S. Cymesuredd Bwrdd Peg
| Introduction |
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| An activity on the coordinate grid. It combines two mathematical strands: constructing and using the coordinate system for mirror reflection, and exploring the number relations involved, extending to the use of generalised number. |
| 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: Constructing the coordinate system and generating results |
| Children label a row of dots on a number line, including zero position. They move to the two-coordinate system, place a ‘mirror line’ and record the two-dimensional reflection of the points. They write coordinates of pairs of points reflected in the mirror line from either side, tabulating these, recognising the sameness of one coordinate and then attempting to describe the constant addition relationship of the other. In the sharing phase they check the rules, and reflect on why this happens. |
| Episode 2: Looking for reasons and ways of describing general relationships |
| Children are likely to either a) relate points and their images to the mirror line coordinate, for example in (4, 6) and (6, 6) the 4 is one less and the 6 one more than the 5 of the mirror line; or b) recognise that the x coordinates in each pair always add up to 10. In either case they move on to describe the relationship mathematically using brackets. In words or symbols, they approach either (5 – x) + (x + 5) = 10, or x + (10 – x) = 10. They are asked to explain 10 in relation to the mirror line, and begin to think about other mirror lines. |
| Reflection: Awareness of the mathematics and logical reasoning involved |
| Children review the thought processes they used and talk about how generalisations are made from the consideration of a number of individual cases. |
| BEFORE YOU TEACH |
| This activity is not intended as practice of the use of coordinates. Rather, the coordinate system is used as a context for children to explore and generalise number relationships. Hence, it is important that children have had some prior experience with coordinates and reflection. |