Interpret (a/b) × q as Parts of a Partition

Students interpret (a/b) × q as finding a parts of a partition of q into b equal parts. For example, (2/3) × 12 means partition 12 into 3 equal parts and take 2 of those parts. Students use visual models such as number lines and area diagrams.

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Grade 5 · Multiplying Fractions · question 1 of 3

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20 rungs. A star at the top.

= 1/6 × 12

How it is taught

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A fraction times a whole splits that whole into equal parts, then takes some.

The bottom tells how many parts, and the top tells how many to take.

Read it: A fraction of a set

1/5 × 25 is 1/5 of 25: split the 25 into 5 equal groups of 5, and take 1 group. 1/5 × 25 = 5.

Split the set into as many equal groups as the denominator says: 5.
Count one group: 25 ÷ 5 = 5.
Take as many groups as the numerator says: 1 group is 5.

1/5 of a set is 1 of its 5 equal groups.

25 split into 5 equal groups is 5 in each.

1/4 × 8 works the same way: 8 split into 4 groups of 2, and 1 group is 2.

To find a fraction of a number, divide by the denominator, then take as many groups as the numerator.

Multiplying 25 by 5 instead of splitting it into 5 groups.

The denominator says how many groups: 25 ÷ 5 = 5 in each group.

4/5 × 20 = ___ — 16. Split 20 into 5 equal groups of 4, then take 4 of them: 16.

(2/3) × 12

Imagine twelve marbles. We want to find two-thirds of twelve. How many marbles is that?

We write this as two-thirds times twelve.

The bottom number — the denominator three — tells us to split twelve into three equal parts.

Here are the three equal parts of our twelve marbles.

Each part holds four marbles, because twelve divided by three is four.

The top number — the numerator two — tells us to take two of those parts.

Grade 5 · Finding two-thirds of twelve marbles

Shade two of the three parts.

Four plus four equals eight.

So two-thirds of twelve is eight marbles!

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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