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S5 Int 1 The Circle Circumference of the circle www.mathsrevision.com Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter.

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Presentation on theme: "S5 Int 1 The Circle Circumference of the circle www.mathsrevision.com Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter."— Presentation transcript:

1 S5 Int 1 The Circle Circumference of the circle www.mathsrevision.com Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter

2 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 2 Starter Questions 7cm www.mathsrevision.com S5 Int 1

3 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To revise the basics of the circle. Main Parts of a Circle 1.Know the terms circumference, diameter and radius. 2.Identify them on a circle. 3.Calculate the circumference using formula. S5 Int 1

4 www.mathsrevision.com S5 Int 1 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty4 Main parts of the circle Main part of a Circle radius O Circumference Diameter

5 www.mathsrevision.com S5 Int 1 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty5 Main part of a Circle 10cm 2cm

6 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Ex Int 1 TJ Book www.mathsrevision.com Main part of a Circle

7 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 7 Starter Questions 5cm www.mathsrevision.com S5 Int 1

8 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 8 Stars In Your Eyes “Today Matthew we are going to be” Archimedes of Syracuse www.mathsrevision.com S5 Int 1

9 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 9 The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is S5 Int 1ly considered to be the greatest mathematician of ancient times. He is credited with determining the relationship between the diameter and the circumference of a circle. This was first recorded by Archimedes in the book Measurement of a Circle (225 BC). In this investigation we are going to attempt to follow Archimedes steps and arrive at the equation for determining the circumference for any given circle. History of Circles 75 years old www.mathsrevision.com S5 Int 1

10 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 10 Parts of the Circle Circumference O O = centre of circle The radius is measured from the centre of the circle to the edge. radius diameter The diameter is measured from one edge to the other passing through the centre of the circle. www.mathsrevision.com S5 Int 1

11 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 11 Circle Investigation Construct a table shown below to enable us to record our results. www.mathsrevision.com S5 Int 1

12 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 12 Investigation of the Circle To find a relationship between the diameter and circumference of a given circle. How can we measure the diameter and circumference O Our Investigation Question ? www.mathsrevision.com S5 Int 1

13 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 13 Measuring the Diameter of a circle The diameter is the largest distance between one side of a circle to the other passing through the centre O. O O Use a ruler www.mathsrevision.com S5 Int 1

14 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 14 Measuring the Circumference of a circle Flexible tape measure Take a tape measure and put it round the circle Read off the measurement O www.mathsrevision.com S5 Int 1

15 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 15 Measuring the Circumference of a circle Roll along an even surface One complete rotation equals the length of the circumference Be careful to avoid slip! Starting point End point www.mathsrevision.com S5 Int 1

16 Circle Investigation Tuesday, 09 June 2015Created by Mr Lafferty16 S5 Int 1

17 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty 17 Circle Investigation Using your results write down, in your own words, an approximate relationship between the circumference and diameter for a given circle. “Circumference approximately equals three and bit diameters” Actual value is 3.14 which we write as π Pronounced “Pi” www.mathsrevision.com S5 Int 1

18 9-Jun-15Created by Mr. Lafferty Maths Dept. No Exercise www.mathsrevision.com Circle Investigation S5 Int 1

19 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 4 S5 Int 1

20 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To revise the basics of the circle. Main Parts of a Circle 1.Know the terms circumference, diameter and radius. 2.Identify them on a circle. 3.Calculate the circumference using formula.

21 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Main Parts of a Circle Main parts of the circle radius O Circumference Diameter

22 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Calculating the Circumference 10cm 2cm Example : Find the length of the circumference (Perimeter) of each circle www.mathsrevision.com

23 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty23 Q. Calculate the curved part of this shape. Solution 6m 90 o www.mathsrevision.com S5 Int 1 Calculating the Circumference

24 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Ex Int 1 TJ Book www.mathsrevision.com Main part of a Circle

25 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 4

26 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Recall knowledge of circles so far. 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. Composite Perimeter 2.Solve mixed problems by applying all our knowledge so far.

27 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Things to think about when doing exercise. The perimeter of a semicircle ……. Find whole circle then half it ! The perimeter of a quarter circle ……. Find whole circle then quarter it ! Composite perimeter ……. Find each perimeter and add them together ! Composite Perimeter

28 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty28 Q. Find the perimeter for the semi-circle shape ? Solution 180 o www.mathsrevision.com Composite Perimeter S5 Int 1

29 Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty29 Q. Find the perimeter of the shape below ? Solution 8cm 90 o www.mathsrevision.com Composite Perimeter S5 Int 1

30 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Example 1 : Find the perimeter of this shape 20cm 5 cm Perimeter = 3 sides + semicircle Composite Perimeter

31 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Ex Int 1 TJ Book www.mathsrevision.com Composite Perimeter

32 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 2cm

33 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Recall knowledge of circles so far. 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. Composite Area 2.Solve mixed problems by applying all our knowledge so far.

34 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Example 1 : Find the area of the shape 20cm 5 cm Area = rectangle + semicircle Composite Area

35 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Example 1 : Find the area of the red part. 10cm 4cm Area = Big Circle – Small Circle Composite Area

36 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Example 2 : A circle is contained in a square. Find the grey shaded area below. Area = square - circle 8cm Composite Area

37 S5 Int 1 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Ex Int 1 TJ Book www.mathsrevision.com Composite Area

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