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Maths art for IGCSE and GCSE: curve stitching, tessellations and graph pictures

A calm end-of-term lesson that makes something to put on the wall: curves from straight lines, tiling patterns that fit perfectly, and pictures drawn with equations, with the maths behind each one.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Algebra: straight lines and simultaneous equations; Geometry: interior angles of polygons; Graphs: lines and quadratics
Equipment
No calculator needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minCurve stitching
Main: task B12 minTessellations
Main: task C11 minGraph pictures
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick questions while the paper goes out.

  1. Find each angle of an equilateral triangle.
  2. Find the gradient of the line through (0, 8) and (2, 0).
  3. Work out 360 ÷ 120.

Main activity (35 minutes)

Task A: Curve stitching (12 min)

On squared paper, mark 1 to 9 along both axes. Join (1, 0) to (0, 9), (2, 0) to (0, 8), and so on up to (9, 0) to (0, 1). The straight lines make a curve.

  1. Find the equation of the line joining (2, 0) and (0, 8).
  2. Find the equation of the line joining (3, 0) and (0, 7).
  3. Find where these two lines cross.

Task B: Tessellations (12 min)

A tessellation covers the page with no gaps. At every corner, the angles must add to 360°.

  1. Find the interior angle of a regular hexagon. How many fit together round a point?
  2. Explain why regular pentagons do not tessellate.
  3. A tiling has two regular octagons and a square at every corner. Show that the angles fit.

Task C: Graph pictures (11 min)

Draw a house and a smile with equations, on graph paper or in a graph plotter.

  1. The left side of a roof goes through (0, 4) with gradient 1. Write its equation.
  2. The right side goes through (0, 4) with gradient −1. Where does it meet the x-axis?
  3. A smile is y = x2 − 4 for −2 ≤ x ≤ 2. Find its lowest point and where it meets the x-axis.

Extension (10 minutes)

For fast finishers.

  1. Find the equation of the curve-stitching line from (5, 0) to (0, 5).

For teachers

Teacher notes and full worked answers
  • Bring squared paper, rulers and coloured pencils.
  • Make it a display: curve stitching in coloured pencil (or thread on card), a tessellation tile coloured in groups, and the graph pictures printed with their equations underneath.
  • Task C works well in any free online graph plotter: students type the equations and screenshot the picture.

Starter

  1. 60°
    • 180 ÷ 3
  2. −4
    • (0 − 8)/(2 − 0)
  3. 3
    • 120 × 3 = 360

Task A: Curve stitching

  1. y = −4x + 8
    • Gradient = (8 − 0)/(0 − 2) = −4
    • y-intercept 8
  2. 7x + 3y = 21
    • Gradient −7/3, intercept 7: y = −7x/3 + 7
    • Multiply by 3: 7x + 3y = 21
  3. (0.6, 5.6)
    • −4x + 8 = −7x/3 + 7
    • −12x + 24 = −7x + 21, so x = 3/5
    • y = −12/5 + 8 = 28/5

Task B: Tessellations

  1. 120°; 3
    • Exterior angle 360 ÷ 6 = 60, so interior 120
    • 360 ÷ 120 = 3
  2. Each angle is 108°, and 108 does not divide 360
    • Interior angle 180 − 72 = 108
    • 360 ÷ 108 = 3.33…, not a whole number, so there is a gap.
  3. 135 + 135 + 90 = 360
    • Octagon: 180 − 45 = 135
    • 135 + 135 + 90 = 360, so there is no gap.

Task C: Graph pictures

  1. y = x + 4
    • y = mx + c with m = 1, c = 4
  2. (4, 0)
    • y = −x + 4 = 0 at x = 4
  3. (0, −4); x = −2 and 2
    • The lowest point is at x = 0.
    • x2 = 4

Extension

  1. x + y = 5
    • Gradient −1, intercept 5

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

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