National 4 EF 1.2a The Circle Circumference of the circle Diameter = Circumference ÷ π Area of a circle Composite Area Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty2 Starter Questions 7cm

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.

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

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

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

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty7 Starter Questions 5cm

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

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 ( 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

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.

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.

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 ?

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

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

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

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty16 Circle Investigation

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 π Pronounced “Pi”

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. No Exercise Circle Investigation

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 4

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.

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

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

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

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

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 4

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.

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

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

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

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

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 6E (page 125) Composite Perimeter

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

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.

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

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. C = 62.8 cm Example : Find the diameter of each circle given the circumference. 2 0 c m C =15.7 cm 5 c m Finding the Diameter The Circle

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 4E (page 32) Finding the Diameter

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

National 4 EF 1.2a What do we call the distance AB in terms of the large circle. Area of a Circle O A x O A x B What do we call the distance OA in terms of the large circle. circumference Peeling an orange

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. What is the formula for the area of a right-angle triangle. O A x B Use this formula to work out the area for a circle. Area of a Circle

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. Area of a Circle

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty thinner and thinner sectors If we cut the sectors Thinner and thinner then we get closer and closer to a rectangle. Hence we can represent the area of a circle by a rectangle. Area of a Circle

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty42 But the area inside this rectangle is also the area of the circle Area of a Circle

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Area of a circle Q.Find the area of the circle ?Solution 4cm

National 4 EF 1.2a Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Tuesday, 09 June 2015Created by Mr Lafferty44 The Area of a circle Q. The area of a circle is cm 2. Find its radius?Solution

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Area of a circle Q. The diameter of the circle is 60cm. Find area of the circle?Solution

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Extension booklet 5E (page 35) Area of a Circle

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 2cm

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 Area 2.Solve mixed problems by applying all our knowledge so far.

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Example 1 : Find the area of the shape 20cm 5 cm Area = rectangle + semicircle Composite Area

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Example 1 : Find the area of the red part. 10cm 4cm Area = Big Circle – Small Circle Composite Area

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Example 2 : A circle is contained in a square. Find the grey shaded area below. Area = square - circle 8cm Composite Area

National 4 EF 1.2a 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Extension booklet 6E (page 38) Composite Area