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Themed maths

Christmas maths escape room for IB Maths

The elves have locked the workshop, and the presents are stuck inside. Teams solve six locks in order; each code is needed for the next. Printable clue cards, a teacher answer key and a bonus lock for the fastest team.

Level
IB Maths SL and HL (AA and AI)
Time
41 minutes, plus a 10-minute extension
Topics
Exponents and logarithms; Sequences and series; The binomial theorem; Differentiation
Equipment
No GDC needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: lock 16 minThe wrapping room
Main: lock 26 minThe list
Main: lock 36 minThe lights
Main: lock 46 minThe power lock
Main: lock 56 minThe cracker
Main: lock 66 minThe workshop door
Extension10 minFast finishers or homework

Starter (5 minutes)

Warm-up before the locks: quick questions on the board.

  1. Evaluate 210.
  2. Evaluate log10 1000.
  3. Differentiate 5x2.

Main activity (36 minutes)

Lock 1: The wrapping room (6 min)

The first lock shows a logarithm.

  1. Solve log2 x = 5. This is code 1.

Lock 2: The list (6 min)

An arithmetic sequence has u1 = 3 and d = 4.

  1. Find un when n = code 1 ÷ 4. This is code 2.

Lock 3: The lights (6 min)

A string of lights doubles: 1, 2, 4, 8, …

  1. Find the sum of the first n terms, where n = (code 2 + 9) ÷ 4. This is code 3.

Lock 4: The power lock (6 min)

The lock asks for a power of 2.

  1. Code 3 + 1 = 2k. Find k. This is code 4.

Lock 5: The cracker (6 min)

Inside the cracker is a binomial expansion.

  1. Find the coefficient of x2 in (1 + x)n, where n = code 4. This is code 5.

Lock 6: The workshop door (6 min)

The last lock.

  1. f(x) = x3. Find f′(a), where a > 0 and a2 = code 5 − 9. It opens the door.

Extension (10 minutes)

Bonus lock for the fastest team.

  1. Three presents are opened. Each one, independently, is a book with probability 1/4. Find the probability that at least one is a book.

For teachers

Teacher notes and full worked answers
  • How to run it: print the student sheet and cut out the six lock cards. Give each team lock 1. When a team brings you the right code, give them the next card (the answer key is in the answers PDF). The first team to open lock 6 escapes. Teams can also have every card at once and race through them in order.
  • Each code is used in the next lock, so check every code before the team moves on: one slip early on breaks the chain.

Starter

  1. 1024
    • 210 = 1024
  2. 3
    • 103 = 1000
  3. 10x
    • Multiply by the power and reduce it by 1.

Lock 1: The wrapping room

  1. 32
    • x = 25 = 32

Lock 2: The list

  1. 31
    • n = 8
    • u8 = 3 + 7 × 4 = 31

Lock 3: The lights

  1. 1023
    • n = 10
    • S10 = (210 − 1)/(2 − 1) = 1023

Lock 4: The power lock

  1. 10
    • 1024 = 210

Lock 5: The cracker

  1. 45
    • 10C2 = 45

Lock 6: The workshop door

  1. 108
    • a2 = 36, so a = 6
    • f′(x) = 3x2, so f′(6) = 108

Extension

  1. 37/64
    • 1 − (3/4)3 = 1 − 27/64 = 37/64

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

Practise the topics

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