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Themed maths · February

Women in maths: mathematician cards for IGCSE and GCSE

A ready-to-teach lesson for February: three ‘mathematician cards’, each built on maths that carries a woman mathematician’s name or that she is known for. A 5-minute starter, a 35-minute main activity (one card per task), an extension and full worked answers.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Primes and prime factors; Tables of values and graphs; Solving equations; Sectors: area and arc
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 A11 minCard 1: Sophie Germain primes
Main: task B12 minCard 2: the witch of Agnesi
Main: task C12 minCard 3: Nightingale’s rose diagram
Extension10 minFast finishers or homework

Starter (5 minutes)

No calculator.

  1. Is 2 × 11 + 1 a prime number?
  2. Write 95 as a product of prime factors.
  3. Find the area of a sector of radius 6 cm and angle 60°, in terms of π.
  4. Work out 8 ÷ (22 + 4).

Main activity (35 minutes)

Task A: Card 1: Sophie Germain primes (11 min)

A prime p is a Sophie Germain prime when 2p + 1 is also prime. For example, 5 is one, because 11 is prime.

  1. Find all the Sophie Germain primes less than 50. How many are there?
  2. Find the smallest prime p for which 2p + 1 is not prime.
  3. Start at 2 and keep doubling and adding 1. Which is the first number in the chain that is not prime?

Task B: Card 2: the witch of Agnesi (12 min)

The curve y = 8/(x2 + 4) is one of a family known as the witch of Agnesi, after Maria Gaetana Agnesi.

  1. Complete a table of values for x = 0, 1, 2, 3 and 4, giving y to 2 decimal places where needed. Use symmetry for negative x, and draw the graph.
  2. Write down the coordinates of the highest point and the equation of the line of symmetry.
  3. Solve 8/(x2 + 4) = 1/2, giving your answers to 3 significant figures.

Task C: Card 3: Nightingale’s rose diagram (12 min)

Florence Nightingale is known for polar area diagrams (‘rose diagrams’): 12 months drawn as 12 equal sectors, where the area of each sector shows the number. The numbers here are made up.

  1. What is the angle of each sector?
  2. One sector has radius 5 cm. Find its area, to 3 significant figures.
  3. Each 1 cm2 stands for 10 cases. About how many cases does the sector in part (b) show?
  4. Another month needs 4 times the area. What radius should its sector have?

Extension (10 minutes)

For fast finishers, or as homework.

  1. Find all the Sophie Germain primes between 50 and 100.
  2. In a rose diagram, one sector has radius 3 cm and another has radius 6 cm. How many times as many cases does the bigger one show?

For teachers

Teacher notes and full worked answers
  • Print the three tasks as cards and rotate groups between them.
  • The cards name each mathematician only through the maths named after her or that she is known for: invite students to research one of them for homework from a reliable source.
  • In card 3, students often double the radius for double the cases: ask what happens to the area.

Starter

  1. Yes, 23
    • 23 has no factors except 1 and 23.
  2. 5 × 19
    • 95 ÷ 5 = 19, and 19 is prime.
  3. 6π cm2
    • 60/360 × π × 62 = 6π
  4. 1
    • 8 ÷ 8 = 1

Task A: Card 1: Sophie Germain primes

  1. 2, 3, 5, 11, 23, 29, 41: seven
    • 2 → 5, 3 → 7, 5 → 11, 11 → 23, 23 → 47, 29 → 59, 41 → 83 are all prime.
    • The other primes give 15, 27, 35, 39, 63, 75, 87, 95, which are not prime.
  2. p = 7 (2 × 7 + 1 = 15)
    • 2, 3, 5 give 5, 7, 11, all prime. 7 gives 15 = 3 × 5.
  3. 95 = 5 × 19
    • 2 → 5 → 11 → 23 → 47 → 95, and 95 = 5 × 19.

Task B: Card 2: the witch of Agnesi

  1. 2, 1.6, 1, 0.62, 0.4
    • 8/4 = 2, 8/5 = 1.6, 8/8 = 1, 8/13 = 0.615…, 8/20 = 0.4
    • x and −x give the same y, because x2 is the same.
  2. (0, 2); x = 0
    • x2 + 4 is smallest when x = 0, so y is biggest there.
  3. x = ±3.46
    • x2 + 4 = 16, so x2 = 12.
    • x = ±√12 = ±3.464…

Task C: Card 3: Nightingale’s rose diagram

  1. 30°
    • 360° ÷ 12 = 30°
  2. 6.54 cm2
    • 30/360 × π × 52 = 25π/12 = 6.544…
  3. 65 cases
    • 6.544… × 10 = 65.4…, so about 65.
  4. 10 cm
    • Area is proportional to radius squared, so the radius is multiplied by √4 = 2: 5 × 2 = 10.

Extension

  1. 53, 83, 89
    • 53 → 107, 83 → 167 and 89 → 179 are prime.
    • 59 → 119 = 7 × 17, 61 → 123, 67 → 135, 71 → 143 = 11 × 13, 73 → 147, 79 → 159 = 3 × 53, 97 → 195 are not.
  2. 4 times
    • Area scale factor = (6/3)2 = 4.

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

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