Why do this problem?
is a good way of consolidating properties of shapes and visualising changes in their properties. The interactive enables learners to satisfy their curiosity and try out ideas, when at first the task might seem very challenging.
You could introduce this problem by giving pegboards and elastic bands to pairs of children. If they have not used pegboards recently a few minutes of free play helps concentration later! Alternatively, learners could use the interactive virtual geoboard
to explore the challenges given. If you have an interactive whiteboard, using the virtual geoboard would be a good way
to share ideas with the whole class during the lesson.
Children will discover that there is more than one way to do the first part of the problem. How many ways can they find? You could talk about how they know they have got them all - perhaps by looking at each vertex in turn in a systematic way. The problem will encourage children to think hard about what makes a triangle a right-angled one. You could ask them to investigate the other changes
that occur when the length of sides of the rectangle are doubled (for example, what about the area?).
Learners could draw their answers on square dotty paper
or write instructions in words (which is much harder!).
Which pegs have you tried to move?
Can you make the shape by moving any other pegs instead?
Are there any other ways to do it?
Learners could make up similar puzzles for others to do using the virtual geoboard
or paper. They may also like to have a go at the challenge More Transformations on a Pegboard
which focuses on areas of triangles.
Using a real pegboard with elastic bands will make this more accessible for many children. They could use two bands in different colours so that one can be left in the original place all the time.