Starter How many buttons can you name on

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. I was a mathematician who became famous for discovering something interesting about right-angled triangles.

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.

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

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

8² = A C 64 2. 8 B D 16 2

12² = A C 3. 4 144 B D 24 3. 5

√ 36 = 1296 72 A B C D 6 18

√ 49 = 2401 98 A B C D 24. 5 7

16² = A C 4 256 B D 32 8

√ 9 = A C 81 18 B D 4. 5 3

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…

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

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

a² + b² = c² 7² + 6² 7 cm ? = 49 + 36 = 85 √ 85 6 cm = 9. 2 cm (to 1 d. p. )

a² + b² = c² 8² + 5² 5 cm ? 8 cm = 64 + 25 = 89 √ 89 = 9. 4 cm (to 1 d. p. )

a² + b² = c² 11² + 10² = 121 + 100 = 221 ? 10 cm 11 cm √ 221 = 14. 9 cm (to 1 d. p. )

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

Answers Question 1 a) b) c) d) e) f) g) h) 5 cm 10 cm 13 cm 6. 5 cm 15 cm 25 mm 17 m 41 m Question 2 a) b) c) d) e) f) g) h) 8. 1 cm 9. 4 cm 13. 6 cm 12. 1 cm 7. 6 cm 7. 0 mm 12. 4 m 5. 0 m Question 3 a) b) c) d) e) f) g) h) 13. 2 cm 12. 0 cm 19. 4 cm 12. 3 m 7. 9 cm 3. 5 cm 1. 1 m 38. 4 mm 4) 5) 6) 7) 8) 26 km 2. 7 m 13. 4 cm No, the pencil is 1 cm too long. 5. 6 cm and 14 cm²

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!