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Partition Shapes into Equal Parts to Build Fractions

Students will learn to divide shapes (circles, rectangles, squares) into a given number of equal parts. They will understand that all parts must be the same size for the partition to be valid, and they will name the number of equal parts (halves, thirds, fourths, sixths, eighths).

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Partition Shapes into Equal Parts to Build Fractions

Grade 3 · Understanding Unit Fractions · question 1 of 3

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12 rungs. A star at the top.

Uri shares a snack tray at the zoo. He cuts it into 2 equal parts and keeps 1 part. What fraction of the tray does Uri keep?

How it is taught

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A whole can be cut into equal parts.

3 equal parts are called thirds.

Read it: One part, then the shaded parts

A rectangle is cut into 6 equal parts. Each part is 1/6. 2 parts are shaded, so 2/6 is shaded.

  1. Count all the equal parts, shaded or not: 6.
  2. Name one part: 1/6.
  3. Count the shaded parts: 2, so 2/6.

The bottom number counts every equal part of the whole.

The top number counts the parts you are naming.

2 parts of 1/6 make 2/6.

The bottom number counts all the equal parts. The top number counts the shaded ones.

Counting only the parts that are not shaded, and writing 2/4.

Count every part, shaded or not. There are 6, so the bottom number is 6.

A tray is cut into 8 equal parts. 7 parts are shaded. What fraction is shaded? — 7/8. 7 parts of 1/8 each make 7/8.

Partition a rectangle into 4 equal parts (fourths)

Here's a chocolate bar. Four friends want to share it fairly. How can we cut it?

First, let's look at the whole bar — one big piece, not yet shared.

Now we make cuts so each friend gets the same amount. We split it into four pieces.

Look — every piece is the same size. That's what 'equal parts' means.

Share a bar with 4 friendsHow do we cut it fairly?Partition into equal parts1 whole bar✓✓✓✓All parts the same size4 equal parts = fourths1 fourth1 fourth1 fourth1 fourthone piece141 shaded out of 4 equal partsEACH FRIEND GETS14of the bar
Grade 3 · Sharing a chocolate bar with 4 friends

Four equal parts. We call each one a fourth.

Let's color in just one piece — that's one friend's share.

We write it like this: one over four. One out of four equal parts.

Each friend gets one-fourth of the bar. Great job partitioning!

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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