Lesson 7 Which offer shall I take

# Episode 2

Reasoning Resources: None
Whole class preparation and small group work
Tell pupils that the aim here is to do with the Club 2 offer just what they did with Club 1.Tell them that Club 2 gives ‘2 free CDs and then 3 CDs each month’. They are to formulate the rule in any way they feel comfortable with.

Most groups are likely to produce versions of y = mx +c plus talk about ‘You treble it and add two!’ You may wish to stop the class after only three minutes or so and to ask them to quickly share their ideas.
Whole class sharing/discussion
Realising that the two steps are the same in each case, but that the numbers are
different.

Realising that totals increase at different rates.

The values for the tables come from the generalisation or formula rather than the other way round.

The discussion here should focus upon making the equations similar to those for Club 1 and comparing them. Place two or three formulations for Club 1 on the board, and get the class to produce expressions for Club 2 to match.

Focus upon:

• the similarities and differences between the two formulae,
• which club’s offer is better and how the formula reveals this.

Allow some ‘wait time’ as a means of drawing the pupils out if there are no ready answers from the mainstream of the class. Ask the class to make a table, or two lists, for the values for each club for consecutive months.

 Months 0 1 2 3 4 5 6 7 8 9 10 Club 1 8 10 12 Club 2 2 5 8 11
• The table adds to the word formulation and algebra to maximise conceptual learning through different representations. For example:

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.