Operations with Integers
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Finding pairs from sum and difference
Part of: Pairs and moves
Two hidden numbers leave two clues: their total and their gap, where gap means first minus second. Halve total-plus-gap to unhide the first, halve total-minus-gap to unhide the second. With total 31 and gap 13, the pair is 22 and 9. Swapping the two numbers flips the sign of the gap, so order always matters.
Why it matters. It turns blind guessing into a sure method the child can reuse for any hidden-pair riddle.
Try it in two minutes
- Recall that gap means first number minus second number.
- Recall total plus gap halved is the first number.
- Recall total minus gap halved is the second number.
- Link swapping the pair to flipping the sign of the gap.
Try at home. Pick a total and a gap, guess the pair, then check with halves.
Adding integers as directed moves
Part of: Pairs and moves
Every slide carries size plus side: right is up, left is down. Chain slides head to tail from zero and the landing spot is their sum; 6 right then 9 left lands on minus 3. Light and dark counters cancel in pairs to zero, and taking away any slide matches adding its reverse, so 6 minus minus 11 is 17.
Why it matters. It stops sign slips by tying every plus and minus to a visible side.
Try it in two minutes
- Recall right is up and left is down.
- Recall the landing spot is the sum of the slides.
- Recall a light-dark counter pair melts to zero.
- Link taking away to adding the reverse slide.
Try at home. Walk slides on a floor strip and call out each landing spot.
Multiplying integers and the sign rules
Part of: Times, shares and groupings
A bag starts empty: an up count drops token sets in, a down count lifts them out. 4 lots of negative 2 make minus 8, while lifting minus sets out, as in minus 4 lots of minus 2, leaves plus 8. Same sides yield up, mixed sides yield down, order never matters, and each minus-one fold flips the sign. Old Indian scholars framed this as fortunes and debts multiplying.
Why it matters. It replaces sign guessing with a bag picture plus a pattern the child can replay.
Try it in two minutes
- Recall 4 lots of negative 2 is minus 8.
- Recall minus 4 lots of minus 2 is plus 8.
- Recall old Indian fortune-debt rules for signs.
- Link swapping the pair to the same product.
Try at home. Lay out button rows for 3 times negative 4 and count the colour.
Dividing integers and grouping expressions
Part of: Times, shares and groupings
Division undoes multiplication: minus 100 shared by 25 asks which multiplier rebuilds minus 100, namely minus 4. Sign rules match multiplication: mixed sides share down, same sides share up. Chains group freely, so neighbours multiply first in any order, and an odd count of down sides keeps the product down. A multiplier also shares across a sum, as in minus 3 lots of 8 plus minus 5.
Why it matters. It lets the child split, share and regroup integers without fear of long chains.
Try it in two minutes
- Recall minus 100 shared by 25 is minus 4.
- Recall odd counts of down sides stay down.
- Recall neighbours group freely in chains.
- Link splitting a sum first to sharing the multiplier.
Try at home. Rebuild minus 36 from 9 by hunting the missing multiplier.
What your child will practise
- Adding integers as directed moves: Candy Quick Fire (Quick Fire)
- Dividing integers and grouping expressions: Mission Control Quest (Collect the Answer)
- Finding pairs from sum and difference: Candy Puzzle (Clue Puzzle)
- Multiplying integers and the sign rules: Number Quest (Match It Up)
- Multiplying integers and the sign rules: Ocean Quest (Flip and Match)
- Quiz: Adding integers as directed moves (8 questions)
- Quiz: Dividing integers and grouping expressions (8 questions)
- Quiz: Finding pairs from sum and difference (8 questions)
- Quiz: Multiplying integers and the sign rules (8 questions)