Represent Multiplication on a Number Line

Students use number lines to model multiplication as repeated equal-sized jumps. They practice drawing and interpreting skip-counting jumps to connect repeated addition to multiplication, building a bridge from prior knowledge to the new operation.

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Grade 3 · Understanding Multiplication · question 1 of 3

0 of 12

12 rungs. A star at the top.

Which hop plan lands farther from 0: two hops of 9, or four hops of 4?

they land on the same number

two hops of 9

four hops of 4

neither plan leaves 0

How it is taught

0:00 of 3:27

Multiplication is equal jumps on a number line.

Jumps start at 0 and stay the same size.

Read it: Multiply with equal jumps

6 jumps of 4 from 0 land on 4, 8, 12, 16, 20, 24. So 6 × 4 = 24.

Start at 0.
Make the number of jumps, each the same size: 6 jumps of 4.
Read where you land: 6 × 4 = 24.

Each jump of 4 is 1 group of 4, so 6 jumps are 6 groups.

The jumps are all the same size, which is what makes it multiplying.

Where the last jump lands is the total of all the groups: 24.

Equal jumps from 0: the number of jumps times the size of each jump.

Counting the marks instead of the jumps, or starting the first jump at 1.

Start at 0 and count the jumps: 6 jumps of 4 land on 24.

Start at 0 and make 5 jumps of 3. Where do you land? — 15. 3, 6, 9, 12, 15. So 5 × 3 = 15.

4 × 3 = 12

Today let's see multiplication on a number line. Picture a frog making four jumps, and each jump is three steps long. Where will it land?

Here is our number line, starting at zero. Each little tick is one step.

Jump one — three steps from zero lands us on three.

Jump two — three more steps lands on six.

Jump three — three more steps lands on nine.

Jump four — three more steps lands on twelve.

We added three, four times: three plus three plus three plus three equals twelve.

Four equal jumps of three is the same as four times three.

Four times three equals twelve. Multiplication is just repeated equal jumps!

Grade 3 · Four equal jumps of three on a number line

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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