Grade 5 Multiplication and Division Study Guide

Grade 5 Multiplication and Division Study Guide

1) Know how to use strategies to find the answer to multiplication facts up to 9 x 9.

·      Use Repeated Doubling: For example, to find 8 x 4, you can use doubling from an easier fact. 8 x 2 = 16; doubling the product (16) gives you 32, which is the answer to 8 x 4).

·      Skip Counting: For example, to find 5 x 5, you can skip count 5, 5 times.

·      Use Known Facts: For example, if you known 6 x 6 = 36, you can use that fact to help you find 6 x 7.

2) Know how to use strategies to find the answer to 2-digit by 1-digit division.

• Related Multiplication Facts: To find 72 ÷ 8, think 8 times what number is 72? If you know that 8 x 9 = 72, then 72 ÷ 8 = 9.
• Halving: To find 64 ÷ 4, you could think 64 ÷ 2 = 32, and then divide it by 2 again to get 32 ÷ 2 = 16. You can also do Repeated Halving. For example, to find 96 ÷ 8, you could first divide 96 by 2 which is 48, and then divide it by 2 again which is 24, and then divide it by 2 one more time which is 12. Therefore 96 ÷ 8 = 12.
• Repeated Subtraction: This is kind of like the opposite of skip counting. To find 18 ÷ 6 I can keep subtracting 6 from 18 until I get to 0. The amount of times I had to subtract 6 is my answer. 18 – 6 = 12 – 6 = 6 – 6 = 0. So 18 ÷ 6 = 3.
• Understanding how to write a related multiplication and division fact. For example, the related facts for 9 x 2 = 18 include: 2 x 9 = 18, 18/2 = 9 and 18/9 = 2. Know how to use these related facts to solve a problem (use your knowledge of 7 x 4 = 28 to find 28/ 7 =?)

3) Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) to solve problems by using a strategy that works for you, such as:

• Using personal strategies for multiplication
• Using the traditional algorithm.
• Using cross multiplication. 
• Using lattice multiplication.
• Applying the distributive property (this property lets you multiply a sum by breaking down the numbers into their place values, multiplying them separately, and then adding the products). For example, to multiply 14 x 7, the student could multiply the tens (10 x 7) and then the ones (4 x 7), and then add the two numbers).

4) Apply mental mathematics strategies for multiplication, such as:

• Removing and then re-adding zero (for example, to find the answer to 700 x 30, multiply 7 x 3 and add the three 0’s). * Know how to multiply with multiples of 10 up to 1000.

5) Demonstrate an understanding of division (3-digit by 1-digit), and interpret remainders to solve problems.

• Remember the steps for long division, use the family trick (Dad = divide, Mom = multiply, Sister = subtract, Brother = bring down, Rover = Repeat or remainder) to help you! Know how to multiply to check your answer.

6) Remember a variety of estimation strategies to solve products (examples: front end rounding, rounding to the nearest ten, nearest hundred, and using compatible numbers). 

Understand the following language:

Product – The answer to a multiplication problem.

Quotient – The answer to a division problem.

Divisor – The smaller number in a division problem, the one in which the larger number is being divided into. For example, in the division problem 18/4, 18 is the number being divided by the divisor 4.

Dividend – The larger number in a multiplication problem, the one that is being divided (18 in the example above).