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Starter. How many buttons can you name on the calculator?. We are learning to calculate missing lengths of right-angles triangles using Pythagoras’ Theorem. I was born at Samos in Greece and lived from 580 to 500 B.C.

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  1. Starter How many buttons can you name on the calculator?

  2. We are learning to calculate missing lengths of right-angles triangles using Pythagoras’ Theorem I was born at Samos in Greece and lived from 580 to 500 B.C. I was a mathematician who became famous for discovering something interesting about right-angled triangles.

  3. What will I be able to do by the end of the lesson? Find out the diagonal length of your exercise book without measuring it.

  4. Use this button to square a number Let’s practise: 14² = 196

  5. Use this button to square root a number (the inverse of squaring a number) Let’s practise: √81 = 9

  6. 8² = A B C D

  7. 12² = A B C D

  8. √36 = A B C D

  9. √49 = A B C D

  10. 16² = A B C D

  11. √9 = A B C D

  12. Pythagoras discovered that for any right angled triangle, the area of the square drawn on the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the areas of the squares drawn on the other two sides…

  13. Area of + area of = area of 5cm ?cm + = 3cm 4cm 9 + 16 = 25

  14. Copy this into your books: a² + b² = c² c a b

  15. a² + b² = c² 7² + 6² = 49 + 36 = 85 ? 7cm = 9.2 cm √85 (to 1 d.p.) 6cm

  16. a² + b² = c² 8² + 5² = 64 + 25 = 89 ? 5cm = 9.4 cm √89 8cm (to 1 d.p.)

  17. a² + b² = c² 11² + 10² = 121 + 100 = 221 ? 11cm = 14.9 cm √221 (to 1 d.p.) 10cm

  18. a² + b² = c² What’s different this time? 13² - 5² = 169 - 25 = 144 13cm ? = 12 cm √144 5cm

  19. Answers Question 1 Question 3 Question 2 5cm 10cm 13cm 6.5cm 15cm 25mm 17m 41m 8.1cm 9.4cm 13.6cm 12.1cm 7.6cm 7.0mm 12.4m 5.0m 13.2cm 12.0cm 19.4cm 12.3m 7.9cm 3.5cm 1.1m 38.4mm 26km 2.7m 13.4cm No, the pencil is 1cm too long. 5.6cm and 14cm²

  20. What will I be able to do by the end of the lesson? Find out the diagonal length of your exercise book without measuring it. You’re allowed to measure the length and width though! 

  21. G F Calculate the length AF Let’s look at the triangle formed by this line… E A F 7cm 7cm B C C A 8cm A D 6cm We can start by calculating length AC.

  22. G F Calculate the length AF Calculate the length AC… E A C 7cm 4cm D A B 6cm C AC² = 6² + 8² 8cm AC² = 100 A D 6cm AC = √100 = 10cm

  23. G F Calculate the length AF F E A 7cm 7cm C A 10cm B C Now we can calculate AF… 8cm AF² = 10² + 7² A D 6cm AF² = 149 AF = √149 = 12.2cm

  24. Answers 1. 34.4 cm 2. 7.84 cm

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