MathGrade 6ages 11–12
↩️ Inverse operation
A child who thinks of "undo" as simply "do something smaller in the other direction" may try to reverse a multiplication by subtracting, because subtraction feels like the opposite of a growing action.
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Download on the App StoreWhat your child learns
- Adding and subtracting undo each other.
- Multiplying and dividing undo each other.
- Subtraction cannot undo multiplication, because multiplying scales a number up while subtracting only takes a slice off it.
- When two operations happened one after the other, they are undone in the reverse order.
The mistake most kids make here
Undoing a multiplication with a subtraction.
Try one question
A number was multiplied by four. Which operation brings it back?
Multiplied by four
- divide by four
- subtract four
- add four
Answer
divide by four — That's it. The same number, the opposite operation.
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 which operation undoes multiplying by four.
How to help at home
Every operation has exactly one true opposite: addition undoes subtraction, and multiplication undoes division. Using the wrong pair only partly reverses what happened.
Show this with real groups of objects: make 4 groups of 3 buttons (12 total, from multiplying). Ask how to get back to one group of 3 — taking away buttons one at a time works, but dividing by 4 gets there in one clean step that matches how the groups were made.
Ask, before undoing anything: "what action made this number bigger — adding the same amount over and over, or adding one thing at a time?" That tells whether division or subtraction is the real opposite.
A sign they have it: given "a number was multiplied by 5", they say to divide by 5 to undo it, without needing to try subtracting first.
Questions parents ask
- Why does my child try to subtract to undo a multiplication?
- Subtraction feels like a natural opposite to any growing action, but multiplying scales a number up by repeating groups, and only dividing reverses that exact process.
- What is a hands-on way to practice inverse operations?
- Build groups of objects to show a multiplication happening, then compare undoing it by subtracting one at a time versus dividing by the group size in one step.
- What are the two pairs of inverse operations?
- Addition and subtraction undo each other, and multiplication and division undo each other — subtraction never undoes a multiplication, and addition never undoes a division.
- How does Maya teach inverse operations?
- Maya has the child compare undoing a real grouped multiplication by subtracting versus dividing, so the true inverse pair is discovered rather than told.
No card needed. The first lesson is free.
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