Apply the Associative Property of Multiplication

Students learn that when multiplying three numbers, the grouping does not change the product (e.g., (2 x 3) x 4 = 2 x (3 x 4)). They use this property as a strategy to simplify multiplication by choosing the most convenient grouping.

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

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12 rungs. A star at the top.

2 × = (2 × 5) × 7

How it is taught

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When three numbers multiply, grouping can change.

The product stays the same.

Read it: Group the factors either way

7 × 5 × 2: group two first. (7 × 5) × 2 is 35 × 2 = 70. 7 × (5 × 2) is 7 × 10 = 70. The same product, and 5 × 2 first makes 10, the easy way.

Multiply any two of the three factors first.
Then multiply that product by the third factor.
Choose the pair whose product is easy, like a 10.

Grouping does not change the product: 70 either way.

5 × 2 = 10, and 7 × 10 is a fact you know at once.

The parentheses show which two are multiplied first.

Group any two factors first; the product is the same, so start with the easy pair.

Thinking a different grouping gives a different product.

(7 × 5) × 2 = 70 and 7 × (5 × 2) = 70: the same.

(8 × 5) × 3 = ___ — 120. 8 × 5 first makes 40, and multiplying by 40 is easy: 120 either way.

(2 × 3) × 4 = 2 × (3 × 4)

Let's multiply two times three times four. Does it matter how we group the numbers?

First, let's group the two and the three together inside parentheses.

Inside the parentheses first: two times three is six.

Now six times four is twenty-four.

What if we group the three and the four together instead?

Inside the parentheses first: three times four is twelve.

And two times twelve is also twenty-four!

Same answer either way! That's the associative property — how we group the numbers doesn't change the product.

Grade 3 · Grouping 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

Comes after

Apply the Commutative Property of Multiplication

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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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