2. Today’s Trainer:- Pietro Tozzi
33 years’ experience of teaching in London comprehensive schools
Head of Department Experience
Mentored over 55 ITT trainees and NQTs
Delivered training courses at St Mary’s University College, Strawberry Hill
Acted as a case study for an awarding body
Assisted in the writing of the GCSE 2010 Modular, Linked Pair Pilot & A-Level (2017) Schemes of Work
Nominated for a National Teaching Award
Presenter Bio

3. GCSE 2015-18 Some key topic changes and their implications for teaching and learning

4. GCSE ) Quadratic Inequalities (H) 2) Exact Trig Values (F/H) 3) Solving Equations by Iterations (H)

5. Teaching Strategies & Resources Dropbox link to free resources
Teaching Strategies & Resources Dropbox link to free resources. See folder with files containing lesson plans and worksheets for some of the new topics

6. 1) Quadratic Inequalities (New to Higher)

9. Example for Quadratic Inequalities: Find the set of values of x for which x2 + 8x – 3 < 0 Solution: Put (3x − 1)(x + 3) = x = 1/3 and x = − (Boundary Values) Prior knowledge is:- 1) Solving Quadratics by Factorisation 2) Expressing Linear Inequalities on a number line Full worksheet with notes and questions in your Pack (Green Sheet)

10. Example for Quadratic Inequalities: x = 1/3 and x = −3 Solution has to look like one of these.

11. Find the set of values of x for which 3x2 + 8x – 3 < 0
Find the set of values of x for which x2 + 8x – 3 < Full worksheet with notes and questions in your Pack (Green Sheet)

12. Find the set of values of x for which 3x2 + 8x – 3 < 0
Find the set of values of x for which x2 + 8x – 3 < Full worksheet with notes and questions in your Pack (Green Sheet)

13. Example for Quadratic Inequalities: Find the set of values of x for which x2 + 8x – 3 < 0 Solution: (3x − 1)(x + 3)< x = 1/3 and x = − (Boundary Values) Full worksheet with notes and questions in your Pack (Green Sheet)

14. Number Line Method
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15. Number Line Method
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16. Number Line Method
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17. Number Line Method
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18. SAMs Question 20. Find the range of values of x for which x2 − 3x − 10 < 0

19. SAMs Question 20. Find the range of values of x for which x2 − 3x − 10 < 0

20. SAMs Question 20. Find the range of values of x for which x2 − 3x − 10 < Mark Scheme:- ‘Answer may be on a number line in which case the ends must be clearly seen’
-2<x<5

21. 2) Trigonometry (NEW to Foundation)

22. Exact Trigonometric Values (Both Tiers)

23. Table for Students to Learn (1)00
300
450
600
900
Sin
Cos
Tan

29. Exact Values

32. Table for Students to Learn (2)

34. 3) Solving Equations by Iteration (NEW to Higher)

35. Starter:- T & I How many solutions? Solve the following equation:-
Teaching Strategies
Starter:-
Solve the following equation:-
x3 – 3x + 1 = 0
Graph
T & I
How many solutions?

36. 2) Draw the graph to show the roots at 2 & 3
Teaching Strategies
1) Now consider a Quadratic by factorisation. e.g. x2 - 5x + 6 = 0, giving x = 2 & 3 (two solutions)
2) Draw the graph to show the roots at 2 & 3
3) Rearrange the quadratic equation to make the ‘x’ which is squared as the subject of the formula.
Hence x = √(5x – 6)
4) To create an iteration we need to make the two x values different. Therefore we make the iteration: xn+1 = √(5xn – 6)
5) Substitute in the first value (say x1 = 4) into the iteration, then keep recycling your answer. Converges to 3 (one of the roots) [Sometimes the first approx is called x0]

37. x2 - 5x + 6 = 0
xn+1 = √(5xn – 6)
6) What happens if we start with x1 = 1?
7) Rearrange the original quadratic to make the middle ‘x’ as the subject. Hence x = (x2 + 6) /5 or the new iteration:-
xn+1 = (x2n + 6) /5
8) Substitute in x1 = 1, but this time enter ‘1’ then push the ‘=‘ button. Now set up your calculator display as follows: (ANS2 + 6) /5
Repeatedly pushing the ‘=‘ button works out the iterations for x2 , x3 , x4 , etc. (Converges to the second root 2)
This process also works for harder equations which are not quadratics. e.g.) x3 equations (Cubics) etc.

42. Pearson ActiveTeach Question

44. Six Iterations - Same Equation!
Source:- MEI

45. Four Iterations - Same Equation! Source:- MEI

46. Previous GCSE Questions (1988-92)

47. SAMs GCSE Question ( )
An example of testing of understanding of iteration on paper 2H.

48. SAMs GCSE Question ( )

49. SAMs GCSE Question ( )

50. Thank you for your attention Any Questions?