3. Number Play

11 topics2 h

Chapter 3 of NCERT Mathematics for Class 6: Number Play. Four sections — What a number is reporting, Playing with digits, Calculating cleverly and Where number play runs out of answers. 11 videos, 2 h in all.

Worked answers to the 40 exercise questions in this chapter →

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Part 1

What a number is reporting

10 minThe same children, different numbers: a number depends on what is being countedEight children say eight numbers. Rearrange the same eight children and every number changes — so the number was never a fact about the child. Draw one arrow per gap and the whole puzzle collapses into a single sum.10 min · 12 partsहिंदी11 minSupercells: a number's status comes from its neighbours34 is a supercell and 694 isn't, though 694 is twenty times bigger. Once you see that a supercell is a position rather than a size, one impossibility — two of them can never touch — settles every question the section asks.11 min · 12 partsहिंदी10 minPlacing a large number on the number line by feelTwo labelled marks are enough to finish an entire number line — and once you can read the step, 9590 and 9950 stop looking like the same number and land 360 apart.10 min · 12 partsहिंदी

Part 2

Playing with digits

11 minHow many numbers have a given number of digits, and why digit sums behaveThere are 90,000 five-digit numbers, and you can know that without writing one down. The same one move — fix a position, count what can stand there — also explains why 68, 176 and 545 all have digit sum 14.11 min · 12 partsहिंदी11 minPalindromes, and why reverse-and-add usually lands on oneAdd a two-digit number to its reverse and you always get eleven lots of its digit sum — which is symmetric by construction. That one fact explains every reverse-and-add example in the chapter, and where the whole thing breaks.11 min · 12 partsहिंदी10 minKaprekar's 6174: a process that always ends in the same place6174 rebuilds itself out of its own digits — and it is the only four-digit number that does. Which is why every start, all 8991 of them, has nowhere else to end up.10 min · 12 partsहिंदी11 minClock times and calendar dates: patterns the format lets you haveEvery palindromic date this century falls in February — all 29 of them, no exceptions. Not a coincidence: the century picks the month before anybody picks a date.11 min · 12 partsहिंदी

Part 3

Calculating cleverly

10 minRearranging a sum so it can be done in your headOut of every whole thousand there is, exactly one cannot be built from the book's five numbers — 1,000. And the bullseye's beautiful halve-and-double pattern turns out to be false: that outer ring holds eighteen discs, not sixteen.10 min · 12 partsहिंदी10 minEstimation: when an approximate answer is the right answerParomita rounds 96 up to 100 and then multiplies by five year groups — so she did not round once, she rounded five times, all upward. Her “about 500” is not uncertain in both directions; it is guaranteed about 20 too high. Knowing which way you are wrong beats knowing a margin of error.10 min · 12 partsहिंदी

Part 4

Where number play runs out of answers

10 minThe Collatz conjecture: a question a child can ask and nobody can settleFrom 100 the chain rises seven times and never once gets above 100. From 27 — a far smaller start — it takes 111 steps and climbs to 9,232. Its neighbours give no warning: 26 takes 10 steps, 28 takes 18. That is why nobody can prove this.10 min · 12 partsहिंदी9 minWinning strategies: working a game backwards from its endForwards, this game has 223,317 complete plays. Backwards, it has six numbers. And when the target moves from 21 to 22 the winner does not change hands — which is exactly why you do the division instead of trusting your intuition.9 min · 12 partsहिंदी

What you will be able to do

  • State, in your own words, what each child in the picture is counting
  • State the rule that makes a cell a supercell, including what happens at an end
  • Read the step of a number line from two labelled marks
  • State how many whole numbers have exactly one, two, three, four and five digits
  • Decide whether a given number is a palindrome
  • Carry out one round of the procedure on a given four-digit number
  • Explain why a "pretty" time is a fact about the display rather than about time
  • Reach a stated total by combining given numbers, reusing them as needed
  • Say when an exact count is needed and when an estimate will do
  • Work out the rule behind a set of printed sequences by comparing consecutive terms
  • Play the game accurately, adding within the permitted range each turn

What this chapter assumes you already know

  • Counting to small whole numbers, and comparing two quantities as taller / shorter
  • The idea of an ordered line: first position, last position, "next to"
  • Reading a picture as data rather than as decoration
  • Comparing multi-digit whole numbers, up to five digits
  • Reading a row and a grid of cells, and the words left, right, above, below
  • Writing large numbers with commas in the Indian place-value grouping
  • Number lines with small whole numbers, from earlier classes
  • Reading and writing numbers up to five digits, with the comma after the thousands digit

It builds directly on Mathematics is the search for patterns and for why they hold, Counting the parts of a shape sequence produces a number sequence and Every number sequence is a rule, not a list.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "The number belongs to the child."
  • "Saying 0 means you are short."
  • "Saying 2 means you are the shortest."
  • "Any row of 0s, 1s and 2s could happen."
  • "A child at the end could say 2 if they were short enough."
  • "Equal heights count as taller."
  • "Supercell means big."
  • "A cell at the end can't be a supercell, it's only half surrounded."