Fractions in Disguise: common misconceptions

If your child says… “Five shaded columns means 5%.”

Ask together

When you count cells instead of columns, how many shaded parts are there?

What’s true

Count shaded parts and total parts using the same-sized pieces.

If your child says… “A percentage cannot go beyond 100%.”

Ask together

If this whole strip is 100%, what happens when the length extends beyond it?

What’s true

A length greater than the reference strip has a percentage greater than 100%.

If your child says… “Two heads and three tails means heads are two-thirds of the coins.”

Ask together

Are there three coins altogether, or five?

What’s true

The whole includes both heads and tails.

If your child says… “Both are 50%, so both pieces must be the same size.”

Ask together

Did the two starting portions contain the same amount of roti?

What’s true

Equal percentages can give unequal amounts when the wholes differ.

If your child says… “A 50% rise and a 50% fall cancel.”

Ask together

Does the fall remove half of 4 rupees or half of 6 rupees?

What’s true

The fall takes half of a larger amount than the rise used.

If your child says… “Three pieces always mean 75%.”

Ask together

What makes each piece here the same share of the sheet?

What’s true

Counting pieces gives area shares only when those pieces have equal areas.

If your child says… “The tax calculation gives the whole bill.”

Ask together

Where does the original 20 rupees appear in the amount paid?

What’s true

The percentage calculation gives tax alone; the bill also includes the subtotal.

If your child says… “Where can it land?”

Ask together

Which destination completes both the two-square part and the one-square part?

What’s true

The destination must complete both parts of the move.