Grades Grade 3 GeometryPartitioning Shapes into Equal Areas

Partitioning Shapes into Equal Areas

🔷 Geometry

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Partitioning Shapes into Equal Areas

Divide shapes into equal parts and name each part as a fraction of the whole!

When we PARTITION a shape, we divide it into equal parts. Each equal part has the same area. We can name each part as a fraction: if a shape is split into 4 equal parts, each part is 1/4 of the whole shape.

A square divided into 4 equal parts (2 × 2 grid):

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Each small square = 1/4 of the whole. All 4 together = 4/4 = 1 whole.

Steps to partition and name parts:

1Decide how many equal parts you want (e.g., 6)

2Draw lines that create 6 parts of EQUAL area

3Each part = 1/6 of the whole

4Two parts shaded = 2/6 (which can simplify to 1/3)

🎂Dividing a birthday cake

Cut a square cake into 8 equal rectangles.
Each piece is 1/8 of the cake.

If 3 pieces are eaten, 5/8 of the cake remains.
All 8 pieces together = 8/8 = 1 whole cake.

Equal parts ✓

Each section has the same area — valid partition

Unequal parts ✗

Sections have different sizes — NOT a valid partition for fractions

Only truly equal partitions let us use fraction names accurately!

\text{Equal parts: each part} = \frac{1}{n} \text{ of the whole}

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Remember This!

Different shapes can show the same fraction. A circle cut into 3 equal "pie" pieces and a rectangle cut into 3 equal strips both show thirds — even though the shapes look very different!

✏️ Try It!

A rectangle is partitioned into 6 equal parts. You shade 4 of them. What fraction of the rectangle is shaded?

Take Quiz 📝 — 25 Questions