1. Welcome to the Year 7 Maths Workshop Start the activities on your table Make sure everyone knows how to do them

2. Starter Problems 1 You can write on this sheet If this is true: 356 × 96 = 34176 then are the following statements also true? True False True False True False True False Do not use a calculator 34176 ÷ 96 = 356 356 ÷ 34176= 96 96 ÷ 356 = 34176 34176 ÷ 356 = 96

3. Starter Problems 1 You can write on this sheet If this is true: 356 × 96 = 34176 then are the following statements also true? True False True False True False True False Do not use a calculator 34176 ÷ 96 = 356 356 ÷ 34176= 96 96 ÷ 356 = 34176 34176 ÷ 356 = 96

4. Starter Problems 2 You can write on this sheet Work out the missing number in these calculations You may use a calculator for this task _____ ÷ 9 = 12 _____ ÷ 24 = 5 10 ÷ ____ = 0.5 1.6 ÷ ____ = 0.02 _____ ÷ 6 = 0.42 _____ ÷ 24 = 1.5 60 ÷ ______ = 3 _____ ÷ 4 = 0.36 12 ÷ _____ = 0.25 0.3 ÷ _____ = 0.05

5. Starter Problems 2 You can write on this sheet Work out the missing number in these calculations You may use a calculator for this task _____ ÷ 9 = 12 _____ ÷ 24 = 5 10 ÷ ____ = 0.5 1.6 ÷ ____ = 0.02 _____ ÷ 6 = 0.42 _____ ÷ 24 = 1.5 60 ÷ ______ = 3 _____ ÷ 4 = 0.36 12 ÷ _____ = 0.25 0.3 ÷ _____ = 0.05 10836 120 20 80 2.526 48 1.44 20

6. Making use of patterns in Mathematics

7. Acceleration stage Climbing stage Take-off

8. How far above the houses will the aircraft pass? What information do you need to answer this question? How will you answer it?

9. Can the airport designers use what Mathematicians know about triangles to help design their runway?

10. Using Graphs Russia Hungary £93 4100 Roubles 27000 Forints

11. Russian Roubles British Pounds (£)

12. Hungarian Forints British Pounds (£)

13. width height hypotenuse angle Right Angled Triangle

14. 35° width height hypotenuse

15. Graph 1 Plot your angle against the value of HEIGHT ÷ HYPOTENUSE Angle Height ÷ Hypotenuse

16. Graph 1 Plot your angle against the value of HEIGHT ÷ HYPOTENUSE Angle Height ÷ Hypotenuse

17. Graph 2 Plot your angle against the value of WIDTH ÷ HYPOTENUSE Angle Width ÷ Hypotenuse

18. Graph 3 Plot your angle against the value of HEIGHT ÷ WIDTH Angle Height ÷ Width

19. Graph 1 Plot your angle against the value of HEIGHT ÷ HYPOTENUSE Angle Height ÷ Hypotenuse

20. Graph 2 Plot your angle against the value of WIDTH ÷ HYPOTENUSE Angle Width ÷ Hypotenuse

21. Graph 3 Plot your angle against the value of HEIGHT ÷ WIDTH Angle Height ÷ Width

22. The relationship between the sides of a right angled triangle and the angle is predictable

23. 60° 10 cm 20 cm hypotenuse width Width ÷ Hypotenuse = 0.5 10 ÷ 20 = 0.5

24. 35° 10 cm 7 cm height width Height ÷ Width = 0.7 ? ÷ 10 = 0.7 ? = 7

27. A Guide To Finding A Missing Side Step by Step Guide Which two sides are involved? Height, Width or Hypotenuse? Use the correct graph to look up the value for the angle. Write the sum out using the two sides and the value from the graph. Now work out the unknown side. An example 12 cm 30° ? Width & Hypotenuse 0.87 Width ÷ Hypotenuse = 0.87 ? ÷ 12 = 0.87 ? = 10.44

28. A Guide To Finding An Angle Step by Step Guide Which two sides are involved? Height, Width or Hypotenuse? Find the correct graph. Perform the calculation for the graph. Look up the value on the graph, and read off the correct angle. An example 6 cm ?° 13 cm Height & Width Height ÷ Width ? = 25° = 6 ÷ 13 = 0.461538461... 0.46 25

29. How far above the houses will the aircraft pass? The runway is 4.5km long in total. The acceleration stage is 3.5km. The take off angle is 10°. The housing estate is 7.5km from the end of the runway. Acceleration stage Take-off End of runway The diagram is not drawn to scale. Take-off angle

30. How far above the houses will the aircraft pass? The runway is 4.5km long in total. The acceleration stage is 3.5km. The take off angle is 10°. The housing estate is 7.5km from the end of the runway. 3.5 km Take-off End of runway The diagram is not drawn to scale. Take-off angle 1 km 7.5 km 10°

31. How far above the houses will the aircraft pass? The diagram is not drawn to scale. 1 km 7.5 km 10° 8.5 km ? Height ÷ Width =0.18 ? ÷ 8.5 = 0.18 ? = 1.53 Roughly 1.5km above.

32. The tower is 72 metres tall. Angle of rope The angle of the rope is 25°. How long should the piece of rope be? A piece of rope is attached to the top of a tower and the ground several metres away. How far away is the rope fixed from the tower? The diagram is not drawn to scale. Rope Tower

33. Trigonometry width height hypotenuse angle opposite adjacent sine cosine tangent sine = opposite ÷ hypotenuse cosine = adjacent ÷ hypotenuse tangent = opposite ÷ adjacent

34. The workshops so far...