Lesson 1a Algebra: Exploring area on a grid

# Episode 2

Reasoning Resources:
Isometric, dotty grid on board or OHT, Worksheet 1
Whole class preparation
A grid restricts possibilities but also simplifies shapes in terms of numbers. Show the isometric dotty grid on the board or projector. Discuss . .
with the class what triangles can be drawn on the isometric grid, and why they all are equilateral. They should appreciate °
that on this grid a single number can describe a triangle:a
3, 3,3 triangle can be called a 3-triangle.
Pair and small group work
Ask the class to work in pairs on part B of Worksheet 1 and to try other triangles if they wish, to find the areas and explore the relationship between the lengths of the sides and the areas of the triangles. They should not worry excessively about neatness on the sheet. Ask them to write down any patterns that they notice and use this information to create a rule. What do you notice? Is there a link between the side and area of the triangles?
Whole class sharing and discussion
Generalisation may arise from constructing a rhombus and halving it, or from a table of numbers and seeing the square pattern.Revisiting relationships in less familiar context than the rectangle. Draw out pupils' ideas, listing rules on the board. Some pupils would recognise that a triangle is a half of the rhombus, and may easily construct the rhombus, the area of which was covered in the previous episode.
The question 'Why?' leads to higher level exploration. Others may choose to make a table of values from which the square pattern emerges: side squared = area. A good question is: Why does this happen?leading to seeing the variables in the shapes directly.
Flexible connections. Some advanced pupils may look for other connections. They may recognise that halving the slanted side would produce a parallelogram. Halving the side cancels the doubling noticed in the formula for the parallelogram, in Episode 1.