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Teaching mathematics
Teaching mathematics

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Pentominoes as an activity with learners

I remember the first time I met this activity. I was working as a Special Needs teacher in the mathematics department of a large college and was supporting the class teacher of a low attaining group of 15-year olds. She had found the activity in a publication and had printed it out. The activity engaged the learners and they were all able to make a start at it. No one individual found all of the twelve pentominoes but between the whole class all twelve were found and displayed on the board.

Activity 14 Preparing a lesson using pentominoes

Timing: Allow 20 minutes

Imagine that you are going to use the pentominoes task with the group of 15-year-olds. List the equipment you will need for the lesson.


Think about how you will introduce the task to the learners. Can you expect a whiteboard in the room, or an interactive whiteboard? Will you draw on the board? Will you make tiles which can be moved around?

Think about the learners investigating the task for themselves and the equipment they are likely to need. Square paper is useful. It may be that learners are given square tiles to use to create the pentominoes which can then be drawn on the square paper.

Now read this:

In the lesson with the 15 year old low attaining group the class teacher began by drawing a domino and talking about it as two squares put together along their edges. She established with the class that it had to be whole lengths of the edges placed together so that

A lesson about polyominoes
Figure 13 A lesson about polyominoes

She told the class that triominoes were made from three squares placed together along their edges, gave them some thinking time and then got learners at the board to draw two possible different triominoes.

The learners were next asked to find as many tetrominoes as they could and to draw them on squared paper. Some time was given for this and then the teacher asked for volunteers to draw the results on the board. She drew attention to the systematic way of finding all of the five tetrominoes and how this helps us to be sure that we have found all possible. It also gave her the opportunity to talk about congruency, which is where we have two tetrominoes of the same shape, if only we could cut them out and sit one on top of the other. A tetromino which is congruent to one of the others is not allowed as they all need to be different.

In the last part of the lesson the learners were set to task finding the twelve pentominoes, which they drew on squared paper.

The lesson was engaging for the pupils because it was simple enough for them all to make a start. They could find more of the polyominoes by drawing, using visual intuition. the task encouraged them to be logical and systematic as a way of identifying all possible shapes. The class experienced individual working but also collaborative working when they came together frequently as a group to discuss whether they had found all shapes.