# Project Maths Website The Circle Advisor: Arlene Murphy Email: [email protected] p u n g

i S ow n tinyurl.com/LessonStudy2019 2 Lesson Study Resource Bank

3 Project Maths Website 4 How do you teach the circle?

What difficulties do your students have in this area? http://tinyurl.com/thecirclecounts Password: Thecircle The Circle Learning Outcomes Recognise the importance of Pythagoras Theorem in making sense of the equation of a circle.

Understand that often new mathematical knowledge may be developed using knowledge students already have. 6 Link to Syllabus Prior Knowledge

Coordinate Geometry Pythagoras Theorem Application of Pythagoras Theorem Geometry (Theorems) Going in circles with Pythagoras Write down the coordinates of as many points as possible that are equidistant from the origin?

9 Going in circles with Pythagoras How would you use this diagram to guide students to the discovery of the equation of a circle when the centre is not at (0, 0)? Write down the coordinates of as

many points as possible that are equidistant from the point (3, 2)? 10

Co-ordinate Geometry Equation of a Circle

( ) + ( ) = ( ) + ( ) = 2 y-2 x-3 11

r x-h y-k

Trigonometry Pythagoras, The Unit Circle and Trigonometric Identities (Cos , Sin ) h

a Cos 12 o Sin

The Circle Learning Outcomes Recognise the importance of Pythagoras Theorem in making sense of the equation of a circle. Understand that often new mathematical knowledge may be developed using knowledge students already have. 15

PDST School Support 16 17