We Distribute, Yet Things Multiply: common misconceptions

If your child says… “Adding both strips finishes the rectangle.”

Ask together

Which place remains empty after both strips are added?

What’s true

The strips leave a corner that also needs counting.

If your child says… “Terms with x can all join together.”

Ask together

When x is two, are x and x squared equal?

What’s true

Combine terms only when their letters and powers match.

If your child says… “I can write every digit sum beside the next.”

Ask together

Where does the extra hundred go when the tens add up?

What’s true

A place holds one digit, so larger sums need carrying.

If your child says… “I just square each part and add.”

Ask together

Which pieces sit between the two squares?

What’s true

That count leaves out both rectangles.

If your child says… “The little square must be subtracted too.”

Ask together

How many sets of shading cover that corner?

What’s true

The corner already belongs to both subtracted bands.

If your child says… “I can put the two inside each square.”

Ask together

When both factors double, how many copies of the original product result?

What’s true

Doubling before squaring makes four copies of the original square.

If your child says… “Subtracting squares means squaring the difference.”

Ask together

Are the length and width of our remaining rectangle equal?

What’s true

The rectangle's sides are a plus b and a minus b.

If your child says… “An unfinished line must be incorrect.”

Ask together

Did expanding change how many coins the expression counts?

What’s true

An equality can hold before its terms are fully combined.