Operations with Integers: common misconceptions

If your child says… “Swapping the numbers keeps their difference the same.”

Ask together

After swapping, does the first pile have extra coins or fewer coins?

What’s true

First minus second changes sign when unequal numbers exchange places.

If your child says… “I subtract the smaller distance from the larger one.”

Ask together

Does moving just 1 cm right even reach zero?

What’s true

Movement across zero includes the distance on both sides.

If your child says… “Three is positive, so the answer must be positive.”

Ask together

If every jump goes left from zero, can the final position be positive?

What’s true

Repeating a negative amount a positive number of times gives a negative total.

If your child says… “The answers stay at zero once the table reaches zero.”

Ask together

Why would removing the next negative group leave the answer unchanged?

What’s true

The same change continues when the first factor passes zero.

If your child says… “I must subtract a loss even when it already has a minus sign.”

Ask together

Would subtracting negative four make this cooling temperature rise?

What’s true

Add a change already written as negative; subtracting it would reverse the loss.

If your child says… “I multiply the answer by the first number to check division.”

Ask together

In our multiplication line, which number multiplies q?

What’s true

Multiply the answer by the divisor to recover the number being divided.

If your child says… “The outside number multiplies only the first number inside brackets.”

Ask together

If every group has two parts, can multiplying whole groups leave one part unchanged?

What’s true

Each term inside an addition bracket receives the outside multiplier.

If your child says… “Three factors always give a negative answer.”

Ask together

Which of these three factors actually carry negative signs?

What’s true

Without zero factors, count negative factors alone to choose the product’s sign.