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Bridges in Mathematics Grade 5 Student Book Answer Key Unit 1 Module 1
Bridges in Mathematics Grade 5 Student Book Unit 1 Module 1 Session 3 Answer Key
Work Place Instructions 1A The Product Game
Each pair of players needs:
• a 1A The Product Game Record Sheet to share
• 2 game markers
• pencils
1 Players decide who is going first. Player 1 is O and Player 2 is X.
2 Player 1 places one of the game markers on any factor.
3 Player 2 places the other game marker on a factor. Then, he multiplies the two factors, draws an X on
the product, and writes an equation to match the combination.
Player 1 I choose 5.
Player 2 I choose 7. Let’s see, 5 × 7 is 35, and I’m X, so I’ll put my X on 35.
4 Player 1 moves one game marker to get a new product. She can move either of the markers.
Player 1 I’ll move the factor marker from the 5 to the 3. Since 7 × 3 is 21, I get to put an O on 21.
5 Play continues until a player gets four products in a row across, up and down, or diagonally.
• Only one factor marker can be moved during a player’s turn.
• Players can move a game marker so that both are on the same factor. For example, both markers can be on 3. The
player would mark the product 9 because 3 × 3 = 9.
• If the product a player chooses is already covered, the player loses that turn.
Game Variation
A Players play for five in a row.
2 Explain how you decided which problems to solve.
Product Game Problems
ex Chloe and Ava were playing The Product Game. Their factor markers were on 4
and 5. Ava decided to move the marker from 5 to 7. Write a numerical expression to
represent her move.
4 × 7
1. Chris and Katie were playing The Product Game. Their factor markers were on 9
and 2. Chris decided to move the marker from 2 to 6. Write a numerical expression
to represent his move.
Answer:
9 × 6
Explanation:
9 × 2 is 18, and I’m X, so I’ll put my X on 35.
The factor marker from the 2 to the 6.
Now, one maker is on 9 and other is on 6.
So, Number 9 x (2 + 4) = X
Number = 9 × 6 = 54
Therefore, 9 × 6 = 54 is a numerical expression to represent his move.
2. Eric and William were playing The Product Game together. William put an X on
42. One factor marker was on 6. The other factor marker was on _______.
Answer:
If 6 is used the other factor is 7
1, 2, 3, 4, 6, 7, 14 and 21 are possible ways to represent 42 as a product of two factors.
Explanation:
Given,
William put an X on 42.
One factor marker was on 6.
42 ÷ 6 = 7
If 6 is used the other factor is 7
1 x 42 = 42
2 x 21 = 42
3 x 14 =42
6 x 7 = 42
7 x 6 = 42
14 x 3 = 42
21 x 2 =42
Therefore, 1, 2, 3, 4, 6, 7, 14 and 21 are possible ways to represent 42 as a product of two factors.
3. Cindy placed an X on the product 36. What are all the possible locations of the two
factor markers?
Answer:
1, 2, 3, 4, 6, 9, 12 and 18 are possible ways to represent 36 as a product of two factors.
Explanation:
Given,
Cindy placed an X on the product 36.
The following are all the possible locations of the two factor markers,
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36
Therefore, 1, 2, 3, 4, 6, 9, 12 and 18 are possible ways to represent 36 as a product of two factors.
4. Eli placed an O on the product 24. What are all the possible locations of the two
factor markers?
Answer:
24 ×1 =24
12 × 2 = 24
6 × 4 = 24
4 × 6 = 24
1 , 2 , 4, 6 , 12
There are possible ways to represent 24 as a product of two factors.
Explanation:
Given,
Eli placed an O on the product 24.
The following are all the possible locations of the two factor markers,
1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
6 × 4 = 24
8 × 3 = 24
24 × 1 = 24
5. Hannah and Sean were playing The Product Game. Hannah needed to land on the
product 18 to win the game. The markers were on 4 and 6.
a. Which factor marker should Hannah move?
b. Where should she place it?
Answer:
a. She should move factor marker 4.
b. She should place it on 3.
Explanation:
Given,
Hannah needed to land on the product 18 to win the game.
The markers were on 4 and 6.
Now, one maker is on 4 and other is on 3.
So, the numerical expression is (4 x 3) + 6 = 12 + 6 = 18
Question 6.
Solve the following problems.
Answer:
Explanation:
Fact connections are the basic Mathematical expressions that are made up of three numbers.
8 × 10 = 2 × (10 × 4) To find 8 × 10, I can double 10 × 4.
8 × 5 = 2 × (5 × 4) To find 8 × 5, I can double 8 × 5.
4 × 6 = 2 × (6 × 2) To find 4 × 6, I can double 6 × 2.
8 × 6 = 2 × (6 × 4) To find 8 × 6, I can double 6 × 4.
6 × 12 = 2 × (12 × 3) To find 8 × 12, I can double 12 × 3.
8 × 12 = 2 × (12 × 4) To find 8 × 12, I can double 12 × 4.
4 × 8 = 2 × (8 × 2) To find 4 × 8, I can double 8 × 2.
Bridges in Mathematics Grade 5 Student Book Unit 1 Module 1 Session 3 Answer Key
More Product Game Problems
Question 1.
Jack and Connor are playing The Product Game. They are using light and dark markers instead of X’s and O’s to cover their products on the game board.
a. Jack is using the light markers. What move should he make next? Tell why.
Answer:
Jack’s next move : 3 to 4
Explanation :
Jack’s marker is on 9
multiples of 9 are 3 and 3
Jack has to move his marker to 12
multiples of 12 are 4 and 3
So, he has to move his marker from 3 to 4
Jack’s next move : 3 to 4
b. Connor is using the dark markers. What move should he make next? Tell why.
Answer:
Connor’s next move : 7 to 3
Explanation :
Connor’s marker is on 42
multiples of 42 are 6 and 7
Connor has to move his marker to 18
multiples of 18 are 6 and 3
So, he has to move his marker from 7 to 3
Connor’s next move : 7 to 3
Question 2.
Melanie and Jasmine are also playing The Product Game.
a. Melanie is using the light markers. What move should she make next? Tell why.
Answer:
Melanie’s next move : 2 to 7
Explanation :
Melanie’s marker is on 14
multiples of 14 are 2 and 7
Melanie has to move his marker to 49
multiples of 49 are 7 and 7
So, he has to move his marker from 2 to 7
Melanie’s next move : 2 to 7
b. Jasmine is using the dark markers. What move should she make next? Tell why.
Answer:
Jasmine’s next move : 3 to 4
Explanation :
Jasmine’s marker is on 15
multiples of 15 are 3 and 5
Jasmine’s has to move his marker to 20
multiples of 20 are 4 and 5
So, he has to move his marker from 3 to 4
Jasmine’s next move : 3 to 4
Question 3.
Solve the following.
Answer:
Explanation:
Fact connections are the basic Mathematical expressions that are made up of three numbers.
11 × 8 = 2 × (11 × 4) To find 11 × 8, I can double 11 × 4.
11 × 4 = 2 × (11 × 2) To find 11 × 4, I can double 11 × 2.
7 × 3 = 1 + (4 × 5) To find 7 × 3
7 × 6 = 2 × (7 × 3) To find 7 × 6, I can double 7 × 3.
9 × 4 = 2 × (9 × 2) To find 9 × 4, I can double 9 × 2.
9 × 5 = (9 × 10) ÷ 2
9 × 9 = 3 × (9 × 3) To find 9 × 9, I can triple 9 × 3.
Bridges in Mathematics Grade 5 Student Book Unit 1 Module 1 Session 4 Answer Key
Facts & Boxes
Question 1.
To multiply numbers by 5, Kaylee first multiplies by 10 and then finds half the product.
a. Write an expression with parentheses to show how Kaylee would solve 9 × 5.
Answer:
9 × 5 = (9 × 10) ÷ 2
Explanation:
Given,
To multiply numbers by 5.
let the unknown number be x.
Kaylee first multiplies by 10 and then finds half the product.
x × 5 = (x × 10) ÷ 2
9 × 5 = (9 × 10) ÷ 2
b. What is 9 × 5?
Answer:
45
Explanation:
A fact family is a group of math facts using the same numbers.
Given,
To multiply numbers by 5.
Kaylee first multiplies by 10 and then finds half the product.
9 × 5 = (9 × 10) ÷ 2
45 = 90 ÷ 2
45 = 45
C. Marshall says he would rather use 10 × 5 to find 9 × 5. Write an expression with parentheses that uses 10 × 5 to find 9 × 5.
Answer:
9 × 5 = (10 × 5) – 5
Explanation:
Marshall says he would rather use 10 × 5 to find 9 × 5.
The expression with parentheses that uses 10 × 5 to find 9 × 5 is as follows,
9 × 5 = (10 × 5) – 5
45 = 50 – 5
45 = 45
Match each expression with the correct box.
Answer:
Explanation:
The Box of Facts is a collection of ready-made visual aids to students to develop mathematics thinking strategies for basic facts in multiplication as shown above.
Question 5.
Fill in the dimensions of this box: 
Answer:
(6 ×2) × 2
Explanation:
Dimensions of each layer is (6 ×2) and number of layers are 2.
6 layers of 2-by-2 cubes is written as (6 ×2) × 2
Question 6.
Solve the following problems.
Answer:
Explanation:
Fact connections are the basic Mathematical expressions that are made up of three numbers.
8 × 4 = 2 × (8 × 2) = 32
8 × 8 = 2 × (8 × 4) = 64
12 × 10 = 3 × (10 × 4) = 120
12 × 5 = 2 × (5 × 6) = 60
3 × 7 = (4 × 5) + 1
7 × 6 = 2 × (7 × 3) = 42
Bridges in Mathematics Grade 5 Student Book Unit 1 Module 1 Session 5 Answer Key
Fact Connections
Question 1.
Fill in the facts. Look for relationships.
Answer:
Explanation:
Fact connections are the basic Mathematical expressions that are made up of three numbers.
3 × 2 = 6 or 3 + 3 = 6
3 × 4 = 2 × (3 × 2) To find 3 × 4, I can double 3 × 2.
3 × 8 = 2 × (3 × 4) To find 3 × 8, I can double 3 × 4.
6 × 2 = 2 × (3 × 2) To find 6 × 2, I can double 3 × 2.
6 × 4 = 2 × (6 × 2) To find 6 × 4, I can double 6 × 2.
6 × 8 = 2 × (6 × 4) To find 6 × 8, I can double 6 × 4.
Question 2.
Use the above information to help you fill in the blanks.
a. 3 × 4 = _____________ × (3 × 2) = _______________
Answer:
3 × 4 = 12 2 × (3 × 2) = 12
Explanation:
Given,
3 × 4 = _____________ × (3 × 2) = _______________
3 × 4 = 12 ;
4 is written as 2 x 2
2 × (3 × 2) = 12
b. 3 × 8 = _____________ × (3 × 4) = _____________
Answer:
3 × 8 = 24 2 × (3 × 4) = 24
Explanation:
Given,
3 × 8 = _____________ × (3 × 4) = _____
3 × 8 = 24
8 is written as 2 × 4
2 × (3 × 4) = 24
C. 6 × 2 = (3 × 2) × _____________ = ______________
Answer:
6 × 2 = (3 × 2) × 2 = 12
Explanation:
Given,
6 × 2 = (3 × 2) × _____________ = ______________
6 is written as 2 × 3
6 × 2 = (3 × 2) × 3 = 12
d. 6 × 4 = 2 × (6 × ____________) = _____________
Answer:
6 × 4 = 2 × (6 × 2) = 24
Explanation:
Given,
6 × 4 = 2 × (6 × ____________) = _____________
4 is written as 2 × 2
6 × 4 = 2 × (6 × 2) = 24
e. 2 × (6 × 4) = ___________ × 8 = ____________
Answer:
2 × (6 × 4) = 6 × 8 = 48
Explanation:
Given,
2 × (6 × 4) = ___________ × 8 = ____________
4 × 2 is written as 8
2 × (6 × 4) = 6 × 8 = 48
Question 3.
Fill in the facts. Look for relationships.
Answer:
Explanation:
Fact connections are the basic Mathematical expressions that are made up of three numbers.
4 × 2 = 2 × (2 × 2) To find 4 × 2, I can double 2 × 2.
4 × 4 = 2 × (4 × 2) To find 4 × 4, I can double 4 × 2.
4 × 8 = 2 × (8 × 2) To find 4 × 8, I can double 8 × 2.
8 × 2 = 2 × (2 × 4) To find 8 × 2, I can double 2 × 4.
8 × 4 = 2 × (8 × 2) To find 8 × 4, I can double 8 × 2.
8 × 8 = 2 × (8 × 4) To find 8 × 8, I can double 8 × 4.
Question 4.
Use the above information to help you write an equation that includes parentheses.
ex: 8 × 4 = 2 × (8 × 2) “To find 8 × 4, I can double 8 × 2.”
a. 4 × 6 = _____________
Answer:
4 × 6 = 24
Explanation:
Given, 4 × 6
4 × 6 = 2 × (6 × 2)
To find 6 × 4, I can double 6 × 2.
LHS = RHS
24 = 12 + 12
24 = 24
b. 4 × 12 = _____________
Answer:
4 × 12 = 48
Explanation:
Given, 4 × 6
4 × 12 = 2 × (12 × 2)
To find 4 × 12, I can double 12 × 2.
LHS = RHS
48 = 24 + 24
48 = 48
c. 8 × 8 = ______________
Answer:
8 × 8 = 64
Explanation:
Given, 8 × 8
8 × 8 = 2 × (8 × 4)
To find 8 × 8, I can double 8 × 4.
LHS = RHS
64 = 32 + 32
64 = 64
Question 5.
CHALLENGE Complete the following equations.
a. 4 × 67 = ___________ × (2 × 67)
Answer:
4 × 67 = 2 × (2 × 67)
Explanation:
Given,
4 × 67 = ___________ × (2 × 67)
LHS = RHS
4 is written as 2 x 2
268 = 2 x (2 × 67)
268 = 2 × 134
268 = 268
So, 4 × 67 = 2 × (2 × 67)
b. 8 × 198 = 2 × (_________ × 198)
Answer:
8 × 198 = 2 × (4 × 198)
Explanation:
Given,
8 × 198 = 2 × (_________ × 198)
LHS = RHS
8 is written as 2 x 4
8 × 198 = 2 × (4 × 198)
1584 = 2 × 792
1584 = 1584
So, 8 × 198 = 2 × (4 × 198)
C.
__________ × 3,794 = 2 × (4 × 3,794)
Answer:
8 × 3,794 = 2 × (4 × 3,794)
Explanation:
Given,
__________ × 3,794 = 2 × (4 × 3,794)
LHS = RHS
8 × 3,794 = 2 × (4 × 3,794)
30,352 = 2 × 15,176
30,352 = 30,352