Proportional Reasoning: common misconceptions

If your child says… “A bigger rectangle must have a different shape.”

Ask together

What happened to each measurement when you folded the sheet?

What’s true

Rectangles can differ in size while their width-to-height ratios match.

If your child says… “Swapping the numbers means the same thing.”

Ask together

Which bean belongs first when we say rajma to chickpeas?

What’s true

The first number belongs to the quantity named first.

If your child says… “Both numbers grew, so the ratios must match.”

Ask together

What multiplier changed each term from 2 to 3 into 4 to 6?

What’s true

Both terms must grow by one shared multiplier.

If your child says… “Adding the same amount keeps the ratio.”

Ask together

Milk doubled, but did water double?

What’s true

Equal additions affect unequal starting amounts by different factors.

If your child says… “I can double the first number and leave the other alone.”

Ask together

Two doubles to four. What must happen to three to keep the ratio unchanged?

What’s true

Changing only one term changes the ratio.

If your child says… “The bigger packet must be better value.”

Ask together

What would one kilogram cost using the smaller packets?

What’s true

Packet size alone cannot tell us the cost of an equal amount.

If your child says… “If the speed doubles, the travel time doubles too.”

Ask together

Would travelling faster make the same trip take longer?

What’s true

For a fixed distance, doubling speed halves travel time.

If your child says… “Three to one means three raisins for me and one for you.”

Ask together

How many raisins would your plan leave on the plate?

What’s true

The ratio counts parts, and all the raisins must be shared.