1. CONTENT- By the end of the lesson we will… be able to understand and use Pythagoras’ Theorem PROCESS- We will know we are successful… All will work together to understand Pythagoras’ Theorem and how it relates to a triangle Most will work in pairs to use Pythagoras Theorem to find missing sides on a triangle Rally coach Some will be able to use these skills to solve written real-life problems using Pythagoras Theorem and assess each other’s answers using Carousal feedback BENEFITS- We are learning this because… 3000 years ago the Egyptians used Pythagoras Theorem to build the Great Pyramids using knotted rope to make a 90 o angle using a 3,4,5 triangle. Today builders using pieces of wood with length 3ft, 4ft, 5ft to the same thing to get a perfect 90 o right angle

2. I was born at Samos, in Greece, and lived from 580 to 500 B.C. Now you are going to try to find out what I discovered!! I was a Mathematician who became famous for discovering something unique about right – angled triangles.

3. Make accurate copies of the three right-angled triangles below 4cm 3cm 12cm 5cm 8cm 6cm Next measure the length of the longest side of each one. Then complete the table below abc a2a2a2a2 b2b2b2b2 c2c2c2c234 512 68 12 3 4 b a c Can you see a pattern in the last 3 columns? Can you see a pattern in the last 3 columns?. If you can then you have rediscovered Pythagoras’ Theorem If you can then you have rediscovered Pythagoras’ Theorem

4. Make accurate copies of the three right-angled triangles below 4cm 3cm 12cm 5cm 8cm 6cm Next measure the length of the longest side of each one. Then complete the table below abc a2a2a2a2 b2b2b2b2 c2c2c2c234 512 68 12 3 4 b a c Can you see a pattern in the last 3 columns? 513 10 91625 25144169 3664100 a 2 + b 2 = c 2

5. So what is Pythagoras’ Theorem? He said that: “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” Pythagoras a 2 + b 2 = c 2 a b c Area A a 2 Area B b 2 Area C c 2

6. We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle Area A 3 2 = 9 Area B 4 2 = 16 Area C 9 +16 = 25 3cm 4cm x We SQUARE to get the area of the smaller squares Find the Length of side Find the Length of side x We ADD to get the area of the biggest square How do we get the length of side How do we get the length of side x We SQUARE ROOT the area to get the length of side x 25 = 5cm x =  25 = 5cm

7. 1.Square Find the Length of side Find the Length of side x 2. Add 2. Add 7cm 9cm x 3. Square = 130 3. Square x =  130 Root = 11.4cm x = 11.4cm 2 = 130 x 2 = 130 9 2 = 81 7 2 = 49 We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle

8. 1.Square Find the Length of side Find the Length of side x 2. Add 2. Add 4cm 8cm x 3. Square = 80 3. Square x =  80 Root = 8.9 x = 8.9 2 = 80 x 2 = 80 8 2 = 64 4 2 = 16 We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle

9. 1.Square Find the Length of side Find the Length of side x 2. Subtract 2. Subtract 12cm 7cm x 3. Square = 95 3. Square x =  95 Root = 9.7cm x = 9.7cm 2 = 95 x 2 = 95 12 2 = 144 7 2 = 49 7 2 = 49 We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle

10. 1.Square Find the Length of side Find the Length of side x 2. Subtract 2. Subtract 23mm 15mm x 3. Square = 304 3. Square x =  304 Root = 17.4cm x = 17.4cm 2 = 304 x 2 = 304 23 2 = 529 15 2 = 225 15 2 = 225 We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle

11. 25cm 60cm 19m 14m 5cm 11cm For each of the following triangles, calculate the length of the missing side, giving your answers to one decimal place when needed. 12mm 13mm 1.5cm 1.1cm 3cm 6cm Answer = 6.7cm Answer = 9.8cm Answer = 23.6m Answer = 5mm Answer = 1.0cm Answer = 65cm I have met todays Learning Outcome :

12. Answer = 8.5cm Answer = 16.1cm Calculate the length of the diagonal of this square. 6cm If a right angle has short lengths 14cm and 8cm, what is the length of the longest side. 12cm 8cm Calculate the base of this isosceles triangle. isosceles triangle. 10cm 8cm Calculate the height of this isosceles triangle. Answer = 11.3cm Answer = 12cm I have met todays Learning Outcome :

13. Each team-mate has a different real – life problem. Each team-mate has a different real – life problem. On your own solve each of these problems. On your own solve each of these problems. Once you completed, swap with the other pupils on your table and give feedback each others answers Once you completed, swap with the other pupils on your table and give feedback each others answers A boat travels 45 miles east then 60 miles north, how far is it from where it started? (hint: draw a diagram) A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they have swam? (hint: draw a diagram) Answer = 75miles Answer = 27.7m

14. A ladder which is 4m long leans against a wall, the bottom of the ladder is 1.5m from the bottom of the wall, how high up the wall does the ladder go? (hint: draw a diagram) A rope of length 10m is stretched from the top of a pole 3m high until it reaches the ground. How far is the end of the rope to the base of the pole.(hint: draw a diagram) Answer = 3.7m Answer = 9.5m