Understand Non-Unit Fractions as Multiple Unit Fractions

Students will extend their understanding of unit fractions to understand that a fraction a/b is formed by combining 'a' copies of the unit fraction 1/b. For example, 3/4 is 3 copies of 1/4. They will model this with area models and connect the shaded parts to the fraction notation.

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Grade 3 · Understanding Unit Fractions · question 1 of 3

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12 rungs. A star at the top.

2/4 = × 1/4

How it is taught

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A unit fraction has 1 on top.

A non-unit fraction is copies of that unit.

Read it: One piece, added again

1/8 + 1/8 + 1/8 = 3/8. 3 pieces of 1/8 make 3/8.

Find one piece: 1/8.
Add it again and again: 1/8 + 1/8 + 1/8.
Count the pieces: 3 eighths, so 3/8.

Each piece stays 1/8. Adding more does not make the pieces smaller.

The top number counts the pieces of 1/8.

The bottom number stays 8, because the pieces are still eighths.

3/8 is 3 pieces of 1/8: count the pieces for the top, and keep the bottom.

Adding the bottom numbers too, as if two eighths made sixteenths.

The pieces stay eighths. Add the pieces: 1/8 + 1/8 = 2/8.

1/8 + 1/8 + 1/8 + 1/8 + 1/8 = ___/8 — 5. 5 pieces of 1/8 make 5/8: the pieces stay 1/8.

3/4 = 1/4 + 1/4 + 1/4

Here's a chocolate bar. We want to take three-fourths of it. Let's see how.

First, we split the bar into four equal pieces.

Each piece is one-fourth. That's our unit fraction — one out of four equal parts.

Grade 3 · Three-fourths is three copies of one-fourth

Take one piece. That's one-fourth shaded.

Take another piece. Now we have two-fourths — that's two copies of one-fourth.

Take one more piece. Three-fourths shaded — three copies of one-fourth.

We can write it like this: three-fourths equals one-fourth plus one-fourth plus one-fourth.

So three-fourths is just three copies of the unit fraction one-fourth. Great job!

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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