Multiply Two Two-Digit Numbers

Students multiply two two-digit numbers using strategies based on place value and properties of operations, including area models, partial products, and the standard algorithm. They estimate products before calculating to check for reasonableness.

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Grade 4 · Multiplication of Multi-Digit Numbers · question 1 of 3

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20 rungs. A star at the top.

25 × 14 =

How it is taught

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Two two-digit numbers make four smaller multiplies.

Those partial products add to the full product.

Read it: Split by place, multiply each part

47 × 3: split 47 into 40 + 7. 3 × 40 = 120 and 3 × 7 = 21, and 120 + 21 = 141. 47 × 23 splits both numbers, into 4 parts.

Split each number by place: 47 = 40 + 7.
Multiply every part: 3 × 40 = 120 and 3 × 7 = 21.
Add the parts: 120 + 21 = 141.

The 4 in 47 is 4 tens, so 3 × 40 is 120, not 12.

The parts together are the whole rectangle, so their products add up to the whole product.

With 2 two-digit numbers there are 4 parts: every part of one number meets every part of the other.

Split by place, multiply every part, and add the parts.

Multiplying the 4 in 47 as a 4: 3 × 4 = 12 and 3 × 7 = 21, written side by side as 1221.

The 4 is 40: 3 × 40 = 120. Then add the parts: 120 + 21 = 141.

46 × 27 = ___ — 1242. Split by place and multiply every part: 800 + 120 + 280 + 42 = 1242.

23 × 14

Let's multiply twenty-three by fourteen. We'll use an area model to break it into easier parts.

Here's our problem: twenty-three times fourteen.

Break twenty-three into twenty plus three, and fourteen into ten plus four.

Draw a rectangle and split it into four parts — one for each piece.

Twenty times ten is two hundred.

Twenty times four is eighty.

Three times ten is thirty.

Three times four is twelve.

Now add all four partial products: two hundred plus eighty plus thirty plus twelve.

Twenty-three times fourteen equals three hundred twenty-two. Nice work!

Grade 4 · Area model with partial products

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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