Division and the Associative Property

Examples, solutions, and videos to help Grade 4 students learn how to use division and the associative property to test for factors and observe patterns.

Common Core Standards: 4.OA.4

New York State Common Core Math Grade 4, Module 3, Lesson 23

Worksheets for Grade 4

NYS Math Module 3 Grade 4 Lesson 23 Concept Development

Problem 1: Use division to find factors of larger numbers.
Find the unknown factor: 28 = 7 × ___.
Problem 2: Use the associative property to find additional factors of larger numbers.
Problem 3: Use division or the associative property to find factors of larger numbers.

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NYS Math Module 3 Grade 4 Lesson 23 Problem Set

1. Explain your thinking or use division to answer the following.
   a. Is 2 a factor of 84?
   b. Is 2 a factor of 83?
2. Use the associative property to find more factors of 24 and 36.
   a. 24 = 12 × 2
   = ( ___ × 3) × 2
   = ___ × (3 × 2)
   = ___ × 6
   = ___
   b. 36 = ____ × 4
   = ( ____ × 3) × 4
   = ____ × (3 × 4)
   = ____ × 12
   = ____
3. In class, we used the associative property to show that when 6 is a factor, then 2 and 3 are factors, because 6 = 2 × 3. Use the fact that 8 = 4 × 2 to show that 2 and 4 are factors of 56, 72, and 80.
   56 = 8 × 7
   72 = 8 × 9
   80 = 8 × 10

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NYS Math Module 3 Grade 4 Lesson 23 Homework

1. Explain your thinking or use division to answer the following.
   a. Is 2 a factor of 72?
   c. Is 3 a factor of 72?
   e. Is 6 a factor of 72?
   f. Is 4 a factor of 60?
   h. Is 8 a factor of 60?
2. Use the associative property to find more factors of 12.
   a. 12 = 6 × 2
   = ___ × (3 × 2)
   = ___ × 6
   = ___
3. In class, we used the associative property to show that when 6 is a factor, then 2 and 3 are factors, because 6 = 2 × 3. Use the fact that 10 = 5 × 2 to show that 2 and 5 are factors of 70.
4. The first statement is false. The second statement is true. Explain why using words, pictures, or numbers.
   If a number has 2 and 6 as factors, then it has 12 as a factor.
   If a number has 12 as a factor, then both 2 and 6 are factors.

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