Heathside Schools Mathematics Department Lesson Plan Outline
| Teacher: Mr G Wilson
| Class: 8MA3
| Date: Tuesday 8-Dec-09
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| Module/Topic: KS3 / Shape / Area and Volume
| Room: T5
| Lesson: 10.25-11.15
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Learning Objectives (including AFL)
- State and apply the formula for the area of a circle.
| Success Criteria
- Ensure everyone leaves the lesson feeling they are confident quoting and using the formula for the area of a circle.
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Class Management Objectives
- Achieve quiet and the attention of whole class during the instruction phases.
- Handle any low-level disruption.
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In-Class Support
- Role of in-class support by others (where applicable): A supply supervisor will be present at this lesson. If required, they can help them with the worksheet.
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| Lesson Context (including AFL)
| Prior Pupil Knowledge
- Circle terms
- Area of triangle and various quadrilaterals
- Calculate circumference
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Resources/Equipment
- Spare Calculators
- Spare scissors
- Whiteboard pens
- EW pen
- 35 copies of any worksheet
- This lesson plan (two hard copies)
- Whiteboard rubber
- 35 cut-out paper circles
| Provision for EAL/SEN/G&T
- Extension material: p.263 from Impact Maths 2(R)
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Health and Safety
- No abnormal risks -- today will be just worksheet and whiteboard.
| Named Students with Special Needs
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Starter (10 mins)
- I want to start today with an apology. You may be glad to hear that both of the calculators that were lost yesterday have turned up today.
- So, thank you to whoever put the calculators in my box, and my apologies to the rest of you for delaying your lunch yesterday.
- Please note that I won't hesitate to use the measure if anything goes missing again, but I hope I won't need to do so.
- And I want today to be the last day I lend out any calculators. You should all be bringing in your calculators and geometry sets every day. After today, there will be an automatic 15-minute detention for anyone who fails to have their calculator with them.
- While I remain in a good mood, I just want to congratulate those of you who have done well in recent homework. (SHOW SLIDE.) I know I have been slow to hand out merits in the past, but all of you who are mentioned on this slide can collect a merit from me at the end.
- No starter today.
- Take the Register.
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Development activities (including AFL)
- Area recap:
- We now know how to calculate the perimeter of the circle. What is the special word we call the perimeter of a circle? (Circumference)
- And what are the two formulas we know for the circumference? (πd and 2πr)
- Now we come to the area of a circle. Can someone please define area for me? (the amount of space taken up by a two-dimensional object)
- And can someone please remind the class of the recipe we use to work out the area of any 2D shape?
- Decide what the shape is.
- Write down the correct rule.
- Replace the letters with numbers.
- Calculate the answer.
- Use the correct units.
- A = πr2
- Today we're going to apply that recipe to the circle.
- The rule for the area of a circle is A = πr2
- Have you seen this squared symbol before? It means a number multiplied by itself. So 32 = 3x3 = 9. What does 22 equal? (4)
- So we can also write the rule as A = πxrxr.
- As this is an area, can you think about what sort of units you would calculate the area of a circle in? If the radius is measured in cm, what units would the area of the circle be measured in? (cm2)
- Modified Recipe
- Decide that the shape is a circle.
- Use the correct rule: A = πr2
- Replace the letters with numbers.
- Calculate the answer.
- Use the correct units.
- Worked examples
- So what is the area of a circle with radius of 10 cm?
- A = πr2 = 3.14 x 10 x 10 = 3.14 x 100 = 314 cm2
- We didn't need our calculator for that one!
- So what is the area of a circle with radius of 25 cm?
- A = πr2 = 3.14 x 25 x 25 = 3.14 x 625 = 1962.5 cm2
- So what is the area of a circle with diameter of 2m?
- This time they've given us the diameter, not the radius. How do we find out what the radius is? (Half of diameter = 1m)
- A = πr2 = 3.14 x 1 x 1 = 3.14 x 1 = 3.14 m2
- Are you getting the hang of this?
- Can you now have a go at Q1 on the worksheet? If there are any problems, I'll help you as I come round the classroom.
- The question asks for the answer to '2 d.p.'. Does anyone know what 'd.p.' stands for? (decimal places)
- If you are confident with decimal places, then present your answer to 2dp.
- If you're not, then just give the answer that your calculator shows.
- Paper-cutting exercise to transform circle into near-rectangle (as per WhiteboardMaths.com) (20 mins):
- Show a paper circle; show how you can fold it into 2, into 4, etc
- I want some pupils to fold it into 8, and some into 16, or if you're really careful, into 32.
- If I have to fold it once, to get 2 halves, how many times do I have to fold it to get 4 sectors, etc?
- Then I want you to cut along each of the folds.
- Then arrange the sectors alternately.
- What shape are we creating? (A rectangle)
- What is the rule for the area of a rectangle? (l x w)
- What is the width? (roughly the radius)
- Can you measure the width/radius? (About 6.3cm)
- What is the length? (roughly half the circumference)
- Can you measure it? (About 19.8cm)
- Does that check with our expectation of πr? (3.14 x 6.3cm)
- Circumference = 2πr, so half the circumference = πr
- So the area of this rectangle is roughly πr x r = πr2
- But this rectangle contains all the pieces of our circle, nothing more, nothing less.
- So the area of the circle is the same as the area of this rectangle.
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Plenary / AFL
- Ask for comments, R-A-G display of homework diaries
- WWW (what went well?)
- EBI (even better if...)
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| Cross-curricular links (Literacy, Numeracy, Citizenship, Spirituality, ICT)
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Homework
- Set Q5 on back of worksheet.
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