MathGrade 7ages 12–13
📊 Percent change
A child who is not sure which number is the "starting point" of a change may divide by whichever number comes second in the problem, which is often the new price rather than the original one it should be measured against.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- First find the size of the change itself.
- Divide the change by the original value, because that is the starting point everything is measured from.
- That result times a hundred gives the percent.
- A 10 percent rise followed by a 10 percent fall does not return to the original, because the fall is measured off a bigger price.
The mistake most kids make here
Dividing the change by the new price instead of the old one.
Try one question
A price rose from 50 to 60. By what percent?
50 became 60
- 20
- 10
- 17
Answer
20 — That's it. We divided the change by the original price.
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 by what percent a price rose from 50 to 60.
How to help at home
Percent change always measures how big the change is compared to where things started — the original value — not compared to where they ended up.
Take a real, familiar price change: something that cost 50 and now costs 60. Ask your child to find the size of the change first (10), separately from deciding what to divide it by.
Then have them try dividing that 10 by both numbers — by 50 and by 60 — and compare the two percents. Explain that only dividing by the original 50 answers "how much did it grow, compared to what it used to be?"
A sign they have it: given a new price change, they identify the original value first and divide by it, without trying the new value as well.
Questions parents ask
- Why does my child divide by the new price instead of the old one for percent change?
- Without a clear rule for which number is the starting point, either number in the problem can seem like a reasonable choice to divide by.
- What is a hands-on way to practice percent change?
- Use a real price change your child recognizes, find the size of the change, then compare dividing it by the original price versus the new price to see why only one answers the right question.
- Why does a 10% rise followed by a 10% fall not return to the original price?
- Each percent change is measured against a different, changing original value — the fall is 10% of a larger number than the rise was, so it removes more than the rise added.
- How does Maya teach percent change?
- Maya has the child compare dividing by the original value versus the new value on a real example, so the correct starting point is discovered by contrast, not stated as a rule.
No card needed. The first lesson is free.
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