Patterns in Mathematics: common misconceptions

If your child says… “The first increase is one, so we keep adding one.”

Ask together

Does adding one take us from 2 regions to 4?

What’s true

Adding one fails at later counts, while doubling fits every fold.

If your child says… “A square number cannot also be triangular.”

Ask together

Did rearranging the chickpeas change how many we had?

What’s true

A count can fit both arrangements without gaining or losing anything.

If your child says… “Every new ring adds six dots.”

Ask together

How many dots does each group gain when we move to the next ring?

What’s true

Each new ring contains six more dots than the previous ring.

If your child says… “The last odd number is seven, so the total is seven squared.”

Ask together

Will the completed square have four cells along each side, or seven?

What’s true

The number of groups gives the square’s side length.

If your child says… “I can double the whole upward count.”

Ask together

Where is a second peak column in our arrangement?

What’s true

Doubling the upward count includes the peak twice.

If your child says… “The totals must also be 1, 2, 4 and 8.”

Ask together

When we add two after one, does the one disappear?

What’s true

A running total includes earlier groups as well as the latest addition.

If your child says… “The rows have 1, 2 and 3 little triangles.”

Ask together

Which tiles disappear from your count when you count only upward-pointing triangles?

What’s true

Counting tiles pointing both ways gives rows of 1, 3, 5 and 7.

If your child says… “It adds nine segments every time.”

Ask together

Does adding nine take the count from 12 to 48?

What’s true

Every existing segment gets replaced, so the total multiplies by four.