Heathside Schools Mathematics Department Lesson Plan Outline CONFIDENTIAL
| Teacher: Mr G Wilson
| Class: 8A3
| Date: 3-Dec-09
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| Module/Topic: KS3: Perimeter, Area and Volume / π and the Circumference of a Circle
| Room: T3
| Lesson: 13:55-14:45
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Lesson Objectives (including AFL)
- Learn and apply the formula for the Circumference of a circle.
| Success Criteria
- Everyone able to remember and apply the formula for the circumference of a circle.
- Everyone able to write π and know its approximate value.
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Class Management Objectives
- Continue with Emma Bray's strategy to keep them largely quiet and on task.
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| Lesson Context (including AFL)
| Prior Pupil Knowledge
- Area of various quadrilaterals
- Perimeter
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Resources/Equipment
- Whiteboard pens
- IWB pen
- 35 copies of main worksheet
- 15 copies of Extension
- 35 copies of homework sheet
- Strips of graph paper for estimating π.
- This lesson plan (two hard copies)
- Whiteboard rubber
- Spare calculators
- Mega-compasses
- List of star students on PowerPoint
| Provision for EAL/SEN/G&T
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Health and Safety
- No abnormal risks -- today will be just worksheet and whiteboard.
- Students may need to use compasses (for circle construction).
| Named Students
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Starter
- (Write title of today's lesson -- π (Pi) and circumference -- and the date on the whiteboard.)
- (No Starter today. Summarise Mrs HB's views from yesterday)
- Your behaviour was "disgusting". 80% of you misbehaved during that lesson. Several of you should have been issued with detentions in the first 10 minutes.
- Several of you were very rude, largely to me.
- The name-on-the-board process is too slow to deal with some of your offences. If an offence is serious enough, you will leave the room or get a detention straight away.
- Several of you interrupted the flow of the lesson with your equipment problems -- you didn't have an exercise book, or a pencil, or a pen. But I repeat -- these are your problems, not my problems, or the problems of the rest of the class. You need to fix them before the next lesson. So you need to ensure you bring your exercise book, and your pen, your pencil, and your calculator and your geometry set to every one of my lessons.
- Some of you shouted out that you didn't get it, but you didn't even have the courtesy to listen to me explaining it again. So through your selfish actions, you wasted my time and the time of the rest of the class.
- And I agree with her on everything she said. And she's not the only teacher to have said this about you.
- And it is partly my fault, because I am letting it happen.
- So there are going to be some big changes around here, and it is not going to happen again, because I am going to be very swift with the punishments.
- We are going to have quiet, and we are going to get on with doing maths.
- I know that many of you want to get on to more difficult maths, and that is what we will do, and anyone who thinks they can disrupt the lesson and ruin it for everyone else had better think again.
- And when Mrs HB visits again in a couple of week, your behaviour is going to have improved enormously.
- So think about that.
- And just as I need to be swifter with the punishments, I also need to be swifter with the rewards, so I should issue some merit stickers for exceptional performance on recent homework.
- (Show list of star students for this and previous homework. Issue merit stickers at end.)
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Development activities (including AFL)
- Today we're going to meet a new symbol.
- So far in maths, you've encountered a number of symbols: +, - ...
- Can you tell me some more symbols you already know (e.g. = x and /)?
- Today we're going to learn about a symbol called π. Nothing to be frightened of -- it's just a number. And we use it when we are calculating various values of circles.
- And in order to introduce this number, we're going to do a short practical.
- (Draw a circle on the IWB.)
- Can anyone tell me what we call the distance around the outside of the circle? (perimeter, circumference)
- Can anyone tell me what we call the line from the centre of the circle to the outside? (radius)
- And can anyone tell me what we call the line that goes through the centre and touches the edge at both ends? (diameter)
- (Draw various circles of various sizes on the IWB.)
- Notice how the larger the circle is, the larger its diameter, and the larger its circumference.
- In fact, man has known for thousands of years that the circumference is a constant value times the diameter. And that value is Pi.
- Circumference = π x diameter
- C = π x d
- Can you copy this down please?
- So we're now going to do an experiment to see if we can measure what pi is.
- I want you to work in pairs, where you can -- i.e. with the person sitting next to you.
- To do this, you will need a ruler and a calculator between you, and the strip of paper I am going to give you.
- What I want you to do is to fold the strip over a random length -- just to ensure we all measure different sized circles. I want you to measure the length of the strip using your ruler and write it down. This is going to be the circumference of your circle.
- Then I want one of you to form a circle out of the strip, while the other uses the ruler to measure the diameter. Write down the diameter.
- Then I want you to use your calculator to calculate C/d.
- Let me know you have finished by putting up your hand.
- Take the Register while they are doing it.
- Create a table on the board of the results.
- Make the point that π cannot be expressed as a decimal or a fraction with total accuracy.
- 3.14 and 3 1/7 are approximations. As a decimal expression, pi goes on forever. The Japanese have used a computer to calculate the first 16 million decimal places.
- The first 6 decimal places for π are on the poster below the ceiling as you walk down the passage outside. Watch out for them next time you are there.
- If interested, 22/7 is the best approximation containing numbers below 100.
- We said that Circumference = π x diameter
- What is the relationship between the diameter and the radius? (d = 2 x r)
- So where it says 'diameter', we can write 'two times radius' instead.
- So C = π x d = π x 2 x r = 2 x π x r = 2πr (for short)
- Can you copy this down please?
- And 355/113, discovered by the Chinese, is the best approximation below 103,993/33,102.
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- Main worksheet: p.52 of Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9'
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Plenary / AFL
- "If, next lesson, I show you a worksheet of circles of various radius or diameter, how confident will you be that you can calculate the circumference? Show me the R-Y-G from your diaries."
- "Those of you showing me yellow, can you tell me what the difficulty is?"
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| Cross-curricular links (Literacy, Numeracy, Citizenship, Spirituality, ICT)
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| Homework
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