Lesson 1 Algebra: Roofs – isometric trapezia
|Random dots, isometric dotty grid, projector or visualiser, isometric dotty paper|
|Whole class preparation|
|Accepting intuitive ideas from all.||
|Making distinctions and giving descriptions of regularity. Agreeing terms.||
|Gradual focusing on the feature of equal intervals in three dimensions. Agreeing terms.||
|Pair and small group work|
|Following a rule for drawing different quadrilaterals on the grid.
What four-sided shapes with straight sides can you make on the grid using the lines of dots? Pupils should draw large or small shapes as different as possible, with thick lines so that they can show others later. (There may be some dexterity problems here that you could solve through helping, pairing or grouping, rather than making neat drawings an issue.)
|Classification by type.||
|Whole class sharing and discussion: finer differences and using number|
|Rhombus to parallelogram relationship is the same as the square to rectangle. The four shapes could be looked at together||Pupils should quickly agree on the three sets of shapes: trapezia (alternatively described as skirts, roofs, boats). The parallelograms, and rhombi (diamonds).|
|For some pupils turning the rhombus (or square) changes its name||A discussion about having two sets only, with rhombus defined as a special case of the parallelogram, should naturally follow, with pupils verbalising their reasoning using the notion of parallel lines as the main feature that dominates over different lengths of pairs of sides. You may pose the question, is there something similar here about the square and rectangle?
End the episode by shifting the class attention to using numbers for the lengths of sides.
Pupils should see the lengths measured in spaces between dots rather than the dots
themselves.They should write the lengths on their shapes,then generalise for each shape. So they describe the parallelogram in terms of two pairs of parallel sides of equal lengths, and note how more complex the trapezium is. Some pupils may appreciate that there are more complex trapezia where there is no symmetry.
The next episode concerns the trapezium with the longer side at the bottom (roof) drawn in the order shown (left) using a set of four numbers,3,1,3,4.