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Bridges in Mathematics Grade 5 Student Book Answer Key Unit 4 Module 4
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 4 Session 1 Answer Key
Which Estimate Makes the Most Sense?
Question 1.
For problems a-d, circle the estimate that makes the most sense. Explain why you chose the estimate you did.
a. 29 ÷ 4
Why?
Answer:
28 ÷ 4 = 7
So, the estimated quotient is 7.
b. 57 ÷ 9
Why?
Answer:
57 ÷ 9 = 6.33 ≈ 6
So, the estimated quotient is 6.
c. 108 ÷ 10
Why?
Answer:
108 ÷ 10 = 10.8 ≈ 11
So, the estimated quotient is 11.
d. 147 ÷ 12
Why?
Answer:
147 ÷ 12 = 12.25 ≈ 12
So, the estimated quotient is 12.
Question 2.
CHALLENGE In the two boxes below, make up your own division estimation problems to share with a classmate.
a.
Answer:
b.
Answer:
Work Place Instructions 4D Estimate & Check
Each pair of players needs:
- a 4D Estimate & Check Record Sheet to share
- 1 deck of Estimate & Check Cards
- 1 die marked 1-6
- pencils
1. Players shuffle the deck of cards and place them in a stack, face-down, between them. Then they roll the die to determine which of them gets to start.
2. Player 1 takes the first card from the top of the stack and writes the division problem in the first box on his part of the record sheet. The player chooses the best estimate from the six numbers at the top of the sheet and explains his thinking to the other player.
Raven I got 65 ÷ 10. I think the best estimate is 6 because 10 × 6 is 60, and the next number on the estimate list is 9, which is way too big because 9 × 10 is 90.
3. Player 2 takes the next card from the top of the stack and follows the instructions in step 2.
4. Both players use a calculator to find the exact answers to their problems and record those answers on their part of the record sheet. Then they record the differences between their estimates and the answers. They put their cards they just used at the bottom of the stack.
5. Players repeat steps 2-4 until each has taken 5 turns. Then they each add up all the differences between their estimates and the actual answers. The player with the lower score wins.
Game Variations
A. Develop a new set of cards that can be used with the two record sheets.
Answer:
2- by 3-Digit Multiplication
Question 1.
Solve each problem below using the traditional (standard) multiplication algorithm.
Answer:
By multiplying 785 by 39 we get 30,615.
By multiplying 804 by 26 we get 20,904.
By multiplying 653 by 98 we get 63,994.
Question 2.
Choose one problem above that you could solve easily with a different strategy. Explain which strategy you would use and why.
Answer: We can use halving and doubling method to solve the problem.
804 × 26 = 402 × 52 = 20,904
Question 3.
Fill in the boxes.
Answer:
By multiplying 67 and 76 we get 5092.
By multiplying 49 and 27 we get 1323.
Review
Question 4.
Claudia says that 17 × 80 is the same as 17 × 8 × 10. Do you agree or disagree? Explain.
Answer:
17 × 80 = 1360
17 × 8 × 10 = 1360
Yes, I agree with Claudia.
Question 5.
Andre says that 4 × 27 is the same as 4 × 3 × 9. Do you agree or disagree? Explain.
Answer:
4 × 27 = 108
4 × 3 × 9 = 12 × 9 = 108
Yes I agree with Andre.
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 4 Session 2 Answer Key
Story Problem Paper
Division on a Base Ten Grid
Question 1.
Complete the following multiplication problems.
Answer:
14 × 2 = 28
14 × 3 = 42
14 × 10 = 140
14 × 5 = 70
14 × 20 = 280
14 × 30 = 420
Question 2.
Solve the following division problems. Use the multiplication problems above and the grids to help.
a. 322 ÷ 14 = _______________
Answer:
b. 238 ÷ 14 = _______________
Answer:
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 4 Session 3 Answer Key
Water Conservation
Do you want to help conserve water? Here are some water-saving tips. Be sure to show all of your work for each of these problems.
Question 1.
If you leave the faucet running while you take a 5-minute shower, you use about 400 cups of water. How many gallons is that?
Answer:
a. If you get wet, turn off the water to soap up, and turn the water back on to rinse off, you only use about about 64 cups of water. How many gallons is that?
Answer:
We have to convert from cups to gallons.
1 gallon = 16 cups
64 cups = 64/16 = 4 gallons
b. If you take a shower every day and use the method described in part a above, how many gallons of water can you save in a day? How many gallons of water can you save in a week?
Answer:
You save 4 gallons in a day.
1 week = 7 days
4 × 7 = 28 gallons
Thus you can save 28 gallons of water in a week.
Question 2.
If you fill the bathtub all the way, it takes about 576 cups of water. How many gallons is that?
Answer:
Given, it takes about 576 cups of water
We have to convert from cups to gallons.
1 cup = 0.0625 gallon
576 cups = 576 × 0.0625
= 36 gallon
Thus 576 cups of water is equal to 36 gallons.
a. If you fill the bathtub just enough to wash yourself, it takes about 144 cups of water. How many gallons is that?
Answer:
Given, it takes about 144 cups of water
We have to convert from cups to gallons.
1 cup = 0.0625 gallon
144 cups = 144 × 0.0625
= 9 gallons
b. If you take a bath 3 times a week and use the second method described above, how many gallons of water can you save in a week? How many gallons of water can you save in a month?
Answer:
It takes 9 gallons of water to fill the bathtub.
If you take a bath 3 times a week
9 × 3 = 27 gallons of water.
1 month = 4 weeks
27 × 4 = 108 gallons of water.
Water Conservation Challenge
Question 1.
If you leave the hose running the whole time you wash a car, it takes about 4,800 cups of water. If you fill a bucket, wash the car, and then rinse it with the hose, it takes about 240 cups of water. How many gallons of water can you save by using a bucket and hose instead of leaving the water running?
Answer:
Question 2.
Mr. Mugwamp has a leaky faucet. It leaks 2 drops of water every second. If there are 3,840 drops of water in a cup, how many gallons of water will be wasted in a single day (24 hours)?
Answer:
Division with Tables & Sketches
Question 1.
Fill in the ratio table for 19.
Answer:
1 × 19 = 19
2 × 19 = 38
10 × 19 = 190
5 × 19 = 95
20 × 19 = 380
15 × 19 = 285
Question 2.
Solve the two division problems using the ratio table above and sketches to help. You can add to the ratio table if you want to.
ex:
304 ÷ 19 = 16
a. 608 ÷ 19 = _____________
Computation: _____________
Sketch: ______________
Answer:
Computation: 32
b. 456 ÷ 19 = _____________
Computation: _____________
Sketch: ______________
Answer:
Computation: 24
Question 3.
Use the standard multiplication algorithm to solve the problems below. Show your work.
Answer:
By multiplying 84 and 36 we get 3024.
By multiplying 79 and 26 we get 2054.
By multiplying 86 and 32 we get 2752.
By multiplying 92 and 37 we get 3404.
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 4 Session 4 Answer Key
Work Place Instructions 4E Lowest Remainder Wins
Each pair of players needs:
- a 4E Lowest Remainder Wins Record Sheet for each player
- a clear spinner overlay
- 1 die marked 0-5
- 2 dice marked 1-6
1. Players roll one of the dice to decide who goes first. Player 1 then spins the spinner to get the first divisor for both players.
2. Both players start a ratio table for that divisor in the Round 1 box on their record sheet and fill in the table for 1 and 10 groups of the divisor.
Players can add more entries to their ratio tables if they need them while they are playing.
3. Each player takes a turn to roll the 3 dice one time and then arranges the digits any way he or she likes to make a dividend.
Players each try to make a 3-digit number that won’t leave a remainder when it’s divided by the divisor. If they can’t do that, they try to make a number that will leave a very small remainder. Players can add entries to their ratio tables to help them decide how to arrange the digits if they like.
4. Both players record their division problem on their own record sheet and do the division.
Players can continue to add any useful entries to their ratio tables to help as they go along.
5. When both players have finished their division problems, they explain their work to each other. When they both agree that the other’s work is correct, they enter their score and that of the other player’s at the bottom of their record sheet.
A player gets 0 points if she had no remainder. Otherwise, the player gets the number of points that matches her remainder.
6. Players play two more rounds of the game and then add up their scores at the bottom of the sheet to find their total. The player with the lower score wins.
Game Variations
A. Use 2 dice numbered 4-9 instead of the 3 dice on the materials list.
B. Use the challenge record sheets instead of the regular record sheets for this game. The challenge sheets have a spinner with higher divisors.
C. Use 2 dice marked 4-9 and one die marked 1-6 to get higher dividends.
D. Use 2 dice marked 4-9 and 2 dice marked 1-6 to get 4-digit dividends.
Answer:
Divisibility Rules
It’s easy to tell if a small number like 12 is divisible by another number. With bigger numbers, like 435, it can be harder to tell. You already know how to tell if a number is divisible by 2, 5, or 10. There are also rules that can help you tell if any number is divisible by 3, 6, or 9.
Question 1.
Use the chart below to help you figure out if the numbers are divisible by 3, 6, or 9. In the last column, you don’t have to list all the factors of the number. Just list any other numbers you know for sure that the number is divisible by.
ex:
a.
Answer:
987 = 9 + 8 + 7 = 24
24 ÷ 3 = 8
24 ÷ 6 = 4
24 is not divisible by 9.
24 ÷ 12 = 2
b.
Answer:
5 + 4 + 0 = 9
9 ÷ 3 = 3
9 ÷ 9 = 1
9 is not divisible by 6.
c.
Answer:
7 + 6 + 2 = 15
15 ÷ 3 = 5
15 is not divisible by 6
15 is not divisible by 9.
15 is divisible by 5.
d.
Answer:
747 = 7 + 4 + 7 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3
18 ÷ 9 = 2
18 ÷ 2 = 9
e.
Answer:
570 = 5 + 7 + 0 = 12
12 ÷ 3 = 4
12 ÷ 6 = 2
12 is not divisible by 9.
12 is also divisible by 2.
f.
Answer:
645 = 6 + 4 + 5 = 15
15 ÷ 3 = 5
15 is not divisible by 6
15 is not divisible by 9.
15 is divisible by 5.
g.
Answer:
792 = 7 + 9 + 2 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3
18 ÷ 9 = 2
18 ÷ 2 = 9
Bridges in Mathematics Grade 5 Student Book Unit 4 Module 4 Session 5 Answer Key
Multiplication Problems & Mazes
Question 1.
Complete the multiplication problems below. Use problems you have already solved to help solve other ones.
a.18 × 2 = ______________
18 × 3 = ______________
18 × 10 = ______________
18 × 5 = ______________
Answer:
18 × 2 = 36
18 × 3 = 54
18 × 10 = 180
18 × 5 = 90
b. 23 × 2 = ______________
23 × 3 = ______________
23 × 10 = ______________
23 × 5 = ______________
Answer:
23 × 2 = 46
23 × 3 = 69
23 × 10 = 230
23 × 5 = 115
c. 34 × 2 = ______________
34 × 3 = ______________
34 × 10 = ______________
34 × 5 = ______________
Answer:
34 × 2 = 68
34 × 3 = 102
34 × 10 = 340
34 × 5 = 170
Question 2.
Use the problems above to write three more combinations for each number. Show as much work as you need to find each product.
a. 18 × ____________ = _____________
18 × ___________ = ____________
18 × ___________ = ____________
Answer:
18 × 1 = 18
18 × 6 = 108
18 × 8 = 144
b. 23 × ____________ = _____________
23 × ___________ = ____________
23 × ___________ = ____________
Answer:
23 × 1 = 23
23 × 6 = 138
23 × 8 = 184
c. 34 × ____________ = _____________
34 × ___________ = ____________
34 × ___________ = ____________
Answer:
34 × 1 = 34
34 × 6 = 204
34 × 8 = 272
Question 3.
Use multiplication and division to find the secret path through each maze. The starting and ending points are marked for you. You can only move one space up, down, over, or diagonally each time. Write four equations to explain the path through the maze.
ex:
a.
Answer:
240 ÷ 60 = 4
4 × 30 = 120
120 ÷ 20 = 6
20 ÷ 4 = 5
b.
Answer:
420 ÷ 70 = 6
6 × 40 = 240
240 ÷ 8 = 30
30 ÷ 6 = 5