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Mathematics Matters Lesson Accounts 35 - Liner Sequences

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Created on 28 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator

Mathematics Matters Lesson Accounts
A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

Lesson Account 35 - Liner Sequences

Written by Nigel Culverwell
Organisation Manchester Adult Education Service
Age/Ability Range Adults GCSE group.

How was the session/task introduced?
This session was about linear sequences and finding the nth term. Previous session Intro to algebra – converting instructions in words into algebra. I wrote a sequence of numbers on the board and asked them to predict what numbers came next. All engaged and expressed how easy it was.

How was the session/task sustained?
Introduced the idea of terms (ordinals) and asking for numbers for terms further down the line – all doing repetitive adding- then asked for the 100th number in the sequence. Lots of guesses – all wrong – nice situation of confusion – what next?

I talked of the power of mathematics allowing us to find this number without having to inefficiently count up to it.

4 groups (3-4 in each group) set about the task working with the sequence:

  • Position 1 2 3 4
  • Number 3 5 7 9

and came up with different methods. Some methods were descriptive e.g.

  • Add ½ to them term and then double it.
  • Add 1 to term, double it then take away 1.

They were described in words and they all worked. I moved away from the lesson plan and asked: “What’s going on? How can all these different methods work?”
I then got the groups to express their methods currently just words, in algebra following on from the algebra in the previous session.

All agreed that the algebra matched the word descriptions on the board and when put to the vote, the simplest version won unanimously. Then several automatically started working with the algebra and suddenly there were little shouts from around the room “But they’re all the same!” with others in the group saying “what do you mean/” and then a fever of activity as those who had seen it were showing the others that when you worked out the algebra it all boiled down to the simplest version.

How was the session/task concluded?
We had all 4 versions on the board and a representative from the 3 groups with the more complicated versions came up to show how theirs could be simplified.

What were the critical moments?
When students were able to find a connection between the position of the term and the corresponding number in the sequence.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Obvious outcome was an agreed, easy way to find any term of a sequence. Students started automatically undoing the process when I gave a number and asked where it came in the sequence.

How was that mathematics learnt?
No answer

Other memorable outcomes
Comments like “This has totally transformed my idea of and attitude to algebra”.
“I never knew maths could be such fun”.
“I’ve just spent 2 hours messing about with numbers, sequences and algebra and it went like 5 minutes – it was great”.

The standards unit work because it made me say less and just ask questions more. I had no lesson plan for what happened when they came up with 4 different methods. I could just see where to go next with it.


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Strategies for investigation and problem solving
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’
Uses rich, collaborative tasks

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