Area: common misconceptions

If your child says… “Different shapes cannot have equal areas.”

Ask together

How many centimetre squares belong to each share?

What’s true

Different outlines can enclose the same number of unit squares.

If your child says… “I just add both strip areas.”

Ask together

Which patch belongs to both strips?

What’s true

Adding both areas counts their shared square twice.

If your child says… “Doubling the side only doubles the area.”

Ask together

How many small squares fit across, and how many rows fit?

What’s true

Doubling both dimensions makes the area four times as large.

If your child says… “The old height works with any side.”

Ask together

Does the old height meet your new base at a right angle?

What’s true

Each chosen base needs its own perpendicular height.

If your child says… “The more slanted triangle covers more space.”

Ask together

Do the base and perpendicular height change as the top corner moves along the upper line?

What’s true

Moving the top corner along this parallel line leaves the perpendicular height unchanged.

If your child says… “I can leave one triangle out of the total.”

Ask together

Which part of the shaded paper would your total leave uncounted?

What’s true

Add every inside triangle, or subtract all outside corners from the rectangle.

If your child says… “Overlapping the pieces keeps the same covered area.”

Ask together

Would every piece still cover a separate patch if you overlapped them?

What’s true

Overlapping pieces cover less surface because some paper covers paper.

If your child says… “One trapezium has the whole rectangle’s area.”

Ask together

How many matching pieces share the rectangle’s area?

What’s true

The rectangle contains two matching trapeziums, so each occupies half.