TM
New NCERT textbook · Class 8 Maths

Ganita Prakash, period by period — fitted to your timetable.

Tell Meyy your periods and their length; it plans every chapter of Ganita Prakash to fit, and you tick off sections as you teach.

Chapter 1 · Period 1 of 9 · 45 min

Which Lockers Stay Open? Reasoning About Factors

Opening Puzzle: The Locker Problem · Problem-solving

The locker puzzle is designed to surface the idea that perfect squares have an odd number of factors through reasoning, not definition — resist stating this fact before students articulate it. Watch for the common error of listing factors in pairs and forgetting that a square number has one factor that pairs with itself. No textbook exercise accompanies this opening section; the written justification doubles as a rough-and-ready formative check.

0–10Present the Queen Ratnamanjuri locker-problem scenario: 100 lockers, 100 people, person k toggles every kth locker. Students individually read the problem and write a prediction about which lockers are open at the end.
10–25Small groups simulate the process for lockers 1–20 using a toggle-table (columns 1–20, rows for each person, tick = toggle). Groups record which lockers end up open and report back.
25–38Whole-class discussion: Why does a locker end up open? Guide students to see that a locker is toggled once for every factor of its number, and so ends open exactly when it has an odd number of factors — which happens precisely when the number is a perfect square.
38–45Students write a two-sentence justification: 'Locker n stays open because…'. Collect written responses for formative awareness.
Assessment

In a row of 50 lockers numbered 1 to 50, each locker starts closed. Person k opens or closes every locker whose number is a multiple of k, for k = 1, 2, 3, …, 50. After all 50 people have acted, which lockers are open? Explain why exactly those lockers end up open.

Lockers 1, 4, 9, 16, 25, 36, and 49 are open. A locker is toggled once for each of its factors; it ends open only if it has been toggled an odd number of times, which happens exactly when it has an odd number of factors. A number has an odd number of factors if and only if it is a perfect square (because factors pair up except when a factor multiplied by itself gives the number). So the open lockers are precisely the perfect squares up to 50: 1, 4, 9, 16, 25, 36, 49.

Chapter 1 · 9 periods of 45 min

Also saved as 5 periods or 7 periods.

  • 2Building the Squares Table and Spotting Digit Patterns
    Square Numbers
  • 3Odd-Number Sums and the Inverted-L Proof
    Patterns and Properties of Perfect Squares
  • 4Triangular-Number Pairs and Square Root Methods
    Perfect Squares and Odd Numbers
  • 5Finding Square Roots: Three Methods, One Answer
    Square Roots
  • 6Cubes, Units Digits, and the Odd-Number Pattern
    Cubic Numbers
  • 7Prime Factorisation and the Cube-Root Test
    Cube Roots
  • 8Difference Patterns of Cubes and the Language of Roots
    Successive Differences
  • 9Squares, Cubes, and Roots: Four Problems, One Chapter
    Synthesis
Ganita Prakash · Class 8 · 14 chapters

Any 3 chapters free · no payment details · then introductory offer ₹499 per subject-stage, per year.