Number Play: common misconceptions

If your child says… “Zero means it’s the tallest.”

Ask together

Which container behind the shortest one is taller?

What’s true

A taller container can stand behind one whose count is zero.

If your child says… “Adding odd numbers always gives an even answer.”

Ask together

When five spare coins pair up, what remains?

What’s true

An odd count of odd groups leaves a spare after pairing.

If your child says… “Both numbers must be even to make an even product.”

Ask together

Which row has a square without a partner?

What’s true

An even number of columns pairs every row, whatever the number of rows.

If your child says… “It gave an odd answer, so it always will.”

Ask together

When n is even, do three times n or four leave anything unpaired?

What’s true

Three times n plus four changes parity when n changes between odd and even.

If your child says… “Moving the numbers could change the grand totals.”

Ask together

Which entry would be missed when you add all the row totals?

What’s true

Rearranging the entries leaves both grand totals unchanged because each entry is still counted once.

If your child says… “Any number can go in the centre.”

Ask together

Could three copies of 9 account for the extra 15?

What’s true

The centre is fixed because those four lines count it three extra times.

If your child says… “Just double the last number.”

Ask together

Do both first moves leave the same number of stairs?

What’s true

The two first moves leave different numbers of stairs, so their route counts differ.

If your child says… “UT means U times T.”

Ask together

Which place does U occupy in the two-digit answer?

What’s true

Here, neighbouring letters fill digit places rather than multiply.