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The Answer Key for Bridges in Mathematics Grade 5 Home Connections Book

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What’s the Problem?

To find 3 times any number, Maria doubles the number, then adds the number again.

a.Write an expression with parentheses to show how Maria would solve 3 x 6.
Answer: (2 x 6) + 6

b. What is 3 x 6?

c. What is another way to think about 3 x6?
Answer: You could do 3 x 5, which is really easy, and then add 3 more, like this (3 x 5) + 3

1. To find 4 times any number, Susan uses the Double-Double strategy (multiply by 2, then by 2 again). Susan wrote (2 x 9) x 2 to record how she would solve 4 x 9.
a. What is 4 x 9?
b. What is another way to solve 4 x 9?
Note that work will vary. Example: (4 x 4) + (4 x 5) = 16 + 20 = 36
1. To find 5 times any number, Kaylee first multiplies by 10 and then finds half the product.
a. Write an expression with parentheses to show how Kaylee would solve 7 x 5.
Answer: (7 x 10) : 2
b. What is 7 x 5?
c. What is another way to solve 7 x 5?
Answer: Note that work will vary. Example: (5 x 5) + (2 x 5) = 25 + 10 = 35
1. When given any number times 9, Jasper multiplies the number by 10 and then removes one group of the number.
a. Write an expression with parentheses to show how Jasper would solve 3 x 9.
Answer: (3 x 10) – 3
b. What is 3 x 9?
c. What is another way to think about 3 x 9?
Answer: Note that work will vary. Example: (3×5) + (3×4) = 15 + 12 = 27
1. Braden loves multiplying by 8 because he can double-double-double.
a. Write an expression with parentheses to show how Braden would solve 8 x 7.
Answer: ((7 x 2) x 2) x 2
b. What is 8 x 7?
c. What is another way to think about 8 x 7?
Answer: Note that work will vary. Example: (4 x 7) x 2
1. Jonah was asked to add 4 and 7 then multiply the sum by 9. Which expression shows Jonah’s problem? (The sum is the answer to an addition problem)
Answer: a. (4 + 7) x 9
1. Patrick needed to multiply 4 and 6 then subtract 12 from the product. Write an expression with parentheses to show the problem. (The product is the answer to a multiplication problem).
Answer: (4 x 6) – 12 Note: parentheses are not required due to order of operations. Students may omit them.
1. Violet divided 81 by 9 then multiplied the quotient by 3. Write an expression with parentheses to show the problem. (The quotient is the answer to a division problem)
Answer: (81 : 9) x 3 Note: parentheses are not required due to order of operations. Students may omit them.
1. Solve.
a.54 – ( 3 x8)
b. (28 : 7) x 4
1. Rafael was given the problem 44 x 9. Write an expression to show how you would solve the problem.
Answer: (44 x 10) – (44 x 1) = 440 – 44 = 396

Multiplication Connections

1. To multiply a number by 12, Carter likes to multiply the number by 10 and then multiply it by 2 and add the products. Here is a picture of his thinking. (There is a rectangle with length of 16 and wide of 10 and under it, there is another rectangle attached where the length is 2 so that the total wide of the rectangle is 12)
a. Write an expression with parentheses to show how Carter would solve 12 x 16.
Answer: (16 x 10) + (16 x 2)
b. What is 12 x 16?
1. To multiply a number by 99, Sofia likes to multiply by 100 and then subtract 1 group of the factor. (There is a picture which you can see in your book).
a. Write an expression with parentheses to show how Sofia would solve 8 x 99.
Answer: (8 x 100) – (8 x1)
b. What is 8 x 99?
1. Fill in the dimensions of this box: 3 x 3 x 9
2. Solve the following problems.
2 x 13 = 26
4 x 13 = 52
8 x 13 = 104
10 x 28 = 280
28 x 5 = 140
28 x 15 = 420
13 x 4 = 52
1. Find the products.
a. (2 x 5) x 8 = 80
b. (2 x 8) x 5 = 80
c. (5 x 8) x 2 = 80

6. Which of the problems in item 5 is the easiest for you to solve? In other words, in which order would you prefer to multiply the three factors? Why?