Fluently Multiply Multi-Digit Whole Numbers Using the Standard Algorithm

Students apply the standard multiplication algorithm fluently to multiply multi-digit whole numbers, including problems up to 4-digit by 2-digit. They correctly regroup (carry) values and align partial products with accurate place value positioning.

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

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236 × 7 =

How it is taught

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This stacked method multiplies one digit of the second factor at a time.

Each new row of partial products shifts one place left.

Then you add the rows.

Read it: The standard algorithm

347 × 28: write 347 over 28. The ones row: 347 × 8 = 2776. The tens row: write a 0, then 347 × 2 = 694, so 6940. Add the rows: 2776 + 6940 = 9716.

Write the bigger number on top, ones under ones.
Multiply the top number by each digit of the bottom number, one row for each digit.
Start the tens row with a 0 in the ones place, then add the rows.

The rows are partial products: 347 × 8 and 347 × 20, the parts of 28.

The 2 in 28 is 2 tens, so its row is 347 × 20, and the 0 holds the ones place.

This is the area model written short: the same parts, added in two rows.

One row for each digit of the bottom number, a 0 to start the tens row, then add the rows.

Leaving out the 0 in the tens row: 2776 + 694 = 3470.

The tens row is 347 × 20 = 6940: 2776 + 6940 = 9716.

746 × 67 = ___ — 49,982. 746 × 7 = 5222, and 746 × 60 = 44,760: 5222 + 44,760 = 49,982.

245 × 13

When numbers get bigger, we use a method called the standard algorithm. Let's multiply two-hundred forty-five by thirteen.

Stack the numbers, lining the digits up by place value, and draw a line.

Start with the ones. Three times five is fifteen — write the five, and carry the one.

Three times four is twelve, plus the one we carried is thirteen. Write three, carry one.

Three times two is six, plus the one we carried is seven. Write seven. Our first partial product is seven-hundred thirty-five.

Now we move to the tens digit. First, drop a zero in the ones place to hold its spot.

One times five is five.

One times four is four.

One times two is two. Our second partial product is two-thousand four-hundred fifty.

Now add the two partial products together.

Two-hundred forty-five times thirteen is three-thousand one-hundred eighty-five. Great work!

Grade 5 · The standard algorithm with regrouping

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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