Number Play: common misconceptions

If your child says… “Changing plus to minus makes an even answer odd.”

Ask together

Can adding or removing complete pairs leave a new unpaired unit?

What’s true

Switching a sign changes the total by an even amount, including when answers become negative.

If your child says… “Any two even numbers make a multiple of four.”

Ask together

If only one pile leaves a pair, what completes that pair’s group of four?

What’s true

Both counts must have matching remainders when grouped into fours.

If your child says… “Passing the 4 and 6 tests means passing the 24 test.”

Ask together

Does 12 pass both tests while being too small to contain a complete 24?

What’s true

Passing both tests guarantees divisibility by their LCM, which can be smaller than their product.

If your child says… “The remainder is just the leftovers added together.”

Ask together

Can six still be the remainder when another group of five fits?

What’s true

A remainder cannot contain another complete group or be negative.

If your child says… “Ending in 4 means a number divides by 4.”

Ask together

After removing the hundred from 114, does the remaining 14 divide exactly by 4?

What’s true

For division by 4, the final two digits matter because complete hundreds already divide exactly.

If your child says… “Adding all the digits tests 11 too.”

Ask together

In the tens bracket, is the extra unit added or taken away?

What’s true

The tens contribution is subtracted because ten falls one short of eleven.

If your child says… “I stop after adding the digits once.”

Ask together

Does 18 have only one digit?

What’s true

Keep adding the resulting digits until just one digit remains.

If your child says… “Different letters can use the same digit.”

Ask together

If two different letters both mean 1, have they followed the different-digits rule?

What’s true

Each letter keeps its digit, different letters differ, and the first digit cannot be zero.