L. Toeau
| Introduction |
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| An activity based on creating shapes on a grid with numbers, following given rules. This helps children to formulate ideas, talk about them and test patterns in shapes and numbers. |
| This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got. |
| Episode 1: From rules to spatial relationships and generalised number |
| Children discuss the isometric (triangular) grid and the shapes that can be made on it with four straight lines. They look at examples of roof-like and non roof-like shapes, and attempt to formulate the rules for them. In the sharing phase, children sift through the rules generated, recognise similar rules, partial rules and those that are only true for some cases. They find the fewest rules needed and the simplest way of expressing them. The agreed rules should now be used and checked, then refined. You can choose two of the numbers freely, but the other two will be tied to the rules. Use of symbols and algebra are discussed. More able children could tackle questions such as ‘Why would that always work?’ and ‘Which two values determine the shape?’. |
| Episode 2: Use of the idea of a variable in an expression |
| This is a short episode that allows children to find the number of roof-shapes that can be drawn on a given base when only the fourth value in the pattern is known. The generalisation from this episode reinforces the idea of ‘any number’ and the expression of the relationship in everyday language and, if appropriate, in letters. |
| Reflection: Recognising the value of generalisation and abstraction |
| Children should be able to speak about the process they engaged in: following instructions, generating examples, generalising rules or relationships in words, sifting ideas, and more formal abstraction of the mathematical relationships between the four numerical values in the code for constructing a shape. |
| BEFORE YOU TEACH |
| To familiarise a class that has very little experience of working with an isometric grid, ask the children to draw as many different straight four-sided shapes on the grid as possible. Discuss similarities and differences and encourage the children to recognise that there are only two shapes possible: the parallelogram (and the rhombus, a special case of the parallelogram) and the trapezium. Ask the children to decide on the length of the side of their shapes, counting the distance from dot to dot, not the dots. |