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Themed maths

Holi maths for CBSE Class 9 and 10

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, mixing two mixtures and water balloons, an extension and full worked answers. No calculator.

Level
CBSE Class 9 and 10
Time
40 minutes, plus a 10-minute extension
Topics
Ratio and proportion; Pair of linear equations: mixtures; Percentages; Surface areas and volumes; Probability
Equipment
No calculator. Every answer works out exactly.

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)

Quick-fire mental maths.

  1. Write the ratio 12 : 18 in its simplest form.
  2. Share 450 g of colour powder in the ratio 2 : 3.
  3. Find 25% of 360.
  4. 3 packets of colour make 12 cups of paint. How many packets are needed for 20 cups?

Main activity (35 minutes)

Task A: Colour recipes (12 min)

Pink powder is made by mixing red and white in the ratio 1 : 3. Orange powder is made by mixing red and yellow in the ratio 2 : 3.

  1. How much red and how much white are in 200 g of pink?
  2. How much red is needed for 250 g of orange?
  3. You make 200 g of pink and 250 g of orange. How much red do you use altogether? What percentage of the 450 g is red?

Task B: Mixing two mixtures (12 min)

Mix A is red and yellow in the ratio 1 : 4. Mix B is red and yellow in the ratio 3 : 2.

  1. What fraction of each mix is red?
  2. How much of each mix is needed to make 500 g with red and yellow in the ratio 1 : 1?
  3. 300 g of A is mixed with 200 g of B. What percentage of the mixture is red?

Task C: Water balloons (11 min)

A water tank is a cuboid 50 cm long, 40 cm wide and 30 cm high.

  1. Find the volume of the tank in litres. (1 litre = 1000 cm3.)
  2. Each balloon holds 250 ml. How many balloons can be filled from a full tank?
  3. A bag has 6 green, 4 pink and 10 yellow packets of colour. One packet is taken at random. Find the probability that it is not yellow.

Extension (10 minutes)

For fast finishers, or as homework.

  1. How much red must be added to 400 g of pink (red : white = 1 : 3) to make the ratio red : white = 1 : 1?
  2. Red and blue powder are in the ratio 2 : 5. After 30 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 and quantities are made up; no real colour powder is needed.
  • Task B (b) is a pair of linear equations in disguise: let students try a guess-and-check table first, then set up the equations.

Starter

  1. 2 : 3
    • Divide both by 6.
  2. 180 g and 270 g
    • 5 parts: 450 ÷ 5 = 90. 2 × 90 = 180 and 3 × 90 = 270.
  3. 90
    • 360 ÷ 4 = 90
  4. 5
    • 1 packet makes 4 cups, so 20 cups need 5 packets.

Task A: Colour recipes

  1. 50 g red, 150 g white
    • 4 parts: 200 ÷ 4 = 50. Red 50 g, white 150 g.
  2. 100 g
    • 5 parts: 250 ÷ 5 = 50. Red = 2 × 50 = 100 g.
  3. 150 g; 33 1/3%
    • 50 + 100 = 150 g
    • 150/450 × 100 = 100/3 = 33 1/3%

Task B: Mixing two mixtures

  1. A: 1/5, B: 3/5
    • A: 1 part out of 5. B: 3 parts out of 5.
  2. 125 g of A and 375 g of B
    • Let x g of A and y g of B: x + y = 500 and x/5 + 3y/5 = 250.
    • The second gives x + 3y = 1250. Subtract the first: 2y = 750, so y = 375 and x = 125.
  3. 36%
    • Red: 300/5 + 3 × 200/5 = 60 + 120 = 180 g.
    • 180/500 × 100 = 36%

Task C: Water balloons

  1. 60 litres
    • 50 × 40 × 30 = 60 000 cm3 = 60 litres
  2. 240
    • 60 000 ÷ 250 = 240
  3. 1/2
    • 10 of the 20 packets are not yellow: 10/20 = 1/2.

Extension

  1. 200 g
    • 400 g of pink has 100 g red and 300 g white.
    • For 1 : 1 the red must be 300 g, so add 200 g.
  2. 20 g red and 50 g blue
    • Red 2k, blue 5k. 2k + 30 = 5k, so k = 10.

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

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