Another Peek Beyond the Point
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Sliding the point for tens
Part of: Decimals beyond the point
Splitting or growing by 10, 100 or 1000 only slides the point; the slide count matches the zero count, so one zero means one spot. Slides go left for splitting and right for growing. When digits run out, helper zeroes fill the gaps, as in 0.026. Kitchen maths leans on this: grams become kilograms with a three-spot slide.
Why it matters. Zero-counting turns slow measure sums into one quick slide and catches silly answers, like flour weighing more than the cook. Without it, children redo long division for every gram-to-kilogram change.
Try it in two minutes
- Write 437 on paper with a point hiding at its end.
- Ask the child to hop that point two spots left for splitting by a hundred.
- Flip it: grow 5.08 a thousandfold by hopping right, then check digits.
Try at home. Weigh three kitchen packs in grams and slide each into kilograms together.
Counting places in decimal products
Part of: Decimals beyond the point
Decimal multiplication hides a whole-number sum: strip the points, multiply as usual, then return every borrowed point digit to the answer. Two digits plus one digit means three digits after the point. Tiny numbers can shrink answers: two numbers below one always grow into something smaller than both.
Why it matters. The digit-count habit stops wild answers like a ribbon costing hundreds instead of tens. Without it, children trust any point position the pencil lands on.
Try it in two minutes
- Multiply 63 by 4 on paper and get 252.
- Ask the child where the point must sit so the answer stays near 25.
- Try 7 times 6 with three shared point digits and admire tiny 0.042.
Try at home. Price 3 notebooks at a made-up decimal rate and place the point by counting digits.
Long division that reaches past the ones
Part of: Decimals beyond the point
Long sharing marches past the ones: leftover ones regroup as tenths, leftover tenths as hundredths, and the point enters the answer at that crossing. A point divisor is gentled first by growing both numbers until it turns whole. Some shares never settle: ten among three trails threes forever.
Why it matters. Place-by-place sharing handles any split, even awkward ones like grain among boxes. Without it, children freeze the moment a remainder survives the ones.
Try it in two minutes
- Share 486 counters into 4 rings and watch 2 ones survive.
- Trade the survivors for 20 tenth-slips and deal 5 each.
- Mark the point in the answer where tenths began.
Try at home. Split a 7.5 metre tape into 3 parts on paper and name each share.
Checking the calendar with decimals
Part of: Decimals beyond the point
Earth rounds the Sun in about 365 and a quarter days, so plain 365-day years drift against the seasons. A bonus day every fourth year, skipped in century years and rescued every 400th year, keeps the calendar close: after a thousand years it lags truth by only a fifth of a day.
Why it matters. Calendar fixing shows decimals judging real plans, not just sums. Without it, leap years look like magic rules instead of careful decimal bookkeeping.
Try it in two minutes
- Multiply the yearly extra 0.2422 by 100 and read 24.22 days.
- Ask the child why a naked 365-day calendar would starve the seasons.
- Sort 2024, 2100 and 2000 into leap or skip piles.
Try at home. List the next eight leap years from this year using the divide-by-four test.
What your child will practise
- Checking the calendar with decimals: Space Quick Fire (Quick Fire)
- Counting places in decimal products: Desert Puzzle (Clue Puzzle)
- Long division that reaches past the ones: Mission Control Quest (Collect the Answer)
- Sliding the point for tens: Jungle Quest (Flip and Match)
- Sliding the point for tens: Number Quest (Match It Up)
- Quiz: Checking the calendar with decimals (8 questions)
- Quiz: Counting places in decimal products (8 questions)
- Quiz: Long division that reaches past the ones (8 questions)
- Quiz: Sliding the point for tens (8 questions)