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Themed maths · 31 October

Halloween maths activities for CBSE Class 10

A ready-to-teach Halloween lesson for Class 10: a 5-minute starter, a 35-minute main activity in four short tasks, an extension and full worked answers. It practises APs, spheres, probability and coordinate geometry.

Level
CBSE Class 10 (Class 9 can try most of it)
Time
40 minutes, plus a 10-minute extension
Topics
Arithmetic progressions; Surface areas and volumes; Probability; Coordinate geometry: distance and section formulae
Equipment
No calculator. Every answer works out exactly; use π = 22/7 where a question says so.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A9 minThe lantern parade
Main: task B10 minPumpkins and candles
Main: task C8 minThe sweet bowl
Main: task D8 minHaunted house maze
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths.

  1. Find the 10th term of the AP 3, 7, 11, …
  2. Find the distance of the point (6, 8) from the origin.
  3. A die is thrown once. Find the probability of getting a prime number.
  4. Find the surface area of a sphere of radius 7 cm. (Use π = 22/7.)

Main activity (35 minutes)

Task A: The lantern parade (9 min)

Children walk in a lantern parade. The first row has 5 children, and each row has 3 more children than the row in front.

  1. How many children are in the 12th row?
  2. How many children are in the first 12 rows altogether?
  3. There are 390 children in the parade, and every row is full. How many rows are there?

Task B: Pumpkins and candles (10 min)

Use π = 22/7.

  1. A pumpkin is a sphere of radius 10.5 cm. Find its volume.
  2. Find the surface area of the same pumpkin.
  3. A cylinder of wax of radius 7 cm and height 14 cm is melted and made into spherical ‘eyeball’ candles of radius 3.5 cm. How many candles can be made?

Task C: The sweet bowl (8 min)

A bowl has 8 toffees, 5 lollipops and 7 chocolate bars. One sweet is taken at random.

  1. Find the probability that it is a lollipop.
  2. Find the probability that it is not a chocolate bar.
  3. Two toffees are eaten first. Now find the probability of taking a toffee.
  4. Starting again with the full bowl, how many extra toffees must be added so that the probability of a toffee is 1/2?

Task D: Haunted house maze (8 min)

A ghost glides in a straight line from A(−2, 3) to B(6, −3) on the plan of a haunted house.

  1. Find the length AB.
  2. A trapdoor P divides AB in the ratio 1 : 3. Find P.
  3. The chest is at C(6, 3). Show that triangle ABC has a right angle at C, and find its area.

Extension (10 minutes)

For fast finishers, or as homework.

  1. Find the point on the y-axis that is the same distance from A(−2, 3) and B(6, −3).
  2. The radius of a spherical pumpkin increases by 50%. By what percentage does its surface area increase?

For teachers

Teacher notes and full worked answers
  • In the lantern parade, students find two roots of the quadratic: insist they reject the negative one with a reason.
  • In the candle question, cancel before multiplying: 2156 × 3 ÷ 539 is 4 × 3 = 12 because 539 × 4 = 2156.
  • The section formula slip to watch for: putting the 1 with the first point instead of the second.

Starter

  1. 39
    • a = 3, d = 4: a10 = 3 + 9 × 4 = 39
  2. 10
    • √(62 + 82) = √100 = 10
  3. 1/2
    • The primes are 2, 3 and 5: 3 out of 6 outcomes, so 3/6 = 1/2.
  4. 616 cm2
    • 4 × 22/7 × 7 × 7 = 616

Task A: The lantern parade

  1. 38
    • a12 = 5 + 11 × 3 = 38
  2. 258
    • S12 = 12/2 × (5 + 38) = 6 × 43 = 258
  3. 15 rows
    • n/2 × (10 + 3(n − 1)) = 390 gives 3n2 + 7n − 780 = 0.
    • Discriminant = 49 + 9360 = 9409 = 972, so n = (−7 + 97)/6 = 15.
    • (The negative root does not make sense.)

Task B: Pumpkins and candles

  1. 4851 cm3
    • 4⁄3 × 22/7 × 10.5 × 10.5 × 10.5
    • = 4⁄3 × 22/7 × 1157.625 = 4851
  2. 1386 cm2
    • 4 × 22/7 × 10.5 × 10.5 = 4 × 22/7 × 110.25 = 1386
  3. 12 candles
    • Cylinder: 22/7 × 7 × 7 × 14 = 2156 cm3.
    • One candle: 4⁄3 × 22/7 × 3.5 × 3.5 × 3.5 = 539/3 cm3.
    • 2156 ÷ 539/3 = 2156 × 3/539 = 12

Task C: The sweet bowl

  1. 1/4
    • 5 out of 20: 5/20 = 1/4
  2. 13/20
    • 1 − 7/20 = 13/20
  3. 1/3
    • 6 toffees out of 18 sweets: 6/18 = 1/3
  4. 4
    • (8 + x)/(20 + x) = 1/2 gives 16 + 2x = 20 + x, so x = 4.

Task D: Haunted house maze

  1. 10 units
    • √((6 + 2)2 + (−3 − 3)2) = √(64 + 36) = 10
  2. P(0, 3/2)
    • x = (1 × 6 + 3 × (−2))/4 = 0
    • y = (1 × (−3) + 3 × 3)/4 = 6/4 = 3/2
  3. Right angle at C; area 24 square units
    • AC = 8 and BC = 6, and AB = 10.
    • 82 + 62 = 100 = 102, so by the converse of Pythagoras the angle at C is 90°.
    • Area = ½ × 8 × 6 = 24

Extension

  1. (0, −8/3)
    • Let the point be (0, y). Then 22 + (y − 3)2 = 62 + (y + 3)2.
    • 4 + y2 − 6y + 9 = 36 + y2 + 6y + 9, so −12y = 32 and y = −8/3.
  2. 125%
    • The new radius is 1.5r, so the new area is 4π(1.5r)2 = 2.25 × 4πr2.
    • The area is multiplied by 2.25: an increase of 125%.

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

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