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Holi maths activities for IGCSE and GCSE

A ready-to-teach lesson for Holi, whenever it falls: mixing colours is ratio and proportion. A 5-minute starter, a 35-minute main activity on colour recipes, mixtures and water balloons, an extension and full worked answers.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Ratio and proportion; Percentages; Simultaneous equations: mixtures; Volume of a cylinder; Inverse proportion
Equipment
The starter is non-calculator. A calculator is allowed in the main activity.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minColour recipes
Main: task B12 minMixing two mixtures
Main: task C11 minWater balloons
Extension10 minFast finishers or homework

Starter (5 minutes)

No calculator.

  1. Write 15 : 25 in its simplest form.
  2. Share 360 g in the ratio 4 : 5.
  3. Find 30% of 250.
  4. 6 packets of colour make 21 cups of paint. How many cups do 10 packets make?

Main activity (35 minutes)

Task A: Colour recipes (12 min)

Pink powder is red and white in the ratio 2 : 5. Orange powder is red and yellow in the ratio 3 : 4.

  1. How much red and how much white are in 350 g of pink?
  2. You have 120 g of red and plenty of white. What is the most pink you can make?
  3. 350 g of pink is mixed with 350 g of orange. What percentage of the mixture is red, to 3 significant figures?

Task B: Mixing two mixtures (12 min)

Mix A is 25% red and mix B is 75% red; the rest of each is yellow. They cost £3.20 and £4.00 per 100 g.

  1. How much of each is needed to make 400 g of a mixture that is 40% red?
  2. Find the cost of the mixture in part (a).
  3. 200 g of A is mixed with 300 g of B. What percentage of the mixture is red?

Task C: Water balloons (11 min)

A cylindrical water tank has radius 30 cm and height 80 cm.

  1. Find the volume of the tank in litres, to 3 significant figures. (1 litre = 1000 cm3.)
  2. Each balloon holds 0.3 litres. How many balloons can be filled completely from a full tank?
  3. 4 people take 30 minutes to fill all the balloons. How long would 6 people take, working at the same rate?

Extension (10 minutes)

For fast finishers, or as homework.

  1. How much red must be added to 700 g of pink (red : white = 2 : 5) to make red : white = 1 : 1?
  2. Red and blue powder are in the ratio 3 : 7. After 40 g of red is added the ratio is 1 : 1. How much of each was there at first?

For teachers

Teacher notes and full worked answers
  • Holi falls on a different date each year: use this pack in the weeks around it.
  • All recipes, quantities and prices are made up.
  • In task A (c), students often average the two percentages: the masses are equal here, so ask what would change if they were not.

Starter

  1. 3 : 5
    • Divide both by 5.
  2. 160 g and 200 g
    • 9 parts: 360 ÷ 9 = 40.
  3. 75
    • 10% is 25, so 30% is 75.
  4. 35
    • 1 packet makes 3.5 cups; 10 × 3.5 = 35.

Task A: Colour recipes

  1. 100 g red and 250 g white
    • 7 parts: 350 ÷ 7 = 50.
  2. 420 g
    • 120 g of red is 2 parts, so 1 part is 60 g.
    • 7 parts = 420 g
  3. 35.7%
    • Red in pink: 100 g. Red in orange: 3/7 × 350 = 150 g.
    • 250/700 × 100 = 35.71…%

Task B: Mixing two mixtures

  1. 280 g of A and 120 g of B
    • a + b = 400 and 0.25a + 0.75b = 160.
    • Substitute a = 400 − b: 100 − 0.25b + 0.75b = 160, so 0.5b = 60.
    • b = 120 and a = 280.
  2. £13.76
    • 2.8 × 3.20 + 1.2 × 4.00 = 8.96 + 4.80 = 13.76
  3. 55%
    • Red: 50 + 225 = 275 g.
    • 275/500 × 100 = 55%

Task C: Water balloons

  1. 226 litres
    • π × 302 × 80 = 72 000π = 226 194.6… cm3
    • 226 litres (3 s.f.)
  2. 753
    • 226.19… ÷ 0.3 = 753.98…, so 753 full balloons.
  3. 20 minutes
    • Inverse proportion: 4 × 30 = 120 person-minutes. 120 ÷ 6 = 20.

Extension

  1. 300 g
    • 700 g has 200 g red and 500 g white. Red must become 500 g, so add 300 g.
  2. 30 g red and 70 g blue
    • 3k + 40 = 7k, so k = 10.

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

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