Lesson 7 Which offer shall I take
|Reasoning||Resources: Worksheet 1 on board or OHT, and for pupils|
|Pair/group work on drawing graphs|
|The variables only have whole-number values, so bar charts will be valid representations. However we can join the points up with a dashed line which will indicate the linear pattern of the discrete data, as distinct from a continuous linear function. The fact the intermediate points are meaningless need not be emphasised.||Ask pupils what they notice about the values, so they realise that the values will ‘cross each other‘ This is the appropriate time to ‘see’ the club offers in a different way, as graphs, which may help them to make greater sense of things.
Explain how to draw the graphs (using different colours) on the same axes, and allow pupils time to do this. They can join the dots to see what happens and should label each line with its equation. As they draw their graphs, draw your own ready to show on the OHP or the board.
|Whole class sharing/discussion|
|Step and rise visual comparisons are translated to numbers for the gradient (slope/slant).
Intercept is experienced as start-up/beginning value.
|This episode centres around how the graphs help us to compare the two Club offers by seeing the gradient and intercept in the formula in a meaningful way and using natural language. Key questions are: What do you see/notice? What is similar/different?
The slope can be represented visually by the amount of ‘rise’ for each ‘step’ The step can be made as one month, and the rise then can be read numerically as either 2 or 3. Ask pupils to draw the step and rise at different months. For the ‘intercept’ pupils could use ‘starting value’ or the ‘value at zero!
Typical comparisons go along the lines of:
Allow time for pupils to match features of the graphs to terms in the formula and to natural language.
Linking to other similar situations.
|Extension: imagining and adding new clubs to the graphs|
|A form of peer assessment, which ends the lesson with all of the pupils engaged.||Tell the class in groups to invent a new club just like the two they have been looking at today. They have to draw the line on a new sheet of squared paper and pass it to another group.Their job is to write the formula for the line, add the values to the table and describe the pattern in a sentence.|
|End of lesson Reflection||Why are equations a useful way to describe relationships? How do graphs help us to see things differently?|