Finding Common Ground
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Biggest piece that fits both
Part of: Splitting into shared parts
Some jobs need one size that fits two measures exactly: tiles on a floor, equal grain bags, or jumps landing on two marks. The sizes that fit both are shared dividers, and the biggest of them is the HCF. Listing both divider lists and choosing the greatest shared number always works, and a bigger shared size means fewer pieces.
Why it matters. It picks the largest safe shared size, so floors need few tiles and packs stay fair.
Try it in two minutes
- List dividers of both numbers.
- Circle the shared ones.
- Pick the greatest shared one.
Try at home. Find the biggest square tile for a 12 by 18 mat using paper squares.
Breaking numbers into prime bricks
Part of: Splitting into shared parts
Every number above 1 is built from prime bricks multiplied together. The division ladder peels off one prime at a time until only a prime is left, and every factor of the number is some subpart of those bricks. Splitting in a different order always lands on the same bricks.
Why it matters. Prime bricks make shared dividers quick and certain, with no missed numbers.
Try it in two minutes
- Divide by the smallest prime that fits.
- Write the answer below and repeat.
- Stop at a prime and collect the side primes.
Try at home. Peel 60 with the ladder and list six of its factors from the bricks.
First moment both repeat together
Part of: Meeting at shared repeats
When two rhythms repeat, their shared landing moments are common multiples, and the first one is the LCM. Listing multiples suits small numbers, while bigger ones need the highest count of each prime from both brick lists. Multiples never end, so there is no biggest shared landing.
Why it matters. It predicts the next shared bell, bus or lamp blink without waiting.
Try it in two minutes
- List a few multiples of each number.
- Mark the shared ones.
- Pick the smallest shared one.
Try at home. Clap every 4 and hum every 6, and catch the first shared beat.
Fast ladders and the product link
Part of: Meeting at shared repeats
The joint ladder divides both numbers by shared factors together until the bottom row shares nothing, and the side numbers multiplied give the HCF. Doubling both numbers doubles the HCF, and for any pair, HCF times LCM equals the product. When one number divides the other, the smaller is the HCF and the larger the LCM.
Why it matters. It finds both answers in one short climb and checks them with the product link.
Try it in two minutes
- Pick a prime dividing both numbers.
- Write both answers below and repeat.
- Stop when answers share no prime.
Try at home. Run the joint ladder for 24 and 36 and check HCF times LCM.
What your child will practise
- Biggest piece that fits both: Candy Quick Fire (Quick Fire)
- Biggest piece that fits both: Mission Control Quest (Match It Up)
- Breaking numbers into prime bricks: Number Sort (Sort It Out)
- Fast ladders and the product link: Space Quick Fire (Quick Fire)
- First moment both repeat together: Desert Puzzle (Clue Puzzle)
- Quiz: Biggest piece that fits both (8 questions)
- Quiz: Breaking numbers into prime bricks (8 questions)
- Quiz: Fast ladders and the product link (8 questions)
- Quiz: First moment both repeat together (8 questions)