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Decomposing a shape into more equal shares

Understand that decomposing a shape into more equal shares creates smaller shares

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What a learner can do afterwards

  • Explain that a quarter of a pizza is smaller than a half of the same pizza
  • Demonstrate that fourths are smaller pieces than halves
  • Compare the size of halves and quarters of the same shape

1 · Read

You already know how to cut a shape into halves and fourths. Now watch what happens when the same shape is cut into more equal shares. The shape never grows, so every extra cut makes each piece smaller.

Tap to shade 1 of the 4 parts.
This circle is cut into 4 equal pieces. The shaded piece is one fourth, just one of the four pieces.
Try it together

Leo and Mia split a square herb bed into 4 equal parts, one herb in each part. Then they want 8 herbs in the same bed, so they mark 8 equal rows instead. The bed did not get any bigger, so each row is thinner than the 4 parts were.

Tap to shade 1 of the 8 parts.
Good to know

Here is the rule: cutting a shape into more equal shares always makes each share smaller, as long as the whole shape stays the same size.

The more equal shares a shape is cut into, the smaller each share becomes, so a fourth is always smaller than a half of the same shape.

2 · Watch

3 · Play

step 1 of 6

At Meadow Lane you cut the square herb bed into 4 equal parts last time. One part each for mint, parsley, chives and thyme.

Leo wants 8 herbs in the same bed, so he marks 8 equal rows instead. What happens to each row?

Tap to shade 1 of the 4 parts.

Take it off screen

Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.

Where it sits

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.

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Decomposing a shape into more equal shares · Mathematics, ages 6 to 7 · LightMySky