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Maths art for CBSE Class 9 and 10: curve stitching, tessellations and designs

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

Level
CBSE Class 9 and 10
Time
40 minutes, plus a 10-minute extension
Topics
Linear equations in two variables; Pair of linear equations; Coordinate geometry and angles of polygons
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 minCurve stitching
Main: task B12 minTessellations
Main: task C11 minGraph-paper designs
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick questions while the paper goes out.

  1. Find each angle of an equilateral triangle.
  2. Work out 360 ÷ 120.
  3. Find each exterior angle of a regular hexagon.

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-paper designs (11 min)

Draw a design that is symmetric in the y-axis.

  1. Reflect the point (3, 5) in the y-axis.
  2. Find the distance between (3, 5) and its reflection.
  3. Find the midpoint of (2, 7) and (6, 3), the centre of the design.

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 A, question 3 is a pair of linear equations: students can check the crossing point on their stitching.

Starter

  1. 60°
    • 180 ÷ 3
  2. 3
    • 120 × 3 = 360
  3. 60°
    • 360 ÷ 6

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-paper designs

  1. (−3, 5)
    • Change the sign of the x-coordinate.
  2. 6
    • √((3 − (−3))2 + 02) = 6
  3. (4, 5)
    • ((2 + 6)/2, (7 + 3)/2)

Extension

  1. x + y = 5
    • Both points satisfy x + y = 5.

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

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