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

2. I was born at Samos in Greece and lived from 580 to 500 B.C.
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 = 64 16
2.8 2 A B C D

7. 12² =
3.4 24
144
3.5 A B C D

8. √36 =
1296 6 72 18 A B C D

9. √49 =
2401
24.5 98 7 A B C D

10. 16² = 4 32
256 8 A B C D

11. √9 = 81
4.5 18 3 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
?cm
5cm =
3cm
4cm
= 25

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

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

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

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

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

19. 5cm 10cm 13cm 6.5cm 15cm 25mm 17m 41m 8.1cm 9.4cm 13.6cm 12.1cm 7.6cm
Answers
Question 1
Question 2
Question 3
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
8cm A 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 B A
6cm C
8cm
AC² = 6² + 8²
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 cm cm