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Common Core Math3rd GradeOperations & Algebraic Thinking

3.OA.5: Use Properties to Multiply and Divide

Also written as 3.OA.B.5 and CCSS.MATH.CONTENT.3.OA.B.5 · Cluster: Understand properties of multiplication and the relationship between multiplication and division.

Make a 3.OA.5 WorksheetAll 25 3rd Grade Math Standards

The Official Wording

Apply 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.)

Common Core State Standards, Grade 3, Operations & Algebraic Thinking · Read it at the source · Checked October 14, 2026

What 3.OA.5 Means in Plain English

Third graders use the rules of multiplication as shortcuts. Knowing 3 × 8 = 24 gives 8 × 3 for free, 2 × 9 × 5 is easiest as 10 × 9, and 7 × 6 splits into 5 × 6 and 2 × 6, which add to 42.

Students don’t need the words commutative, associative and distributive yet, only the moves, usually made by turning or cutting an array. Splitting a factor grows into 4th-grade multi-digit multiplication (4.NBT.5) and into expressions like 3(2 + x) in 6th grade (6.EE.3).

3.OA.5 I Can Statements

  • I can use a fact I know to find its turnaround fact.
  • I can split a hard fact into two easier facts.
  • I can multiply three numbers in whichever order is easiest.

3.OA.5 Worked Example

A fact many third graders don’t know yet, built from two they do.

Problem

Find 7 × 6 using facts you already know.

Finding 7 × 6 from easier facts
  1. I don’t know 7 × 6 yet, but fives and twos are easy. 7 is 5 + 2.7 × 6 = (5 + 2) × 6
  2. Cut the array of 7 rows into 5 rows and 2 rows. Nothing is added or lost.7 × 6 = (5 × 6) + (2 × 6)
  3. Five sixes is 30. Two sixes is 12.30 + 12
  4. Put the two pieces back together.30 + 12 = 42
  5. Turn it around: 6 × 7 is the same array on its side, so it is 42 too.6 × 7 = 42
Answer7 × 6 = 42

Check it: Count by sixes seven times: 6, 12, 18, 24, 30, 36, 42.

Common Mistakes with 3.OA.5

Multiplying only one piece

7 × 6 = (5 × 6) + 2 = 32

Try this: Draw the 7-by-6 array and cut it into two pieces. Each piece is its own rectangle, so each gets multiplied by 6.

Working out the turnaround from scratch

Knows 3 × 8 = 24, then counts by threes eight times to find 8 × 3

Try this: Turn a 3-by-8 array of counters a quarter turn and ask whether any counters were added or lost.

Turning division around too

12 ÷ 3 = 4, so 3 ÷ 12 = 4

Try this: Share 12 counters among 3 people, then try sharing 3 counters among 12 people. The turnaround rule stops at multiplication.

Where 3.OA.5 Fits

Comes Before2.OA.4Write an array’s total as a sum of equal addends.2.NBT.9Explain why addition and subtraction strategies work, using place value and properties.
Alongside3.OA.7Know all one-digit multiplication facts from memory by the end of the year.3.MD.7Use area models to show the distributive property, like a 7-by-6 rectangle cut in two.
Comes Next4.NBT.5Multiply multi-digit numbers by splitting them by place value.6.EE.3Use the distributive property to rewrite expressions, like 3(2 + x) as 6 + 3x.

Practice 3.OA.5

Multiplication Worksheet GeneratorFree ToolPick the facts students find hardest, the sixes, sevens and eights, and have them split each one into two easier facts before answering.6s, 7s and 8sAnswer key
Make a Worksheet

Quick Check

  1. If 9 × 4 = 36, what is 4 × 9?
  2. Find 2 × 7 × 5 the easy way.
  3. Use 6 × 5 = 30 to find 6 × 7.

3.OA.5: Other Names

3.OA.53.OA.B.5CCSS.MATH.CONTENT.3.OA.B.5

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.