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### Transcript of Www. National 4 EF 1.2a The Circle Circumference of the circle Diameter = Circumference ÷...

• Slide 1
• www.mathsrevision.com National 4 EF 1.2a The Circle Circumference of the circle Diameter = Circumference Area of a circle Composite Area Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty2 Starter Questions 7cm
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. 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.
• Slide 4
• www.mathsrevision.com National 4 EF 1.2a 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
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty5 Main part of a Circle 10cm 2cm
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch9 (page 100) Main part of a Circle
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty7 Starter Questions 5cm
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty8 Stars In Your Eyes Today Matthew we are going to be Archimedes of Syracuse
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty9 The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is generally 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
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty10 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.
• Slide 11
• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty11 Circle Investigation Construct a table shown below to enable us to record our results.
• Slide 12
• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty12 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 ?
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty13 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
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty14 Measuring the Circumference of a circle Flexible tape measure Take a tape measure and put it round the circle Read off the measurement O
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty15 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
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty16 Circle Investigation
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• www.mathsrevision.com National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty17 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 Pronounced Pi
• Slide 18
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. No Exercise Circle Investigation
• Slide 19
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 4
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. 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.
• Slide 21
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Main Parts of a Circle Main parts of the circle radius O Circumference Diameter
• Slide 22
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Calculating the Circumference 10cm 2cm Example : Find the length of the circumference (Perimeter) of each circle
• Slide 23
• www.mathsrevision.com National 4 EF 1.2a 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 Calculating the Circumference
• Slide 24
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch9 (page 100) Main part of a Circle
• Slide 25
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 4
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. 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.
• Slide 27
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. 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
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• www.mathsrevision.com National 4 EF 1.2a 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 Composite Perimeter
• Slide 29
• www.mathsrevision.com National 4 EF 1.2a 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 Composite Perimeter
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Example 1 : Find the perimeter of this shape 20cm 5 cm Perimeter = 3 sides + semicircle Composite Perimeter
• Slide 31
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 6E (page 125) Composite Perimeter
• Slide 32
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions
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• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. To explain how we can find diameter of a circle if we know the circumference. Finding the Diameter The Circle 2.Solve diameter problems. 1.Understand how to rearrange circumference formula to find diameter.
• Slide 34
• www.mathsrevision.com National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. We can easily rearrange the circumference formula so that we have the diameter D on one side. Finding the Diameter The Circle You have 1 minute to rearrange equation. Remember change side change sign
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