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Themed maths

Maths about me: a start-of-term icebreaker for IGCSE and GCSE

A first lesson that gets everyone talking and doing maths straight away: number facts built from a birthday, ‘Who am I?’ riddles in pairs and the four 4s challenge. Everything is on paper and nothing personal is collected.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Number: primes, factors, HCF and LCM; Number: order of operations; Counting arrangements
Equipment
No calculator needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minMaths about me
Main: task B10 min‘Who am I?’ in pairs
Main: task C13 minFour 4s
Extension10 minFast finishers or homework

Starter (5 minutes)

‘Who am I?’ riddles on the board as students arrive.

  1. I am a two-digit prime. My digits add up to 10 and my tens digit is bigger than my units digit. Who am I?
  2. I am a square number between 50 and 100, and I am 1 more than a multiple of 8. Who am I?
  3. I am a multiple of 6 and of 15, and I am less than 50. Who am I?
  4. I am a cube number bigger than 1. Add 1 to me and you get a square number. Who am I?

Main activity (35 minutes)

Task A: Maths about me (12 min)

Work through Sam’s made-up numbers first. Then do the same with your own birthday and favourite numbers on paper.

  1. Sam’s birthday is the 24th, and Sam’s house number is 132. Write 24 and 132 as products of prime factors.
  2. Find the HCF and the LCM of 24 and 132.
  3. Sam was born in month 9, so the birthday digits are 2, 4, 0 and 9. How many 4-digit numbers use each of these digits once? How many of them are even?

Task B: ‘Who am I?’ in pairs (10 min)

Solve these with a partner. Then each write a riddle of your own with exactly one answer and swap.

  1. I am between 100 and 200. I am a multiple of 7 and of 11, and my digits add up to 10. Who am I?
  2. I am the smallest number bigger than 1 that leaves remainder 1 when divided by 2, 3, 4, 5 or 6. Who am I?
  3. I am a two-digit number. Add me to the number with my digits reversed and you get 121. My two digits differ by 5. Who could I be?

Task C: Four 4s (13 min)

Use exactly four 4s with +, −, ×, ÷ and brackets to make each target. You may also join two 4s to make 44. Other answers are possible.

  1. Make 2.
  2. Make 7.
  3. Make 9.
  4. Make 20.

Extension (10 minutes)

For fast finishers.

  1. Make 15 and 17 with four 4s.
  2. Find every two-digit number that is 4 times the sum of its digits.

For teachers

Teacher notes and full worked answers
  • Nothing personal is collected: students work on paper, and nothing is typed into the site or stored. If a student would rather not use a real birthday, any date works.
  • Pairs for task B: each student writes one riddle with exactly one answer and swaps with a partner, who checks that only one number fits.
  • Mindset prompts for the first lesson (for you to read out or put on the board; nothing is collected or stored): ‘A time maths felt hard, and what helped’; ‘One topic from last year I could teach a friend’; ‘What I do when I am stuck’; ‘How I want this class to feel’.
  • Four 4s: keep a class list of the targets from 1 to 20 that have been made, and add to it during the first weeks of term.

Starter

  1. 73
    • Two-digit primes with digit sum 10: 19, 37, 73.
    • Only 73 has the bigger tens digit.
  2. 81
    • The squares are 64 and 81.
    • 64 = 8 × 8 and 81 = 8 × 10 + 1.
  3. 30
    • The LCM of 6 and 15 is 30.
    • The next common multiple is 60, which is too big.
  4. 8
    • 8 + 1 = 9 = 32.
    • No other cube up to 10 000 works: 27 + 1 = 28, 64 + 1 = 65, 125 + 1 = 126, …

Task A: Maths about me

  1. 24 = 23 × 3 and 132 = 22 × 3 × 11
    • 24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3
    • 132 = 2 × 66 = 2 × 2 × 33 = 2 × 2 × 3 × 11
  2. HCF = 12, LCM = 264
    • HCF: the common prime factors 22 × 3 = 12
    • LCM: the highest powers 23 × 3 × 11 = 264
  3. 18 numbers; 14 are even
    • All orders: 4 × 3 × 2 × 1 = 24. Those starting with 0 are not 4-digit numbers: 3 × 2 × 1 = 6. So 24 − 6 = 18.
    • Ending in 0: 3 × 2 × 1 = 6. Ending in 2: 2 × 2 × 1 = 4 (the first digit cannot be 0). Ending in 4: also 4. Even: 6 + 4 + 4 = 14.

Task B: ‘Who am I?’ in pairs

  1. 154
    • Multiples of 77 between 100 and 200: 154 only.
    • 1 + 5 + 4 = 10
  2. 61
    • One less than me is a multiple of 2, 3, 4, 5 and 6.
    • LCM(2, 3, 4, 5, 6) = 60, so I am 60 + 1 = 61.
  3. 38 or 83
    • (10a + b) + (10b + a) = 11(a + b) = 121, so a + b = 11.
    • Digits adding to 11 and differing by 5: 8 and 3. So 38 or 83.

Task C: Four 4s

  1. 4/4 + 4/4 = 2
    • 1 + 1 = 2
  2. 44/4 − 4 = 7
    • 44 ÷ 4 = 11, and 11 − 4 = 7
  3. 4 + 4 + 4/4 = 9
    • 8 + 1 = 9
  4. (4 + 4/4) × 4 = 20
    • 4 + 1 = 5, and 5 × 4 = 20

Extension

  1. 4 × 4 − 4/4 = 15 and 4 × 4 + 4/4 = 17
    • 16 − 1 = 15 and 16 + 1 = 17
  2. 12, 24, 36 and 48
    • 10a + b = 4(a + b) gives 6a = 3b, so b = 2a.
    • a = 1, 2, 3, 4 give 12, 24, 36, 48 (a = 5 would need b = 10).

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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