Tag Archives: Loci

80. Sunshine and constructions

Here is a quick consolidation/revision/application task for constructions, which involves very little preparation. If the sun isn’t shining you could always adapt this for indoors.


Chunky chalk (look in your local pound shop)
Straight edge and tape measure or just a metre stick
Usual classroom textbook/notes

A company has sketched out a set of new signs and it is your job to accurately draw them without a protractor. The task is differentiated by sign design.

Sign 1
Made from a rectangle and two equilateral triangles.


Sign 2
Same as sign 1, but with a border of constant width


Sign 3
Made from a rectangle, an equilateral triangle and a right angled isosceles triangle.


Sign 4
Same as sign 3, with a border of constant width.


Skills used:
Constructing an equilateral triangle (1,2,3,4)
Constructing the locus of a moving point (2,4)
Bisecting an angle (3,4)
Constructing a perpendicular bisector (optional in all cases)

Once the signs are allocated, each group must present a plan to the teacher on how they will draw it. They may use their notes, textbooks and smartphones (if your school allows this).

When the groups are outside, they can easily increase their understanding by moving on to the next design or developing their own arrows.

Examples of work



Health Warning!
These signs, when viewed from the end, can look rather like rockets. All I will say is:
rockets + construction arcs + pink chalk + teenager boys’ level of humour= ….

78. Gather round one and all!

All you need is you, a class and a playground. Easy!

Loci around a single point
You stand in the middle of the yard and the class must all stand 2m away. Hopefully you will end up with a circle of radius 2m. Discuss why this happens.

Equal distance from two lines/Bisecting an angle
Find part of the playground which has two edges, ideally at 90 degrees. The class must stand the same distance from each edge – this should look like an angle bisector. Discuss.

Locus of a line
Get a few pupils to stand in a straight line. Everyone must stand 1m away from them. Discuss why the lines are parallel and the ends are semi-circles.

Locus around an object
Repeat the previous task around an object eg building, bench. Why do right angles produce quarter circle loci?

38. Quick Constructions

A quick idea today.


Most Maths Departments use squared paper exercise books. Great for lots of mathematical concepts, but not constructions.

How many times have you seen a perpendicular bisector drawn using the right angle from the squared paper with some freehand scrawled ‘construction’ lines?

The solution to this topic is so simple – use plain paper. But then they forget to stick in their book or lose it!

The best activity I have used is to use folded A4 plain paper for the whole constructions topic. Pupils must annotate their work with instructions and revision hints. When you finish, you give them a coloured paper or card cover to attach. You could include a printed summary of skills on it.

The final homework is to illustrate the cover of the booklet with their favourite technique or related design.

This task is so easy to do, involves little preparation, creates a useful revision resource and promotes independent learning.

(The diagram is from BBC bitesize website which has some nice revision activities on this)