Penta Place

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Tetrafit

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Tessellating Transformations

Stage: 2 Challenge Level:

Why do this problem?

I cannot recommend this activity too highly you should try it for yourself. When you do so, notice all the confusions that arise about which way up the shape should go to "fit in". These confusions provide motivation for lively discussion between pupils (where they will need to use relevant mathematical vocabulary) and a great deal of hands-on trial and improvement.

Possible approach

Present the children with some equilateral connecting triangles. Then set them the problem showing them the examples on the site. It is also very worthwhile to look at using other basic 6-triangle shapes. Some have lots going for them and others are not so good, but this in itself is useful to talk about with pupils as they try other shapes.

Here are two to be going on with that I tried:

At some stage you may reach a definition for "tessellation" that the children come up with and find useful when deciding if a pattern is ok or not.

Key questions

Tell me about the shapes that you've made.

Possible extension

An extension would be to use two different basic shapes to tessellate with and discuss the advantages and disadvantages of doing this. At some stage you may reach a definition for "tessellation" that the children come up with and find useful when deciding if a pattern is ok or not.

Possible support

Some pupils may need help manipulating the triangles spme computer programs may be helpful.

Practical Activity. Investigations. Combinations. Area. Sequences. Addition & subtraction. Working systematically. Tessellations. Multiplication & division. Equilateral triangles.

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