Algebra Play: common misconceptions

If your child says… “I can subtract my starting number before halving.”

Ask together

If you subtract first, will the starting number also get halved?

What’s true

Halving first and subtracting first act on different amounts.

If your child says… “I just add every bottom number once.”

Ask together

Where does the middle 2 appear in the first line?

What’s true

The middle bottom number enters both neighbouring sums, so it reaches the top twice.

If your child says… “I divide the total by four, then subtract sixteen.”

Ask together

Does the sixteen belong to each date, or to the whole total?

What’s true

Remove the extra sixteen before sharing the remaining total between four equal copies.

If your child says… “The biggest two-digit number must give the biggest product.”

Ask together

Does the largest two-digit candidate give the largest result here?

What’s true

The multiplier acts on both places, so both factors affect the product.

If your child says… “Subtracting and dividing by nine gives the digit sum.”

Ask together

After collecting matching letters, are the digit terms added or subtracted?

What’s true

Larger minus smaller gives nine times the positive difference between their digits.

If your child says… “Adding back what was removed gives the starting amount.”

Ask together

After restoring the removed flowers, are you before or after the doubling?

What’s true

Adding back restores the doubled amount, so halving is still needed.

If your child says… “The next block includes all the coloured cells.”

Ask together

Which coloured cells were already there before the yellow block was added?

What’s true

The next block contains only the newly added cells.

If your child says… “I can pay first and double afterwards.”

Ask together

Starting with seven coins, could you pay eight before doubling?

What’s true

Payment follows doubling, and the doubled pile must contain enough coins for the fee.