Circle Theorems: Enhancing Mathematical Skills

Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Where are we in our journey? Real life cross/curricular links? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Enhance Mathematical basic skills knowledge. (Which PLT skills?) • Accurately calculate missing angles using circle theorems. (Grades B/A). AUTHOR

Which ones are you using? LEARNING JOURNEY Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK 3) Distance = 105miles Speed = 42mph Time = ……….minutes 2) 1) 6cm 10m Work out the perimeter 11cm Area shaded black? N Write the bearing. Solve: 3x - 5y = 5 5x - 3y = 15 Write in standard form: 6) 4) 5) 0.3334 EXTENSION Find the sum of one exterior angle in an regular decagon and one exterior angle in a regular dodecagon?

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager o o xo yo yo xo PLT Skills CIRCLE THEOREMS INTRODUCTION xo xo o o a + b = 180° DIAMETER ao x + y = 180° 2xo 2xo xo bo yo Angle made by a diameter is 90°. Angle at centre is twice the angle at the circumference. Angle at centre is twice the angle at the circumference. Opposite angles in a cyclic quadrilateral add up to 180° yo xo RADIUS yo RADIUS xo Alternate segment theorem. Angles subtended by an arc or a chord in the same segment are equal. Angle between a tangent and a radius make 90°

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager n° g° 60o 30° j° q° 45o p° h° o k° 70o i° PLT Skills CIRCLE THEOREMS EXAMPLES 4) 2) 3) 1) fo 30° 42° o o 57° 82° ao 86° bo eo 98° 123° 31° 60° 43° 6) 5) 7) 90° co 31° l° 38° 38° 20° 45° 90° 42° m° 38° do 90° 75° 60° 60°

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CIRCLE THEOREMS PLT Skills TASK 1) 2)

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CIRCLE THEOREMS PLT Skills TASK (EXAM QUESTIONS) 3) 4)

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CIRCLE THEOREMS PLT Skills TASK (EXAM QUESTIONS) 7)

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CIRCLE THEOREMS PLT Skills TASK (EXAM QUESTIONS) 10)

Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately calculate missing angles using circle theorems. What grade are we working at? DISCOVERY PLT Skills

What grade we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about calculating missing angles using circle theorems. It can be a skill or a reflection, or something else that might be prominent in your brain.

Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Which ones are you using? PLT Skills How well do you understand the task? . I fully understand I don’t understand I nearly understand

Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work.

Circle Theorems: Enhancing Mathematical Skills