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Themed maths · February

National Science Day maths for CBSE Class 9 and 10

A ready-to-teach lesson for National Science Day in February, about the maths scientists use every day: a 5-minute starter, a 35-minute main activity on light and standard form, similar triangles in a pinhole camera and halving patterns, an extension and full worked answers. No calculator.

Level
CBSE Class 9 and 10
Time
40 minutes, plus a 10-minute extension
Topics
Exponents and standard form; Similar triangles; Linear equations in two variables; Number patterns: halving
Equipment
No calculator. Every answer works out exactly; each question gives the values to use.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minLight and standard form
Main: task B12 minPinhole cameras and shadows
Main: task C11 minHalving and straight lines
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths.

  1. Write 300 000 000 in standard form.
  2. Work out (2.5 × 103) × (4 × 102) in standard form.
  3. A train covers 150 km in 2.5 hours. Find its average speed.
  4. Simplify (23)2 and write it as a number.

Main activity (35 minutes)

Task A: Light and standard form (12 min)

Take the speed of light as 3 × 108 m/s and the distance from the Earth to the Sun as 1.5 × 1011 m (rounded values).

  1. How far does light travel in 1 minute? Give your answer in standard form.
  2. How many seconds does light take to travel from the Sun to the Earth?
  3. Write your answer to part (b) in minutes and seconds.

Task B: Pinhole cameras and shadows (12 min)

Light travels in straight lines, so a pinhole camera and a shadow both make similar triangles.

  1. A pinhole camera is 10 m from a 2 m tall person. The screen is 20 cm behind the pinhole. How tall is the image?
  2. With the screen 15 cm behind the pinhole, a 6 m tall tree makes an image 3 cm tall. How far is the tree from the pinhole?
  3. At the same time of day, a 1.5 m stick casts a 2 m shadow and a tower casts a 48 m shadow. Find the height of the tower.

Task C: Halving and straight lines (11 min)

Two patterns that scientists meet all the time. The numbers are made up.

  1. A 640 g sample of a radioactive substance halves every 5 days. How much is left after 20 days?
  2. After how many days are only 5 g left?
  3. The length of a spring is L = 20 + 2m cm when a mass of m kg hangs from it. Find the length for 3.5 kg, and the mass that makes it 31 cm long.

Extension (10 minutes)

Sound. Take the speed of sound in air as 340 m/s.

  1. You hear thunder 6 seconds after you see the lightning. How far away is the storm? (Light arrives almost at once.)
  2. You clap and hear the echo from a cliff 1.5 seconds later. How far away is the cliff?

For teachers

Teacher notes and full worked answers
  • Every physical value is given in the question as a rounded value to use, so no prior science knowledge is needed.
  • In task B, remind students to use the same units on both sides before writing a ratio.
  • The echo question in the extension is the classic slip: the sound travels there and back.

Starter

  1. 3 × 108
    • Move the decimal point 8 places: 3 × 108.
  2. 1 × 106
    • 2.5 × 4 = 10 and 103 × 102 = 105.
    • 10 × 105 = 106
  3. 60 km/h
    • 150 ÷ 2.5 = 60
  4. 26 = 64
    • (23)2 = 26 = 64

Task A: Light and standard form

  1. 1.8 × 1010 m
    • 3 × 108 × 60 = 180 × 108 = 1.8 × 1010
  2. 500 s
    • (1.5 × 1011) ÷ (3 × 108) = 0.5 × 103 = 500
  3. 8 minutes 20 seconds
    • 500 = 8 × 60 + 20

Task B: Pinhole cameras and shadows

  1. 4 cm
    • The triangles are similar: image height ÷ 20 cm = 2 m ÷ 10 m = 1/5.
    • Image height = 20 ÷ 5 = 4 cm
  2. 30 m
    • Distance ÷ 15 cm = 6 m ÷ 3 cm = 600 cm ÷ 3 cm = 200.
    • Distance = 15 × 200 = 3000 cm = 30 m
  3. 36 m
    • Height ÷ 48 = 1.5 ÷ 2 = 3/4, so height = 36 m.

Task C: Halving and straight lines

  1. 40 g
    • 20 days = 4 halvings: 640 → 320 → 160 → 80 → 40.
  2. 35 days
    • 640 ÷ 5 = 128 = 27, so 7 halvings.
    • 7 × 5 = 35 days
  3. 27 cm; 5.5 kg
    • 20 + 2 × 3.5 = 27
    • 20 + 2m = 31 gives m = 5.5

Extension

  1. 2040 m
    • 340 × 6 = 2040
  2. 255 m
    • The sound goes there and back: 340 × 1.5 = 510 m in total.
    • 510 ÷ 2 = 255 m

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

Practise the topics

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