Lesson 7 Which offer shall I take

# Which offer shall I take?

Overview Resources
An activity in a familiar setting that allows pupils to generate the two-step
linear relation of the type y = mx + c in natural language and in algebra. This
involves making sense of such relationships with different values, and using
different representations, including graphs. It ends with relating the features
of graphs to the algebra and the real-life settings themselves.
Worksheet 1
• Link intuitively recognised patterns with algebra,
• Link elements of language descriptions with corresponding elements in algebra and graphs.
• Symbolisation, including misconceptions in algebra,
• Graphs, including intuitive gradient and intercept.
• EPISODE 1
Exploring a common subscription offer
The problem is introduced as deciding which of two CD club subscriptions to take out. Both clubs cost the same amount each month. Club 1 gives 8 free CDs when you join and then 2 every month. The pupils record this information in the best way they can to make mathematical sense of it. Primarily this is to find out how many CDs you get after any given number of months.

In the sharing phase the different representations are compared and the relationship between natural language sentences and algebra is explored.
EPISODE 2
Looking at a 'similar-but-different' offer
Club 2 is introduced which gives â€˜2 free and 3 each monthâ€˜ and pupils are encouraged to express the situation in the same way as they did with Club 1. Key questions that follow are:

• What is the same/different about the clubs/formulae?
• Which offer is better? How can you tell?
• EPISODE 3
Expressing the data graphically
Both relationships are plotted on the same axis. The pupils are asked to comment upon;

• What they see? (How many it goes up? What the add 8 means? Why they cross over?),
• How the graph helps them to understand the differences between the clubs better?,
• What connections they make between the graphs and the equations?

To consolidate this part of the lesson each group is now asked to think up a new club (of the same type) draw the line and pass this to another group. They then have to write the equation for that particular line.

The emphasis here is on intuitive, visual sense-making of algebraic equations and their graphical representation. This activity is about making connections and sowing seeds, allowing the pupils to develop a feel for the meaning of linear relations and the equations of lines. The clubs and their relationships have been chosen to allow both to be shown on the same axis and made richer as the two lines intersect before the end of 12 months.