2. We are learning to: - Finding connections between different words. (Which PLT skills?) -Accurately find missing sides in right-angled triangles using Pythagoras’ Theorem. (Grade C) Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curricular links? www.mistrymaths.co.uk

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

4. . 0 0 0 STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 1) Value of: 2) Value of: 5 2 + 2 3 3)4) 5) 1) = 7 x 7 7 2 Value of: 12 2 Value of: 2 3 6) Value of: 7) Value of: 9 2 + 3 3 8) Value of: 6 2 - 2 4 9) Value of: 8 2 - 2 5 10) Value of: 0.2 x 0.3 11) EXTENSION Explain your answer = 49 = 12 x 12 = 144 = 2 x 2 x 2 = 8 = 4 and -4 = 8 and -8 = 11 and -11 = 5 x 5 + 2 x 2 x 2 = 25 + 8 = 33 = 9 x 9 + 3 x 3 x 3 = 81 + 27 = 108 = 6 x 6 - 2 x 2 x 2 x 2 = 36 - 16 = 20 = 8 x 8 - 2 x 2 x 2 x 2 x 2 = 64 - 32 = 32 = 0. 0 0 0 6 6 0 02 x 0 3. 0 = No negative number has a real square root. Imaginary numbers are used when working with negative square roots.

5. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PYTHAGORAS’ THEOREM INTRODUCTION 25 9 16 3 4 5 169 144 25 5 12 13 What connections can you find above?

6. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PYTHAGORAS’ THEOREM PERIGAL’S DISSECTION Gravestone Inscription Henry Perigal (1801 – 1898)

7. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PYTHAGORAS’ THEOREM EXAMPLES 1) 2) Longest side (opposite the right angle) Hypotenuse Longest side 1) Square sides 2) Add them 3) Square root Shorter side 1) Square sides, 2) Subtract them 3) Square root Hypotenuse Right angle 7cm 11cm 13m 25m Hypotenuse Working out the longest side Hypotenuse Working out the shorter side ONLY WORKS FOR RIGHT ANGLED TRIANGLES

8. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TASK (GRADE C) EXTENSION (GRADE C) 1)2) PYTHAGORAS’ THEOREM 3cm 4cm 5cm 8cm 3) 9cm 6cm 4) 11m 15m 5) 14m 21m 6)7) 8cm 15cm 19cm 7cm 8) 21cm 12cm 9) 43m 19m 10) 72m 21m A 5 metre ladder is positioned 3.2 metres away from a vertical building wall. Will the ladder reach a window which is 4 metres from the ground? Show your working. 5cm 9.4cm (1d.p.) 10.8cm (1d.p.) 18.6m (1d.p.) 25.2m (1d.p.) 12.7cm (1d.p.) 17.7cm (1d.p.) 17.2cm (1d.p.) 38.6m (1d.p.) 68.9m (1d.p.)

9. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY Calculate the length of the diagonal in the rectangle above PYTHAGORAS’ THEOREM 15m 8m

10. DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately find missing sides in right- angled triangles using Pythagoras’ Theorem. What grade are we working at?

11. PLENARY ACTIVITY EXAM STYLE QUESTION 24m 13m Calculate the area of the triangle above base vertical height 12m 5m Area of a triangle = x base x vertical heightArea of a triangle = x 24 x 5 Area of a triangle = 60m 2

12. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about finding missing sides in right-angled triangles using Pythagoras’ Theorem. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?

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

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