Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Symmetry Challenge

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Coordinate Challenge

Coordinate Challenge

Here is a grid:

Can you position these ten letters in their correct places according to the eight clues below?

Clues:

The letters at $(1, 1),$ $(1, 2)$ and $(1, 3)$ are all symmetrical about a vertical line.

The letter at $(4, 2)$ is not symmetrical in any way.

The letters at $(1, 1),$ $(2, 1)$ and $(3, 1)$ are symmetrical about a horizontal line.

The letters at $(0, 2),$ $(2, 0)$ have rotational symmetry.

The letter at $(3, 1)$ consists of just straight lines.

The letters at $(3, 3)$ and $(2, 0)$ consist of just curved lines.

The letters at $(3, 3),$ $(3, 2)$ and $(3, 1)$ are consecutive in the alphabet.

The letters at $(0, 2)$ and $(1, 2)$ are at the two ends of the alphabet.

You could use this interactivity to try out your ideas.

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Why do this problem?

There are two main parts to this problem. Firtsly, learners need to identify the symmetries of various capital letters. Secondly, they need to practise reading coordinates. The problem should be approached systematically because some of the clues are not straightforward.

Possible approach

It would be good to have the problem displayed on an interactive whiteboard or data projector so that you can use the interactivity throughout the lesson. Start by arranging some of the letters on the grid and asking the children a few questions about where they are placed which will remind them about symmetry and coordinates. For example, you could ask "Where is the letter that has two lines of symmetry?"; "What do all the letters at ... have in common?".

After this learners could work in pairs on the problem so that they are able to talk through their ideas with a partner. They could either use the interactivity at computers or this sheet which has letters that can be cut out and moved around. Alternatively, the problem could be copied on to squared paper and the letters drawn on in pencil so that they can be altered easily.

If pupils do not have much experience of dealing with clues and prioritising their order as this problem requires, it might be appropriate to read each clue in turn as a whole group before working on the task in pairs. This way, you can reassure the learners that it doesn't matter if you cannot immediately use a clue to place a letter definitively. You can also demonstrate that having the letters to move around, or writing them on the grid in pencil, means that the solution can be refined as more information is revealed.

Key questions

What kind of symmetry does this letter have?
Where could this letter go on the grid? How do you know?
Which letters fit this clue?

Possible extension

Learners could explore and list the symmetries of all the other letters of the alphabet.

Possible support

Children could start by identifying the symmetries of the letters, listing whether they have vertical or horizontal line symmetry, rotational symmetry or no symmetry at all. They can then refer to their list as they try to place letters on the grid.