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Mathematics Matters Lesson Accounts 7 - Index Laws


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 27 May 2008 by ncetm_administrator
Updated on 25 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 7 - Index Law

Written by Bob Vertes
Organisation St Mary’s University College, London
Age/Ability Range Year 8 Set 2 of 8. A PGCE trainee, 1st Block (Autumn/Developmental)
 
 

How was the session/task introduced?

  • Working with powers of numbers. Written on board.
  • Intended learning Outcome: to be able to derive and use index laws.
  • Keywords – Power, base, index, indices.

How was the session/task sustained?
Lesson broken into many short episodes. Pupils came to the board to write answers to questions in involving indices e.g. 2×2×2×2×2 - is there away to simplify this? What then does 3 to the power 4 mean? Is 4 to the power 3 the same? How could we write 1000 in other, similar, ways (powers of 10, or even powers of 2 and 5). Pupils’ answers shared/discussed. Variety of levels of difficulty. Good teacher movement round class. Using successful pupils to explain later.

How was the session/task concluded?
Praise for good work – then an internet based programme that moved up from a point on a leaf to the solar system and back, down to cells. Showing powers of 10 visually (links to science). http://www.powersof10.com/

What were the critical moments?
Getting pupil involvement on to the board.

Asking for examples the pupils invented.

Gaining the addition/subtraction rules for indices from pupils using examples such as (2×2×2×2×2) × (2×2×2); 10×10×10×10× (10×10); 5×5×5×5×5×5×5 divided by (5×5), and (7×7×7) divided by (7×7×7) [to get power zero] by paired and small group discussion to being able to find what ways powers could be played with.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Comfort with combining positive indices to a base.

Appreciation of why anything to the power zero was one and not 0.

How was that mathematics learnt?
Teacher enthusiasm.

Through questioning, good tasks, getting pupils to invent own problems for each other, collaborative learning, informal assessment, praise, recording (on non-IWB) of results.

Other memorable outcomes
“So it’s like another world, Miss, where in one world you multiply, in the other you add”.
“Wow!” at the internet film – many noted the website down to see at home.

Resources
See above – Internet, IWB + plain whiteboard. Notice board and workspace.

 
 

Downloadable PDF

Click here to download this lesson account in PDF format.
 
 

Values & Principles

Fluency in recalling facts and performing skills
Appreciation of the power of mathematics in society
Builds on the knowledge learners already have
Exposes and discusses common misconceptions and other surprising phenomena
Uses resources, including technology, in creative and appropriate ways
 
 

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Lesson Accounts Introduction

Mathematics Matters - What constitutes the effective learning of mathematics? find out more

 

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