Perimeter and Area: common misconceptions

If your child says… “The space inside tells us how much ribbon we need.”

Ask together

Which part of the cover does the string follow?

What’s true

Ribbon around a border uses boundary length.

If your child says… “One length plus one breadth is enough.”

Ask together

Where do you finish after following just one long edge and one short edge?

What’s true

A rectangle has two lengths and two breadths around its boundary.

If your child says… “Every triangle’s perimeter is three times one side.”

Ask together

Do this triangle’s other edges match its shortest edge?

What’s true

Multiplying one side by three works only when all sides match.

If your child says… “Equal sides always make a shape regular.”

Ask together

Besides equal-side marks, which marks show that these shapes are regular?

What’s true

The angles must match too.

If your child says… “I counted squares, so the area is in centimetres.”

Ask together

Are you counting lengths along an edge or squares covering the surface?

What’s true

Centimetre squares measure coverage in square centimetres.

If your child says… “Every square the leaf touches counts as a whole square.”

Ask together

How much of this barely touched square was actually beneath the leaf?

What’s true

Count each edge square according to how much of it the leaf covers.

If your child says… “The narrower-looking triangle covers less.”

Ask together

What happens when you place one triangle exactly over the other?

What’s true

These matching triangles cover equal areas, whichever way they face.