Circles: Circumference and Area Lesson Plans
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1 Circles: Circumference and Area Lesson Plans A set of lessons for year 7. Lesson 1: Circumference of the circle and Pi Lesson 2: Area of the circle Lesson 3: Consolidation and Practice Lesson 1: Circumference of the circle and Pi Time: 1 hour The aim of this lesson is for pupils to learn how to calculate the circumference of a circle. You will need: worksheet 1, OHP slide 1, string, metre rules, 30 cm rules, large quantity of circular objects (tins, bottles, etc.), calculators. Introduction (10 mins): Parts of the circle. Introduce circumference, diameter, radius and area. Students fill in the blanks on their worksheet. Activity (20 mins) In this lesson we will learn how to work out the length of the circumference of any circle. (Students work in pairs: put one object to measure on each table). For each object measure, as accurately as possible, the diameter using the 30cm rule and the circumference using string measured against a metre rule. Fill in the table for each object. (Just write down the first 2 numbers after the decimal point in the last column) Each pair should work out the (mean) average of the values for circumference diameter and fill in the what do you notice space. Exposition (15 mins) Round-up on what do you notice. Students averages should all be fairly close to 3.1. Go through history of π. For most practical purposes we use Scientific calculators often have a π button (demonstrate). Students fill in blanks on their worksheet. If we know that circumference diameter = π. Then Circumference = π diameter. Example 1: 8 cm The circumference = = cm
2 Example 2 : 1 6 m The circumference = = m Exercise: (15 mins) Students do exercise 1. Mark at the end of the lesson Homework Exercise 2 for homework. Lesson 2: Area of the circle Time: 1 hour The aim of this lesson is for pupils to learn how to calculate the area of a circle. You will need: Student worksheet 2, calculators, graph paper, many small circular objects (e.g. coins, counters etc.). Introduction: (10 mins) Recap on lesson 1 (especially parts of the circle, meaning of pi, circumference formula). Activity: (20 mins) Students work in pairs. Draw round an object on the graph paper. Accurately count the squares from the centre to the outside (the radius) and the number of squares inside the circle (making allowance for part squares). Fill in the table on the worksheet. Exposition: (15 mins) Round-up on what did you notice. If we know that Area (radius radius) = π. Then Area = π radius radius. Example 1: 5 cm The Area = = 78 5 cm²
3 Example 2 : 4 6 m The Area = = m² Exercise: (15 mins) Students work through exercise 1 Go through and mark at the end of the lesson. Homework Exercise 2 for homework. Lesson 3: Consolidation and Practice Time: 1 hour The aim of this lesson is for pupils to gain practice in calculating the circumference and area of circles. You will need: Student worksheet 3. Introduction (20 mins) Thorough recap. Parts of the circle Meaning of pi Formulae for Area and circumference. Exercise (30 mins) Students fill in blanks for the 2 formulae on their worksheet. Students work through mixed exercise. Summary (10 mins) Quick practice questions to ensure that formulae, methods and parts of the circle have been memorised.
4 Circles: Student Worksheet 1 Fill in the boxes. Name of Object Circumference Diameter Circumference Diameter What I notice about the numbers in the last column: The average of the numbers in the last column is:... Fill in the blank spaces In any circle, if you work out Circumference Diameter you always get a number very close to... The... found the more accurate value of 3 1 / 8. Around 2200 years ago in ancient... the value of 22 / 7 was in common use. In China... years ago mathematicians had found a very accurate value of Modern computers can calculate the number to thousands of decimal places. It was only in... that the symbol π was first used for this number. It is the letter 'pi' in the Greek alphabet. We don't normally need to use a very accurate value for π. It is most common to use...
5 Now fill in the formula: Circumference = Exercise 1: Work out the circumference of each of these circles: cm 5 m mm 46 cm cm 9 mm 7. Work out the circumference of a circle with diameter 23 cm. 8. Work out the circumference of a circle with radius 7 5 cm 9. Work out the circumference of a circle with diameter 23 4 mm 10. Work out the circumference of a circle with radius 17 6 m * Challenge * 11. Work out the diameter of a circle with circumference 78 5 cm 12. Work out the radius of a circle with circumference m
6 Homework Sheet Exercise 2: Work out the circumference of each of these circles: cm 4 mm m 78 mm cm 92 mm 7. Work out the circumference of a circle with diameter 25 cm. 8. Work out the circumference of a circle with radius 12 mm 9. Work out the circumference of a circle with diameter 18 6 m 10. Work out the circumference of a circle with radius 41 3 cm * Challenge * 11. Work out the diameter of a circle with circumference m 12. Work out the radius of a circle with circumference mm
7 Circles Student Worksheet 2 Name of Object Area Radius Radius Radius (Radius Radius) 3 14 What I notice about the numbers in the last column:......
8 Now fill in the formula: Area = Exercise 3: 1. Copy and complete: The area of this circle = =... cm² Work out the area of each of these circles: cm 12 m 5 cm m cm 9 m 8. Work out the area of a circle with radius 10 cm 9. Work out the area of a circle with radius 3 4 m 10. Work out the area of a circle with diameter 100 mm * Challenge * 11. Work out the radius of a circle with area cm² 12. Work out the diameter of a circle with area m²
9 Homework Sheet Exercise 4: Work out the area of each of these circles: cm 30 m m 30 mm cm 7. Work out the area of a circle with radius 30 m 8. Work out the area of a circle with radius 7 2 mm 9. Work out the area of a circle with diameter 12 cm 10. Work out the area of a circle with diameter 9 4 m * Challenge * 11. Work out the radius of a circle with area m² 12. Work out the diameter of a circle with area mm²
10 Student Worksheet 3 Exercise 5: 1. Copy and fill in these formulae for circles: Circumference = Area = Work out the circumference of these circles: (a) (b) 46 3 cm 8 2 mm 3. Work out the area of these circles: (a) (b) 16 m 12 4 cm 4. Work out the circumference of a circle with diameter 42 cm. 5. Work out the area of a circle with radius 11 cm. 6. Work out the circumference of a circle with radius 9 m. 7. Work out the area of a circle with diameter 18 mm. * Tough Challenge!! * 8. Work out area of a circle with circumference cm
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Name: Date: Period: PIZZA! PIZZA! Area of Circles and Squares Circumference and Perimeters Volume of Cylinders and Rectangular Prisms Comparing Cost Lesson One Day One: Area and Cost A. Area of Pizza Triplets
Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Friday 11 June 2010 Morning Time: 1 hour 45 minutes