1. Experiment #2 – Circles – area & circumference
Action points: Independence. Decision making. Challenge. Motivation through confidence.
Need calculators, decision maps for pupils, worksheet(s)
Follow through from last activity – pupils doing the majority of the work in discovery &
explanations
Starter:
6 random questions. (During this time, I’d be handing decision maps out)
(f) question: possible discussion points:
how many m in 2km? 10 yuan = £1 – how many pounds did it cost?
There are around 50 lengths in the picture – how long is each length?
Main development:
Work involving keywords related to circles-radius, diameter,arc,chord,sector,segment.
(some kids may never have heard those words before, should all be able to guess)
Show pupils circle diagram – ask for hands up when you point to keyword at top of page
(eg radius? Diameter? Chord?) –whilst this is happening, can be discussing the relationship
between diameter and radius etc, but not necessary
At level 7 you are going to be asked to find area or circumference (perimeter) of a circle.
• Using decision maps (again, resist the temptation to explain too much here – let
the pupils drive this) show worked example and ask “where do you think John’s
answer came from?”
Use a calculator to check your thoughts.
• Discuss in pairs for 1 minute – can we translate this decision map into words/a
sentence?
(key question is why – why do you think that? Why has john done that? Could anyone think
of how john could make a mistake? Why would that be wrong?)
* for lower ability classes, we’ll use pi = 3, for higher ability use pi = 3.142*
• Pupils to attempt circle questions using decision maps, emphasise how important
the decisions are (more important than the answer) and encourage them to
communicate their decisions.
(Extension here  the worksheet just tells them radius/diameter, on board questions where
it is labelled on a diagram – they need to decide what it is)
• Encourage checking answers – the idea being that the more confident pupils are
about whether they are right or wrong, the more likely they are to be motivated:
On the harder (3.142) sheet, the integer part of the answer is on the sheet for them (so if it
says 321.______ and they get 321.42, they know they’re right straight away – don’t need to
check with teacher)
On the lower ability sheet, there is a version like this, and a different version with the
answers all jumbled up, so again the kids know if their answer is on the sheet, they’re
probably correct – not sure which would be best?)
Plenary:
Show circle with diameter marked but not labelled, ask how we could find the
circumference? (only one extra step - measure it first)
Then show circle with circumference labelled, how could we find the diameter? (or Radius?)
Ask pupils if they could use their decision maps to help them here?