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Pentominoes ­ Background mathematical notes

This type of activity is a good introduction to investigational mathematics as the variety of activities based on the same theme allows children to engage with the resource at their own level whilst developing their mathematical thinking, problem solving abilities and spatial awareness. Process/Strategy It is important to encourage the children to work systematically in order to avoid duplication. The most obvious starting point would be to make a straight row pentomino.

Then begin to move squares about the original row.

Solutions The obvious mistake that many children will make is to create duplications of the original 12. If children are attempting this activity by drawing the pentominoes, then encourage to cut out each pentomino they create so that they can easily be rotated or flipped so that children can easily check for duplications. Symmetry To work out rotational and reflective symmetry the printable pentominoes could be used or tracing paper.

Tessellation Not all pentominoes will tessellate without being rotated. The following pentominoes will and should look like this.

All of the pentominoes will tessellate when rotated. Examples are below

Solutions to the rectangle puzzles There are a number of solutions, these are an example. (There are many more rectangle puzzles that can be made should you wish to extend this activity ­ The Centre for Innovation in maths teaching is a good place to start: http://www.cimt.plymouth.ac.uk/resources/puzzles/pentoes/pentoint.htm ) 1) 2)

3) 4)

Extension Activities This unit could be used as a starting point for a major project based around pentominoes or it could be used to select a few activities to enhance the teaching of shape and space. There are a great number of extra activities, below are some examples. Paired work is recommended so that mathematical reasoning can be developed. · Nets Which pentominoes will fold into an open topped box? Print the Pentominoes onto card have children investigate. Correct answers are as follows

· Area By using all 12 pentominoes and making sure that each one touches another along at least one edge, what is the largest area that can be enclosed? Children should lay the pentominoes onto squared paper so that they can count the squares that have been enclosed. · Perimeter By joining two pentominoes by one edge, what shape will produce the longest perimeter? · Enlargement Can a pentomino piece be enlarged by a scale factor of 2 by using 4 other pentomino pieces? (Don't use the piece you are enlarging) All pentominoes can be enlarged in this way except for

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