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Themed maths

Maths about me: a first-lesson icebreaker for IB Maths

A first lesson of the year that gets everyone talking and doing maths: number facts built from a birthday, ‘Who am I?’ riddles that preview sequences, logs and counting, and the four 4s challenge. Everything is on paper and nothing personal is collected.

Level
IB Maths SL and HL (AA and AI)
Time
40 minutes, plus a 10-minute extension
Topics
Prime factorisation and number; Sequences and series; Exponents and logarithms; Counting
Equipment
The starter is non-calculator. A GDC is useful for task A.

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 positive integer. My square is 4 more than 3 times me. Who am I?
  2. I am the 10th term of the arithmetic sequence 7, 11, 15, … Who am I?
  3. I am log2 64 + log3 81. Who am I?
  4. I am the number of ways to arrange the letters of the word MATHS in a row. Who am I?

Main activity (35 minutes)

Task A: Maths about me (12 min)

Work through Alex’s made-up numbers first. Then write the same facts about your own numbers on paper.

  1. Alex was born on day 28 of month 6 in 2009. Write 28 and 2009 as products of prime factors.
  2. Find the HCF and the LCM of 28 and 2009.
  3. The arithmetic sequence 6, 28, 50, … starts with Alex’s month and day. Which term is closest to 2009, and what is it?
  4. Solve 2x = 28, giving x to 3 significant figures.

Task B: ‘Who am I?’ in pairs (10 min)

Solve these with a partner. Then each write a riddle of your own, on a topic from last year, with exactly one answer and swap.

  1. I am a three-digit multiple of 9 and of 11, and my hundreds digit is 7. Who am I?
  2. I am the sum of the first n odd numbers, and I am between 200 and 250. Who am I, and what is n?
  3. I am the sum to infinity of a geometric series with first term 12 and second term 4. Who am I?
  4. I am the positive integer n with nC2 = 45. Who am I?

Task C: Four 4s (13 min)

Use exactly four 4s to make each target. Allowed: +, −, ×, ÷, brackets, powers, √ and ! (4! = 24). You may join two 4s to make 44. Other answers are possible.

  1. Make 24 using only +, −, × and ÷.
  2. Make 64.
  3. Make 19.
  4. Make 1024.

Extension (10 minutes)

For fast finishers.

  1. Prove that the sum of any two-digit number and the number with its digits reversed is a multiple of 11.
  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’.
  • The riddles preview the first topics of the course: sequences and series, exponents and logarithms, and counting.

Starter

  1. 4
    • x2 = 3x + 4, so (x − 4)(x + 1) = 0
    • x = 4 (the other root, −1, is not positive)
  2. 43
    • u10 = 7 + 9 × 4 = 43
  3. 10
    • log2 64 = 6 and log3 81 = 4
    • 6 + 4 = 10
  4. 120
    • 5! = 5 × 4 × 3 × 2 × 1 = 120

Task A: Maths about me

  1. 28 = 22 × 7 and 2009 = 72 × 41
    • 28 = 4 × 7 = 22 × 7
    • 2009 = 7 × 287 = 7 × 7 × 41, and 41 is prime
  2. HCF = 7, LCM = 8036
    • HCF = 7 (the only common prime, to the lower power)
    • LCM = 22 × 72 × 41 = 8036
  3. The 92nd term, 2008
    • un = 6 + 22(n − 1)
    • 6 + 22(n − 1) = 2009 gives n − 1 = 91.04…
    • u92 = 6 + 22 × 91 = 2008 (and u93 = 2030)
  4. x = 4.81
    • x = log2 28 = ln 28 / ln 2 = 4.807…

Task B: ‘Who am I?’ in pairs

  1. 792
    • Three-digit multiples of 99: 198, 297, …, 990.
    • Only 792 starts with 7.
  2. 225, with n = 15
    • 1 + 3 + … + (2n − 1) = n2
    • The only square between 200 and 250 is 225 = 152.
  3. 18
    • r = 4/12 = 1/3
    • S∞ = 12 / (1 − 1/3) = 18
  4. 10
    • n(n − 1)/2 = 45, so n2 − n − 90 = 0
    • (n − 10)(n + 9) = 0, so n = 10

Task C: Four 4s

  1. 4 × 4 + 4 + 4 = 24
    • 16 + 8 = 24
  2. (4 + 4) × (4 + 4) = 64
    • 8 × 8 = 64
  3. 4! − 4 − 4/4 = 19
    • 24 − 4 − 1 = 19
  4. 44 + 4/4 = 1024
    • 4 + 4/4 = 5 and 45 = 1024

Extension

  1. (10a + b) + (10b + a) = 11(a + b)
    • Write the number as 10a + b; its reverse is 10b + a.
    • The sum is 11a + 11b = 11(a + b), a multiple of 11.
  2. 12, 24, 36 and 48
    • 10a + b = 4(a + b) gives b = 2a.
    • a = 1, 2, 3, 4 give 12, 24, 36, 48.

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

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