User:Thegn/sandbox/Lesson Plan for 10Eu ALB 4-Mar-10

Date: 4th March 2010

Lesson Start-time: 12:05

Lesson Title: Circle Theorems Consolidation

Lesson Objectives:
 * Be able to recall and use all the theorems we have covered:
 * Angle at centre = 2x angle at circumference
 * Angles on same arc iin same segment are equal.
 * Angle in a semi-circle is 90 degrees.
 * Angle between the tangent and radius is 90 degrees.
 * Two tangents drawn from a point to a circle have equal length.
 * Opposite angles of a cyclic quadrilateral are supplementary.
 * Perpendicular from centre bisects a chord.
 * Alternate segment theorem.
 * Be able to prove them.

Homework:
 * Hand back their homework. Provide comments where appropriate, and mention not having covered the Alternate Segment Theorem.  Praise those who coped despite this.

Starter:
 * Worksheet containing all the theorems they should know -- matching statement to picture, and inserting the missing words.
 * (Encourage them to stick this summary in their exercise books for revision.)

Starter Assessment:
 * Check everyone got this exercise 100% right.

Main Episode 1:
 * Use GCSE question 14: the 'angle at the centre is 2x circumference'. (Work through it with the class.)
 * Work through the proof of the theorem on the board. (Get them to take it down.)
 * Show how the cyclic quadrilateral theorem can be proved from this result. (Get them to copy it down.)

ME1 Assessment:
 * Ask them to prove the 'any angle from the same arc' theorem, by choosing an arc, considering the angle subtended at the centre, and selecting any two points on the circumference.
 * Ask them to prove the 'angle on a semi-circle' theorem, by selecting a suitable angle.

Main Episode 2:
 * Prove the 'two tangents to a circle' theorem.
 * Work through the GCSE Higher tangent question Q16.
 * Q16.b. Challenge them to work out angle APB, perhaps in the smallest number of steps.

ME2 Assessment:
 * Hand out 3 GCSE questions as worksheets: q4, q13 and q4.

Extension:
 * HBA P.248 Qs 4-9 and 11.

Plenary:
 * Two more complex circle diagrams