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Properties of Multiplication Worksheets

17 free PDFsUS Letter PDFsAnswer key includedNo login

The commutative, associative and distributive properties with arrays and numbers, multiplying by 0 and 1, and naming the property. Every page has an answer key.

Download the properties of multiplication worksheets

Commutative property

Read an array two ways, and fill in turnaround facts.

Associative property

Multiply three factors by grouping an easy pair first, and fill in the missing factor.

Distributive property

Break apart arrays with a dashed line, break apart a factor step by step, and fill in the missing numbers.

Properties of 0 and 1, and naming the property

Multiply by 0 and 1, name the property each equation shows, and a review of all three properties.

Print at 100% (actual size) for the cleanest tracing lines.

About these properties of multiplication worksheets

The properties of multiplication are the rules that make multiplying easier. The commutative property says the order doesn't matter: 3 × 8 = 8 × 3. The associative property says you can group three factors any way: (2 × 5) × 7 = 2 × (5 × 7). The distributive property lets you break a hard fact into two easy ones: 7 × 8 = 7 × 5 + 7 × 3.

Third graders don't need the names to use the ideas, but the names help them talk about their thinking. These worksheets show each property with arrays first, then with numbers, so children see why it works. Break Apart Arrays draws a dashed line through an array and asks for the two smaller products.

Every page has an answer key on page 2. Pages print in black and white on US Letter or A4.

Standards

  • CCSS.MATH.CONTENT.3.OA.B.5Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
  • CCSS.MATH.CONTENT.3.OA.D.9Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

How to use them

  1. Start with Commutative Property With Arrays. Turn the page sideways: the rows become columns, and the total stays the same.
  2. Use Associative Property: Three Factors to show how grouping 2 × 5 first makes 2 × 5 × 7 quick.
  3. Teach the distributive property with Break Apart Arrays before the number-only pages.
  4. Use Multiplying by 0 and 1 early in the year. They are the easiest facts and give children confidence.
  5. Finish with Name the Property as a quick check of the vocabulary.

Teaching tips

  • Commutative sounds like commute: the factors can travel back and forth.
  • Associative is about who is grouped together. The factors stay in order; only the parentheses move.
  • Distributive: break the bigger factor into 5 and some more. Most children know their 5s.
  • The identity property: a number times 1 keeps its identity.
  • The zero property: any number times 0 is 0, because 0 groups of anything is nothing.

Questions teachers and parents ask

What are the properties of multiplication?

The commutative property (a × b = b × a), the associative property ((a × b) × c = a × (b × c)), the distributive property (a × (b + c) = a × b + a × c), the identity property (a × 1 = a) and the zero property (a × 0 = 0).

What is the distributive property for 3rd grade?

It means breaking a fact into two smaller facts and adding them. To find 6 × 7, think 6 × 5 = 30 and 6 × 2 = 12, then 30 + 12 = 42. An array split by a line shows why it works.

Do 3rd graders need to know the names of the properties?

The standard asks children to use the properties as strategies. Many classes also learn the names, so we include a Name the Property page.

Are there answer keys?

Yes. Every page has an answer key on page 2 of the PDF.