Apply the Commutative Property of Multiplication

Students learn that the order of factors does not change the product (e.g., 4 x 6 = 6 x 4). They explore this property using arrays — rotating an array shows the same total but swapped rows and columns — and apply it to reduce the number of multiplication facts they need to memorize.

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Real questions from this skill, graded here. No account, and nothing is saved.

Grade 3 · Properties of Multiplication and Division · question 1 of 3

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12 rungs. A star at the top.

2 × = 10

How it is taught

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You can flip factors and keep the product.

An array rotated is the same total.

Read it: The same product, two ways

3 × 5 is 3 rows of 5 squares: 15. Turn the array around and it is 5 rows of 3, still 15. So 3 × 5 = 5 × 3.

Draw the product as an array: rows of squares, the same number in each row.
Turn the array around: the rows become the columns.
Nothing is added and nothing is taken, so the product stays the same.

The squares do not change when the array turns, so neither does their number.

3 × 5 and 5 × 3 are the same 15 squares, counted the other way.

So knowing one fact gives you its turn-around fact for free.

Multiply in either order: the product is the same.

Thinking 5 × 3 must be a new number to work out.

It is the same array turned around: 5 × 3 = 15, the same as 3 × 5.

7 × 4 = 28. What is 4 × 7? — 28. The same array turned around: 4 × 7 = 28.

4 × 3 = 3 × 4

Does the order of numbers matter when we multiply? Let's find out with arrays of dots.

Here are four rows with three dots in each row.

If we count them all up, we get twelve dots.

We can write this as four times three equals twelve.

Now watch what happens when we turn this array sideways.

It becomes three rows with four dots in each row.

Let's count again. Still twelve dots — the same total!

So three times four also equals twelve.

Same dots, just rearranged. Both ways give us twelve.

When we multiply, the order doesn't change the answer. That's the commutative property!

Grade 3 · The order of factors doesn't change the product

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standard

CCSS.3.OA.B.5

Apply properties of operations as strategies to multiply and divide (commutative, associative, distributive)

Grade 3

Quoted from the Common Core State Standards.

Where this sits

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What a star here means

A star here is the top of a twelve-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 3

This is one rung of 104 in Grade 3 mathematics, in the order they build on each other.

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