Pi (π)

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{| border="1" cellpadding="5" cellspacing="0" align="center"
{| border="1" cellpadding="5" cellspacing="0" align="center"
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|+'''Heathside Schools Mathematics Department Lesson Plan Outline'''
+
|+'''Heathside Schools Mathematics Department Lesson Plan Outline''' CONFIDENTIAL
|-
|-
| style="background:#ccffff;" | '''Teacher:''' Mr G Wilson
| style="background:#ccffff;" | '''Teacher:''' Mr G Wilson
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|-
|-
| colspan="3" |'''Class Management Objectives'''  
| colspan="3" |'''Class Management Objectives'''  
-
* Continue with Emma Bray's strategy to keep them largely quiet and on task.
+
* Continue with EB's strategy to keep them largely quiet and on task.
|-
|-
|'''Lesson Context''' (including AFL)
|'''Lesson Context''' (including AFL)
Line 40: Line 40:
* Two examples from Monday's homework on ActivStudio flipchart
* Two examples from Monday's homework on ActivStudio flipchart
| colspan="2" | '''Provision for EAL/SEN/G&T'''
| colspan="2" | '''Provision for EAL/SEN/G&T'''
-
* Stuart Hooker brings his own laptop.
 
* Extension sheet: p.53 from [[Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9']]
* Extension sheet: p.53 from [[Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9']]
|-
|-
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* Students may need to use compasses (for circle construction).  
* Students may need to use compasses (for circle construction).  
| colspan="2" | '''Named Students'''
| colspan="2" | '''Named Students'''
-
* Stuart Hooker (ASD)
 
-
* Paige Barrow (BESD)
 
-
* John Sadikoglu (SLD)
 
-
* Freddie Thompson (BESD)
 
-
* Jake Gaywood (SLD)
 
-
* Curtis Hillier (BESD)
 
-
* Reece Lowden (Moderate LD)
 
-
* Daniel Quest (Language)
 
-
* Emily Ross (SLD)
 
|-
|-
| colspan="3" |'''Starter'''
| colspan="3" |'''Starter'''
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** You can use a calculator if you wish.
** You can use a calculator if you wish.
** 5 minutes, starting now.
** 5 minutes, starting now.
 +
* Write title of today's lesson -- π (Pi) and circumference -- and the date on the whiteboard.
** Take the Register while they are doing it.
** Take the Register while they are doing it.
* Review answers.
* Review answers.
-
* Show list star students for this and previous homework.  Issue merit stickers at end.
+
* Show the list of star students for this and previous homework.  Issue merit stickers at end.
|-
|-
| colspan="3" |'''Development activities''' (including AFL)
| colspan="3" |'''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 = pi 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 pi = C/d.
 +
* Let me know you have finished by putting up your hand.
 +
* Create a table on the board of the results.
 +
* Make the point that pi 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 10 decimal places for pi 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.
 +
** And 355/113, discovered by the Chinese, is the best approximation below 103,993/33,102.
* Main worksheet: p.52 of [[Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9']]
* Main worksheet: p.52 of [[Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9']]
|-
|-

Current revision as of 12:44, 4 February 2010

Heathside Schools Mathematics Department Lesson Plan Outline CONFIDENTIAL
Teacher: Mr G Wilson Class: 8A3 Date: 2-Dec-09
Module/Topic: KS3: Perimeter, Area and Volume / Circumference of a Circle Room: T3 Lesson: 13:55-14:45
Lesson Objectives (including AFL)
  • Review homework -- help them to add and subtract areas.
  • 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.
Class Management Objectives
  • Continue with EB's strategy to keep them largely quiet and on task.
Lesson Context (including AFL) Prior Pupil Knowledge
  • Area of various quadrilaterals
  • Perimeter
Resources/Equipment
  • Whiteboard pens
  • IWB pen
  • 35 copies of Starter worksheets
  • 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
  • Two examples from Monday's homework on ActivStudio flipchart
Provision for EAL/SEN/G&T
Health and Safety
  • No abnormal risks -- today will be just worksheet and whiteboard.
  • Students may need to use compasses (for circle construction).
Named Students
Starter
  • Review specific homework problem about adding and subtracting areas.
    • Some of the shapes were a little more complicated than the quadrilaterals we have been looking at.
    • Break them down into shapes you know the area of.
      • Area of the whole shape is the sum of the areas of the parts.
    • Where you are asked for the area of a shaded part, you will have to do a subtraction.
      • Area of the shaded part is the area of the whole shape minus the area of the unshaded part.
    • Sometimes they may not directly give you the length of a side: you may have to work it out.
  • Issue worksheet.
    • You can use a calculator if you wish.
    • 5 minutes, starting now.
  • Write title of today's lesson -- π (Pi) and circumference -- and the date on the whiteboard.
    • Take the Register while they are doing it.
  • Review answers.
  • Show the list of star students for this and previous homework. Issue merit stickers at end.
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 = pi 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 pi = C/d.
  • Let me know you have finished by putting up your hand.
  • Create a table on the board of the results.
  • Make the point that pi 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 10 decimal places for pi 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.
    • And 355/113, discovered by the Chinese, is the best approximation below 103,993/33,102.
  • Main worksheet: p.52 of Kroll and Mills: 'KS3 Measures, Shape and Space -- Year 9'
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?"
Cross-curricular links (Literacy, Numeracy, Citizenship, Spirituality, ICT)
Homework
Retrieved from "http://editthis.info/teach/Pi_(%CF%80)"
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