt for $0.35 a scoop. Fill in the table to show how much money Vanessa will make if she sells 49 scoops of toppings.
Vanessa will make _____________ if she sells 49 scoops of toppings.
Answer:
Given,
Vanessa will also offer a variety of toppings for her yogurt for $0.35 a scoop.
$0.35 × 1 = $0.35
$0.35 × 2 = $0.7
$0.35 × 5 = $1.75
$0.35 × 10 = $3.5
$0.35 × 20 = $7
$0.35 × 25 = $8.75
$0.35 × 30 = $10.5
$0.35 × 40 = $14
$0.35 × 49 = $17.15
Vanessa will make $17.15 if she sells 49 scoops of toppings.
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 2 Session 4 Answer Key
Over & Under
Question 1.
Use relationships among the problems to help you solve them.
\(\frac{1}{4}\) of 44 is _______________
0.25 × 44 = _______________
25 × 44 = _______________
26 × 44 = _______________
24 × 44 = _______________
0.24 × 44 = _______________
\(\frac{1}{4}\) of 45 is _______________
0.25 × 45 = _______________
25 x 45 = _______________
26 × 45 = _______________
24 × 45 = _______________
0.24 × 45 = _______________
Answer:
\(\frac{1}{4}\) of 44 is 11
1/4 × 44 = 11
0.25 × 44 = 11
25 × 44 = 1100
26 × 44 = 1144
24 × 44 = 1056
0.24 × 44 = 10.56
\(\frac{1}{4}\) of 45 is 11.25
0.25 × 45 = 11.25
25 x 45 = 1125
26 × 45 = 1170
24 × 45 = 1080
0.24 × 45 = 10.80
Question 2.
Use relationships among the problems to help you solve them.
\(\frac{3}{4}\) of 32 is _______________
0.75 × 32 = _______________
75 × 32 = _______________
74 × 32 = _______________
76 × 32 = _______________
0.76 × 32 = _______________
\(\frac{1}{4}\) of 33 is _______________
0.75 × 33 = _______________
75 × 33 = _______________
74 × 33 = _______________
76 × 33 = _______________
0.76 × 33 = _______________
Answer:
\(\frac{3}{4}\) of 32 is 24
0.75 × 32 = 24
75 × 32 = 2400
74 × 32 = 8768
76 × 32 = 2432
0.76 × 32 = 24.32
\(\frac{1}{4}\) of 33 is 8.25
0.75 × 33 = 24.75
75 × 33 = 2475
74 × 33 = 2442
76 × 33 = 2508
0.76 × 33 = 25.08
Question 3.
CHALLENGE Use the answers to the problems above to help solve some of those below.
76 × 48 = _______________
24 × 96 = _______________
0.74 × 32 = _______________
25 × 9 = _______________
75 × 37 = _______________
76 × 112 = _______________
Answer:
76 × 48 = 3648
24 × 96 = 2304
0.74 × 32 = 23.68
25 × 9 = 225
75 × 37 = 2775
76 × 112 = 8512
Making Cupcakes
Question 1.
A fancy cupcake costs $0.85 to make. Fill in the table to show how much it would cost to make 21 fancy cupcakes.
Note: You don’t need to use all the boxes in this table or the other one below. Just use as many as you need and leave the rest.
It would cost ____________ to make 21 fancy cupcakes.
Answer:
A fancy cupcake costs $0.85 to make. Fill in the table to show how much it would cost to make 21 fancy cupcakes.
$0.85 × 1 = $0.85
$0.85 × 5 = $4.25
$0.85 × 9 = $7.65
$0.85 × 10 = $8.5
$0.85 × 12 = $10.2
$0.85 × 15 = $12.75
$0.85 × 20 = $17
$0.85 × 21 = $17.85
It would cost $17.85 to make 21 fancy cupcakes.
Question 2.
How many fancy cupcakes could you make for $85.85? Fill in the table to solve the problem.
You could make ____________ fancy cupcakes for $85.85.
Answer:
$0.85 × 1 = $0.85
$0.85 × 5 = $4.25
$0.85 × 10 = $8.5
$0.85 × 15 = $12.75
$0.85 × 20 = $17
$0.85 × 40 = $34
$0.85 × 50 = $42.5
$0.85 × 100 = $85
$0.85 × 101 = $85.85
You could make 101 fancy cupcakes for $85.85.
Question 3.
Find 47 × 98, using the most efficient strategy you can. Show your work.
Answer:
47 × 98 = 4606.
By multiplying 47 and 98 we get 4606.
Question 4.
Find 987 ÷ 47, using the most efficient strategy you can. Show your work.
Answer:
987 ÷ 47 = 21
47)987(21
987
0
The quotient is 21 and the remainder is 0.