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# What Makes A Good Resource - Simplifying logarithmic expressions

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Created on 16 July 2010 by ncetm_administrator
Updated on 27 August 2010 by ncetm_administrator

# Simplifying logarithmic expressions

Resource description:
The resource is a tarsia jigsaw activity which can be found in the Standards Unit ‘Box’: Improving Learning in Mathematics, A13 – Simplifying logarithmic expressions. Learners are invited to cut out the pieces and rearrange them to form a hexagonal jigsaw, using their knowledge of logarithmic expressions.

Teacher comment:

Although learners can work through sets of questions from text books, they seem to have problems when faced with varied problems that require them to use a breadth of knowledge. I wanted a resource that would allow them to work with a variety of different representations of the same expression as well as practising the rules of logs. I also wanted them to work together and discuss the task in hand to give them a chance to feel more confident about their own knowledge and skills.

## What I did

At the beginning of the session I gave each pair of learners the sheets of jigsaw pieces and some scissors. I was tempted to have a recap session at the beginning of the session but decided that I would find out how much my learners had remembered about the rules of logarithms from previous sessions. As they started to cut out the shapes, I could hear some of the basic rules being articulated by some of the learners as they matched the pieces. Some of the learners started to use the off-cuts as rough paper so I drew attention to this strategy and shared it with the rest of the group (who wanted to do it without writing anything down).

When they were confident that they had assembled the pieces correctly, I asked them to stick down the jigsaw on a ‘big’ piece of paper and then write around the edge. Learners were able to pick out some surprising or interesting equivalences to highlight such as

$\log_a(x^2-1)-\log_a(x+1)$

Reflection:

By using this resource, the learners had an opportunity to re-discover some of their knowledge about logarithmic expressions in an investigative environment. Some of the time they were able to remember facts and for other expressions they were having to reconstruct their knowledge. Some learners were able to use their skills to explain to other learners, which was a mutually beneficial arrangement!

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