Apply the Distributive Property of Multiplication

Students learn to break apart a multiplication problem into two smaller, easier multiplication problems and add the results (e.g., 7 x 6 = 7 x 5 + 7 x 1). They use area models and arrays split into parts to visualize how the distributive property works, building toward fluency with larger facts.

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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.

24 = 4 × ( + 1)

How it is taught

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You can split one factor into two easier facts.

Multiply both parts, then add.

Read it: Split a factor, multiply, add

6 × 7 is a rectangle 6 by 7. Split the 7 into 4 + 3: the parts are 6 × 4 = 24 and 6 × 3 = 18. Add them: 24 + 18 = 42. So 6 × 7 = 6 × 4 + 6 × 3.

Split one factor into two easier numbers.
Multiply the other factor by each part.
Add the two products.

The dashed line cuts the rectangle into two smaller rectangles, and together they cover it.

6 × 4 and 6 × 3 are facts you know, even when 6 × 7 is not.

Splitting changes the work, never the product: 42 either way.

Split a factor, multiply each part, then add the parts.

Multiplying only one part: 6 × 4 = 24.

Both parts count: 6 × 4 + 6 × 3 = 24 + 18 = 42.

9 × (3 + 2) = ___ — 45. 9 × 3 = 27 and 9 × 2 = 18: 27 + 18 = 45.

7 × 8 = (7 × 5) + (7 × 3)

What's seven times eight? It's a tough fact — but we can break it into two easier ones.

Here's our multiplication as a rectangle — an area model.

Grade 3 · Break a hard fact into two easy ones

The side is seven. The top is eight. Seven rows of eight.

We know our fives really well. So let's split the eight into five plus three.

Now we have two smaller rectangles, side by side.

The first rectangle is seven times five. That's thirty-five.

The second is seven times three. That's twenty-one.

Add the two pieces together: thirty-five plus twenty-one.

Fifty-six! So seven times eight is fifty-six. That's the distributive property!

Now you try. Multiply to find this rectangle's area. What area does it cover?

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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