Geometrical activities with string

In many cultures there is a tradition of using a loop of string to make string figures and many of the patterns formed in this way can be the starting point for geometrical activities. Many of the patterns contain examples of triangles or quadrilaterals. Here are some simple activities ideal for small groups in each with a loop of string.

Dynamic Activities with a loop of string

Playing with String

Using string loops can also allow children to see shapes as dynamic and capable of change and transformation. Here is an activity that builds on the special flexibility of a loop of string.

Investigating Triangles

A loop of string is held by three children in a triangular shape. Let them distort the triangle first by changing the length of each by sliding their fingers along the string. Encourage them next to change the size of each angle in turn, first making each one smaller and then bigger. Encourage them to look for connections between the positions of the smallest angle and the shortest side and between the largest angle and the longest side.

String loops can be a very good way of introducing and developing the concept of different kinds of angles and different kinds of triangles. Ask children to create a small angle and gradually make it bigger. Can they stop when it becomes a right angle. Can they make it bigger again?

Can they identify the different kinds of angles in the triangles they make?

Can they make a triangle with three acute angles; with one obtuse angle; with two obtuse angles?

Can they make a triangle with two equal sides? How can they check that the two sides are equal? (bring one side to meet the other)

Can they make a triangle with three equal sides? How would they check that they are all equal?

Investigating Quadrilaterals.

Let children in pairs with one loop of string try and create four sided shapes using their loop of string. The children can experiment and discover ways to make a kite, rhombus, square, rectangle, or parallelogram and then describe their methods to others.

These activities encourage children to work together. The shapes can only work successfully if each child has a hand in their creation.

Making Challenging Shapes

An activity that promotes group participation and discussion. Each group has a piece of string.

Draw the five pointed star on the board and challenge the group to make it from the loop of string. Once successful challenge them to devise a method of making it which they an they describe to others.

The 5 pointed star The 6 pointed star

Then challenge them to try and make stars with more points, 7 and even 8.

Or try and make the net of a pyramid

A Dynamic Quadrilateral

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Figure 1 Figure 2

Place a loop of string over your thumb and little finger (Figure 1 ).

Now pick up both loops with the thumb and little finger of the other hand. You should now have a pattern like the one shown in Figure 2.

Now hold the quadrilateral with someone else as shown in Figure 3.

Figure 3

This shape is a dynamic model which will allow you to investigate the changes that happen as you change the shape of the quadrilateral. By playing with the string together you can turn this quadrilateral into many other quadrilaterals. Watch the diagonals. See how their properties change as you change the quadrilateral a square into a rhombus, into a rectangle, into a kite and into a parallelogram.

Creating Three Dimensional Shapes

Creating a Tetrahedron

But this string pattern has some more surprises. If you twist the quadrilateral a new shape emerges. One person needs to lift on hand and drop the other. Now a three dimensional shape emerges, a tetrahedron which you can adjust and investigate.

Creating a Pyramid.

Go back to the original position and ask third person to pick up the crossing diagonals. Now you have a dynamic pyramid which you together you can adjust and change into a whole variety of pyramids.

Teachers in Sri Lanka investigate the string pyramid

Creating An Octahedron.

If you use a very long loop of string and double it then you can create an octahedron. First make the dynamic quadrilateral as before with the doubled loop of string. Then ask the third person to lift the top pair of diagonals up and to pull down the under pair of diagonals.

Mprophet Sihlabela, who helped develop these ideas, demonstrates the octahedron.

Bogede or Gates

One of the commonest shapes made by children in Bhutan, South Africa, Ecuador and many other countries looks like this. It is often called “Gates”.

There are a whole series of these which become more and more intricate. Here you can see the Two Gates and Four Gates made by children in Swaziland where the pattern is called “bogede”. The even numbered gates are usually easier to create and more and more gates can be added in pairs.

Here is a Three Gate Pattern. It can be transformed into other odd numbered Gate patterns.

Gates are the starting point for a variety of mathematical activities.

Identifying Shapes

The shapes in gates are a mixture of triangles and quadrilaterals. Children can put their fingers inside different shapes and name them. If the pattern is well made children can identify different kinds of triangles (acute, obtuse, right angled, isosceles) and quadrilaterals (rhombi and kites).

Discovering Relationships

Here is a set of Gates. Record the number of quadrilaterals and the number of triangles in each string figure a discover the pattern that emerges.

Number of Quadrilaterals	Number of Triangles
1 2 3 4 5 6	4

Can you predict what would happen when there are 7 quadrilaterals? When there are 10? When there are N?

Can you find other relationships for example between the number of quadrilaterals and the number of vertices or sides, or ?

String Figures are an example of what is sometimes referred to as “ethno-mathematics”, the mathematics arising

out of traditional cultures. Many example of ethnomathematics are interesting but of little parcatical application.

The mathematics of String Figures is an example that actually works.

When ever I do these activities around the world the children invariably know far more than I do about the figuresand are much more skilled in making them. They really are a part of children’s living culture.

Secondly everyone can participate actively in the discovery and investigation of mathematical concepts, the materials are cheap and simple.

Thirdly the mathematics that comes out of string figures can be linked to mainstream mathematical curriculum

content, to angle, to shape, to number and pattern and to a dynamic understanding of geometrical relationships.