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Summer maths puzzle pack for IGCSE and GCSE

A take-home pack for the summer holidays: number puzzles, logic puzzles and shape puzzles that need thinking more than formulas. Print the student sheet; the answers are in a separate PDF for after the holiday.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Number: problem solving; Algebra: forming equations; Counting and shape
Equipment
No calculator needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minNumber puzzles
Main: task B12 minLogic puzzles
Main: task C11 minShape and counting puzzles
Extension10 minFast finishers or homework

Starter (5 minutes)

Try these together before the pack goes home.

  1. Find the next number: 1, 4, 9, 16, …
  2. A brick weighs 1 kg plus half a brick. How much does a brick weigh?
  3. I think of a number, double it and add 7. The answer is 31. What was my number?

Main activity (35 minutes)

Task A: Number puzzles (12 min)

Puzzles about whole numbers.

  1. The numbers 1 to 9 go in a 3 × 3 grid so that every row, column and diagonal has the same total. What must that total be?
  2. In that magic square 5 is in the centre and 2 is in the top-left corner. Which number goes in the bottom-right corner?
  3. Find two consecutive whole numbers whose product is 506.

Task B: Logic puzzles (12 min)

Write an equation, or try and improve.

  1. Ana is 3 times as old as her brother. In 5 years she will be twice as old as him. How old are they now?
  2. A farm has chickens and goats: 20 heads and 56 legs. How many goats are there?
  3. A snail climbs 3 m up a 10 m wall each day and slips back 2 m each night. On which day does it reach the top?

Task C: Shape and counting puzzles (11 min)

Draw a diagram first.

  1. How many squares of any size are there on a 4 × 4 grid?
  2. A square has the same perimeter as a 9 cm by 5 cm rectangle. Which has the bigger area, and by how much?
  3. Ten friends each shake hands once with every other friend. How many handshakes is that?

Extension (10 minutes)

For fast finishers.

  1. What is the last digit of 7100?

For teachers

Teacher notes and full worked answers
  • Take-home: print the student sheet for the last lesson before the summer and set it as optional holiday puzzles. Share the answers PDF in the first week back, or put it up after a week so families can check.
  • Do the starter together in class so everyone knows how to start a puzzle: draw it, try a small case, look for a pattern.

Starter

  1. 25
    • Square numbers: 52
  2. 2 kg
    • Half a brick weighs 1 kg.
  3. 12
    • 31 − 7 = 24, and 24 ÷ 2 = 12

Task A: Number puzzles

  1. 15
    • 1 + 2 + … + 9 = 45, shared equally between 3 rows: 45 ÷ 3 = 15
  2. 8
    • The diagonal through the centre adds to 15: 2 + 5 + ? = 15
  3. 22 and 23
    • √506 is about 22.5
    • 22 × 23 = 506

Task B: Logic puzzles

  1. Ana 15, her brother 5
    • a = 3b and a + 5 = 2(b + 5)
    • 3b + 5 = 2b + 10, so b = 5
  2. 8 goats (and 12 chickens)
    • If all 20 were chickens there would be 40 legs.
    • Each goat adds 2 more: 16 ÷ 2 = 8 goats
  3. Day 8
    • After 7 days and nights it is 7 m up.
    • On day 8 it climbs 3 m to 10 m.

Task C: Shape and counting puzzles

  1. 30
    • 16 + 9 + 4 + 1 = 30
  2. The square, by 4 cm2
    • Perimeter 28 cm, so the square has side 7 cm.
    • 49 − 45 = 4
  3. 45
    • 10 × 9 ÷ 2 = 45

Extension

  1. 1
    • Last digits of 7, 72, 73, 74: 7, 9, 3, 1, then they repeat.
    • 100 is a multiple of 4, so the last digit is 1.

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

Practise the topics

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