Alien Action

In this activity, the students create a design by following a set of instructions expressed in geometrical language.
The activity links to a level 4 suggested learning activity: "Students should be designing shapes comprising circles, rectangles, triangles, and other polygons, and talking about shapes they make using the language of geometry including words such as sector, arc, perimeter, circumference, semicircle, scalene, equilateral,
isosceles, pyramid, vertical, horizontal." Formal construction techniques are a level 5 achievement objective, so the students should focus on understanding the language and ideas rather than on precision. You may find it useful to list the geometrical words used in this activity on the board and check that your students know and understand them.
The following instructions amplify those in the book:
i. Mark off a 10 centimetre line segment using a compass set to this radius. From each end of the line segment, without changing the radius, draw arcs that cross at a point. Join the two ends of the line segment to this point to create an equilateral triangle.
ii. Use a ruler to do this.
iii. At the 2 centimetre marks, draw lines at right angles using a protractor, a set square, or the corner of a piece of cardboard. Measure the point that is 1 centimetre along the lines you have just drawn. Set your compass to a radius of 1 centimetre and draw circles, using as centres the 2 points you have just marked.
iv. Draw 2 diameters of the circles at right angles to each other. Join the points where these intersect with the circumference to create the squares. Erase the diameter lines. You are not given the orientation of the squares, so they may not sit horizontally.
v. This instruction is self-explanatory.
vi. Use a compass set to 2 centimetres to draw the equilateral triangles.
vii. Mark points on the base side of the original big triangle, 1 centimetre either side of the centre. These points form 2 of the 3 vertices of another equilateral triangle. Use a compass set to 2 centimetres to complete this triangle.
viii. Join the top vertex of the original large equilateral triangle to the bottom vertex of the bottom "tooth" to create an axis of symmetry. Measure 2 centimetres down from the top of this axis. Set your compass to a radius of 2 centimetres, centre it on the point you have just marked, and draw an arc below it. Set your compass to a radius of about 2.8 centimetres, centre it on the axis of symmetry about 6.5 centimetres
from the top, and draw an arc above. Join the points where the arcs intersect to the centres of the pairs of arcs so that you create a kite.

If question 3 is too hard for some of the students in your class, you could simplify it by removing the requirement that their instructions describe an alien face. They could design any simple combination of geometrical shapes and then write the instructions for a classmate to follow.

Answers to Activity

1. The face should look similar to this, but bigger:

2. Drawings should look similar but may vary in the details.
3. a -c. Practical activities. Results will vary.