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Enhancing Mathematical Thinking with PLT Skills Lesson

Engage students in exploring angles in polygons and developing critical thinking skills through anagrams and geometry tasks. Reinforce learning objectives with real-life and cross-curricular connections.

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Enhancing Mathematical Thinking with PLT Skills Lesson

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  1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Finding connections between different words. (Which PLT skills?) • Accurately find exterior and interior angles in regular polygons. (Grade C) AUTHOR www.mistrymaths.co.uk

  2. Which ones are you using? BRAIN IN GEAR Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Regular Interior Exterior EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

  3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK 2) 1) Find the value of g Find the value of h ( 6 – 2 ) x Sum of interior angles = 180° ( 8 – 2 ) x Sum of interior angles = 180° Sum of interior angles = x 4 180° Sum of interior angles = x 6 180° Sum of interior angles = 720° Sum of interior angles = 1080° - - - - - 720° 72° 70° 208° 86° 72° - - - - - - - EXTENSION 125° 143° 128° 140° 145° 1080° 150° 135° g = 212° h = 114° Sum of interior angles = Sum of interior angles = (number of sides – 2) (number of sides – 2) x x 180° 180° Anna is drawing this logo for a school magazine. It is made up of four equilateral triangles that are all the same size. She needs to know the sizes of the six angles so that she can draw it accurately. What are the sizes of the six angles? 120º 240º 120º 120º Equilateral triangles Each angle is 60º 60º 60º Hexagon (6 sides) Octagon (8 sides)

  4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS INTRODUCTION POLYGONS NON-POLYGONS QUESTION WHAT IS A POLYGON?

  5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS INTRODUCTION What is the connection? Exterior angle Interior and exterior angle lie on a straight line Exterior angle Interior angle Angles on a straight line Interior angle Interior angle 180º Exterior angle Interior angle Interior angle Exterior angle Exterior angle INTERIOR ANGLE + EXTERIOR ANGLE = 180º

  6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS INTRODUCTION What is the connection? This means that the exterior angles on a polygon add up to 360° 360º 360º NUMBER OF SIDES = EXTERIOR ANGLE = Exterior angle Number of sides

  7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS Interior angle + Exterior angle = 180º 360º 360º Exterior angle = Number of sides = Number of sides Exterior angle LEARN ALLTHREEFORMULAE OFF BY HEART EXAMPLES 1) Calculate the size of the exterior and interior angle for a regular dodecagon 2) The diagram shows the exterior angle of a regular polygon. 18º 162º Dodecagon 12 sides (a) What is the value of the interior angle? (b) How many sides does it have? Number of sides = 20 (c) What is the sum of interior angles?

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS TASK (GRADE C) 2) Each diagram shows an interior angle of a regular polygon. For each polygon, answer the following: (i) What is its exterior angle? (ii) How many sides does it have? (iii) What is the sum of its interior angles? 1) Each diagram shows an exterior angle of a regular polygon. For each polygon, answer the following: (i) What is its interior angle? (ii)How many sides does it have? (iii)What is the sum of its interior angles? (i) 45° (i) 174° (i) 177° (i) 172° (i) 156° (ii) 8 sides (ii) 60 sides (ii) 120 sides (ii) 45 sides (ii) 15 sides (iii) 1080° (i) 20° (i) 15° (iii) 10440° (iii) 21240° (iii) 7740° (iii) 2340° (ii) 18 sides (ii) 24 sides (i) 36° (iii) 2880° (iii) 3960° (ii) 10 sides EXTENSION (GRADE C) (iii) 1440° 1) 2) Each of these cannot be the exterior angle of a regular polygon. Explain why. Each of these cannot be the interior angle of a regular polygon. Explain why. Exterior angles do not divide into 360º exactly

  9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills ANGLES IN POLYGONS MINI-PLENARY Isosceles Triangle Base angles the same 135º 45º Exterior angle Interior angle 67.5º 67.5º Angles in a triangle add to 180º

  10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately find exterior and interior angles in regular polygons. What grade are we working at? DISCOVERY PLT Skills

  11. PLENARY ACTIVITY EXAM QUESTION (GRADE C) A regular hexagon and a regular octagon are joined together along a common side as shown. Exterior angle 120º 360º Exterior angle = = 60º 6 120º Angles around a point add to 360º 105º 135º Can you find a quicker way? 360º = 45º Exterior angle = 8 135º Exterior angle

  12. What grade are 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 finding missing angles in regular polygons. It can be a skill or a reflection, or something else that might be prominent in your brain.

  13. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

  14. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www.mistrymaths.co.uk

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