Year 7 Investigation: Same Same but Different

Linking Number and Algebra

There are at least fives ways in which we can represent a pattern:

1) Using Beads:

Black / White
1 / 4
2 / 6
3 / 8
4 / 10
5 / 12

2) Using Numbers:

3) Using a graph:

4) Using robot machines:

1 ------4

2 ------6

5) Using algebra:

w = 2b +2

Year 7 Investigation: Same Same But Different [∞]

Lesson Plan

Aim:

The core written work that students produce in this lesson is no different perhaps to working through many standard mathematical text book exercises. As well as converting tables and rules into graphs however, the aim is to for students to realise that they are merely representing the same thing in a different medium. If this is realised, this can lead on to asking the question of what is actually studied in mathematics – what is this ‘thing’ that we represent in different ways?...

Suggested Lesson Outline

Students can present their work as a set of answers to a worksheet, or they can present their work as an investigation into the possible ways of communicating mathematics.

There are three main aspects needed for the lesson:

An introduction:

Ask students first to write down on their own what they think the ‘nature’ or the ‘subject’ of mathematics is.

Using the example bead pattern above in groups or as a class discussion, students can brainstorm how many different ways it can be represented. Other ways can also be added such as the use of English. Plotting a graph by first using a table should be demonstrated and emphasised.

Skills practice:

Students can use the worksheet below or other patterns to practice converting between different mediums. Weaker students should focus on creating tables and plotting graphs. The basic skill can of course then be practised in reverse, or applied to more difficult patterns.

Discussion of the nature of mathematics:

Out of all the different ways of representing the same pattern, students need to decide which is the best/easiest/real way. This can lead on to questions such as ‘why do we use algebra?’

Students can then consider what the ‘nature of mathematics’ is, what is the ‘thing’ that we are translating into different mediums?

Further Comments

The question of ‘the nature of mathematics’ can be discussed further perhaps by comparing the different mediums to different languages.

Suggested titles for setting the lesson out as an investigation –

“It’s the same but its different?”

“What is the nature of mathematics?”

“How do we communicate mathematics?”

Further Resources

Black and white counters

Worksheet of patterns below


Year 7 Investigation: Same Same but Different

Linking Number and Algebra

(A) Represent each of these bead patterns using other mediums (i) a table

(ii) a graph

(iii) robot machines

(iv) algebra

1)

2)

3)

4)

(B) Make up two more bead patterns of your own and try to represent it in different mediums.

[∞] created jyp shatincollege Feb07 last edited jyp Feb07