Finding the Unknown: common misconceptions

If your child says… “Removing just one spoon keeps it balanced.”

Ask together

What would match the weight removed from that pan?

What’s true

Removing equal weights preserves the balance.

If your child says… “Each pencil gets another bag charge.”

Ask together

Does buying more pencils add more bags here?

What’s true

The bag charge appears once because there is only one bag.

If your child says… “Getting a number on the left proves it.”

Ask together

What must your result match?

What’s true

A solution, including zero, must make both original sides equal.

If your child says… “The changed expression still equals five.”

Ask together

What happened to the right side when we added two?

What’s true

The totals increase equally, while the same unknown value still works.

If your child says… “The plus two becomes plus two on the right.”

Ask together

Which operation cancelled the added two on the left?

What’s true

The subtraction on the right records what we did to both sides.

If your child says… “I'll subtract the two to leave x.”

Ask together

Does the first line show two added to x or two copies of x?

What’s true

Here, two multiplies x rather than being added.

If your child says… “I'll add the x terms from opposite sides.”

Ask together

Would adding x remove the copy on the right?

What’s true

Subtracting x from each side removes the right-hand copy.

If your child says… “Two multiplies x, but leaves minus one alone.”

Ask together

How many times are we subtracting one?

What’s true

Taking the whole bracket twice also repeats its subtraction.