MathGrade 6ages 11–12
⚖️ A ratio in the shop
A ratio like "2 to 1" written next to "4 to 2" looks, to a child, like the second one must be bigger — because both its numbers are bigger — even though the two describe exactly the same comparison.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- A ratio compares two amounts to each other.
- When both sides are multiplied by the same number each side grows by the same factor, so the ratio does not change.
- Adding the same number to both sides does change the ratio, because a fixed addition is bigger for the smaller side.
- The order in a ratio says which amount is counted first.
The mistake most kids make here
Thinking 2 to 1 is smaller than 4 to 2 because the numbers are smaller.
Try one question
6 sweets for 3 children. What is the ratio per child?
6 to 3
- 2 to 1
- 3 to 6
- 9 to 1
Answer
2 to 1 — That's it. Divide 6 by 3 and each child gets two.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say why 2 to 1 and 4 to 2 are the same ratio.
How to help at home
A ratio compares two amounts to each other, and what matters is how they compare, not how big the individual numbers are. Multiplying both sides of a ratio by the same number keeps the comparison identical, even though the numbers themselves grow.
Use real objects at a pretend shop: 2 apples cost 1 coin, so how much do 4 apples cost? Lay out 2 apples and 1 coin, then 4 apples and however many coins your child thinks is fair, and check by pairing them up two-and-one at a time.
When your child says 4 to 2 must be a "bigger" ratio than 2 to 1, say: "let's pair them up, two apples to one coin at a time, and see if the deal is really different" and physically group the objects to compare.
A sign they've got it: they can say that doubling both numbers in a ratio doesn't change the deal — 4 to 2 buys apples at exactly the same rate as 2 to 1 — while adding the same number to both sides would change it.
Questions parents ask
- Why does my child think 4 to 2 is a bigger ratio than 2 to 1?
- Bigger numbers look like a bigger amount, but a ratio describes a rate of comparison, not a total. Multiplying both sides by the same number keeps that rate identical, which pairing up real objects two at a time makes visible.
- What age do children learn about ratio?
- Ratio is typically introduced around grade 6, building on a solid understanding of multiplication, division, and fractions.
- How is a ratio different from a fraction?
- A ratio compares two separate amounts to each other, like apples to coins, while a fraction usually describes a part of one single whole — though the two ideas share the same underlying math of equal scaling.
- How does Maya teach ratio?
- Maya has the child pair up quantities at the original rate before checking a scaled-up version, so the equal deal becomes visible rather than assumed from the size of the numbers.
No card needed. The first lesson is free.
Download on the App StoreMore Math lessons
- 10% offGrade 6
- The hidden numberGrade 6
- A bar graphGrade 6
- ProportionGrade 6
- ChanceGrade 6
- Radius and diameterGrade 6
- Volume formulaGrade 6
- Inverse operationGrade 6