E ExamMaster

CBSE Class 7 · Mathematics

Number Play

Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Number Play” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 7
  • Easy level
  • 8 concepts

1Numbers Tell us Things

A number can tell parity, a remainder, a place in a sequence. “Tell us things” means a property you can name, not a fortune.

A lucky number story is not this telling.

Figure. A number is a bundle of tests you can run. 12 is even, and it splits by 3 and by 4. The numeral is the name; the tests are the news.

How it works

  1. Pick a numberThis one.
  2. Name a property you can testEven, odd, remainder, place.
  3. Write that propertyWhat it told.

2Picking Parity

Parity is even or odd: even is divisible by 2, odd is not. Sums: even+even and odd+odd are even; even+odd is odd. That is a pick you can rerun.

A last digit of 3 is odd — you do not need the whole crore.

Figure. Parity is a two-bin sort. Even marks sit on the E chips; odd marks sit on the O chips. Pairing decides the bin, not the look of the digit.

How it works

  1. Look at the ones digit (or divide by 2)The test.
  2. Name even or oddParity.
  3. For a sum, combine the two paritiesThe rule.

Parity of a sum

Is 128 + 37 even or odd?

  • 128even
  • 37odd
  • even + oddodd

Pro tip. You only needed the two parities, not the full sum.

3Some Explorations in Grids

A grid can hide a sum, a parity pattern, or a path. Exploration means a rule you try on the cells you have, then check the next cell.

Colouring a grid with no rule is decoration.

Figure. A 3×3 exploration: 2+7+6 = 15, and every other line of this square is 15 as well. The grid is the test, not a decoration.

How it works

  1. State a candidate ruleRow sums to 10, or alternate parity.
  2. Check the cells you already haveEvidence.
  3. Predict one more cellThe play.

4Nature’s Favourite Sequence: The Virahāṅka–Fibonacci Sequence

The Virahāṅka–Fibonacci sequence grows by adding the previous two: 1, 1, 2, 3, 5, 8, … (or 0, 1, 1, 2, … if you start that way). Nature’s favourite here means it shows up in many counts — not that every plant is a proof.

Skipping a term and calling it Fibonacci is a miss.

Figure. Virahāṅka–Fibonacci: each new term is the sum of the two before it. The last step shown is 3+5 = 8.

How it works

  1. Write two starting termsThe given start.
  2. Next = sum of the previous twoThe rule.
  3. Check the next given term if you have oneThen continue.

5Digits in Disguise

A digit in disguise is a digit doing another job: a letter standing for a digit in a cryptarithm, or a hidden place-value. Unmask means name the digit and the job.

A pretty letter is not a digit until you say which 0–9 it is (and that it fits).

Figure. The ink 6 means 60 only in the tens house. Swap the houses and the same digits name 36, not 63. The house, not the mark, is the value.

How it works

  1. See the disguiseA letter, or a hidden house.
  2. Name the digit 0–9 if the puzzle allowsThe unmask.
  3. Check the sum or product still holdsThe disguise worked.

6A definition is a test you can run

Even, odd, Fibonacci-next, grid-rule — each is a test you can run. A definition that is only a name is not play yet.

“Sequence” without a next-term rule is a list.

Figure. Even is a test you can run: split into two equal groups. 8 becomes 4 and 4. 7 becomes 3 and 3 with 1 left over, so it fails.

How it works

  1. Pick one definition from this chapterParity, or the add-two rule.
  2. Run it on a number or a pairThe test.
  3. If you cannot run it, you do not yet have itPlay is a test.

7Name the given before the unknown

The given may be two Fibonacci terms, or a grid row. The unknown is the next term or the missing cell. Name the given first.

Inventing the start 1, 1 when the problem gave 2, 3 is a silent swap.

Figure. Name the given pair before hunting the next Virahāṅka term. 5 and 8 are known; only then is the unknown allowed.

How it works

  1. Write the given terms or cellsThe given.
  2. Name what is missingThe unknown.
  3. Apply the rule only to those givensGiven first.

8One worked case is enough at this class

One next-term or one parity-sum is enough. You do not need twenty Fibonacci terms to hold the add-two rule.

A long clone list is not a new sequence.

Figure. One worked Virahāṅka step is enough at this class: 5 + 8 = 13. The same add-the-two-before rule then repeats.

How it works

  1. Compute one next term (or one parity)The case.
  2. Optional: one more as a checkA second case.
  3. StopThis class.
The next Virahāṅka–Fibonacci term after 5, 8 is
  1. 13
  2. 10
  3. 40

Add the previous two: 5+8=13.

Notes

  • The official chapter title is “Number Play”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • even + even = even
  • odd + odd = even
  • even + odd = odd
  • Fibonacci: next = previous + one-before

Recap

Hold these pegs from the official chapter “Number Play”. The wording is ExamMaster’s teaching, not a textbook recap.

Numbers Tell us Things
A number can tell parity, a remainder, a place in a sequence.
Picking Parity
Parity is even or odd: even is divisible by 2, odd is not.
Some Explorations in Grids
A grid can hide a sum, a parity pattern, or a path.
Nature’s Favourite Sequence: The Virahāṅka–Fibonacci Sequence
The Virahāṅka–Fibonacci sequence grows by adding the previous two: 1, 1, 2, 3, 5, 8, … (or 0, 1, 1, 2, … if you start that way).
Digits in Disguise
A digit in disguise is a digit doing another job: a letter standing for a digit in a cryptarithm, or a hidden place-value.
A definition is a test you can run
Even, odd, Fibonacci-next, grid-rule — each is a test you can run.

Practise Number Play

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.