Multiply Multi-Digit Numbers Using Partial Products

Students use the partial products strategy to multiply multi-digit whole numbers, decomposing factors by place value and finding all partial products before summing. This builds conceptual understanding that prepares students for the standard algorithm.

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Grade 5 · Multi-Digit Whole Number Multiplication · question 1 of 3

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20 rungs. A star at the top.

20 × 30 = .

How it is taught

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Partial products are the place-by-place multiplies.

Every part of one factor meets every part of the other.

Read it: Partial products

38 × 26: split 38 by place, 30 + 8. Multiply each part by 26: 30 × 26 = 780 and 8 × 26 = 208. Add the parts: 780 + 208 = 988.

Split a factor by place: tens and ones, or hundreds, tens and ones.
Multiply every part by the other factor. Split both factors, and every part meets every part.
Add the partial products: their sum is the product.

38 rows of 26 are 30 rows of 26 and 8 more rows of 26, so the parts add to the whole.

A tens part is easy to multiply: 30 × 26 is 3 × 26 with a 0 after it.

The parts are not drawn to size; each box only holds its product.

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

Multiplying the 3 in 38 as 3, not 30: 78 + 208 = 286.

The 3 in 38 is 3 tens: 30 × 26 = 780, and 780 + 208 = 988.

57 × 36 = ___ — 2052. Split both by place and multiply every part: 1500 + 210 + 300 + 42 = 2052.

23 × 14

When numbers get bigger, we can break them apart to multiply. Let's try twenty-three times fourteen using partial products.

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

First, break each factor by place value. Twenty-three is twenty plus three. Fourteen is ten plus four.

Now multiply the parts. Twenty times ten is two hundred.

Next, twenty times four is eighty.

Then three times ten is thirty.

And three times four is twelve.

Almost there! Add up all four partial products.

Two hundred plus eighty plus thirty plus twelve is three hundred twenty-two. Twenty-three times fourteen equals three hundred twenty-two!

Grade 5 · Break each factor by place value, then add

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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