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Today’s Trainer :- Pietro Tozzi

Today’s Trainer :- Pietro Tozzi. 3 3 years’ experience of teaching in London comprehensive schools Head of Department Experience Mentored over 5 5 ITT trainees and NQTs Delivered training courses at St Mary’s University College, Strawberry Hill

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Today’s Trainer :- Pietro Tozzi

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  1. 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

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

  3. GCSE 2015-181)Quadratic Inequalities (H)2) Exact Trig Values (F/H)3) Solving Equations by Iterations (H)

  4. Teaching Strategies & ResourcesDropbox link to free resources.See folder with files containing lesson plans and worksheets for some of the new topics http://tinyurl.com/p6qgbe4

  5. 1) Quadratic Inequalities(New to Higher)

  6. www.examsolutions.co.uk

  7. Example for Quadratic Inequalities: Find the set of values of x for which 3x2 + 8x – 3 < 0 Solution: Put (3x − 1)(x + 3) = 0x = 1/3 and x = −3 (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)

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

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

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

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

  12. Number Line Method fggfffjjjjjjjjf tttttttttttt

  13. Number Line Method fggfffjjjjjjjjf tttttttttttt

  14. Number Line Method fggfffjjjjjjjjf tttttttttttt

  15. Number Line Method fggfffjjjjjjjjf tttttttttttt

  16. SAMs Question20. Find the range of values of x for which x2 − 3x − 10 < 0

  17. SAMs Question20. Find the range of values of x for which x2 − 3x − 10 < 0

  18. SAMs Question20. Find the range of values of x for which x2 − 3x − 10 < 0Mark Scheme:-‘Answer may be on a numberline in which case the endsmust be clearly seen’ -2<x<5

  19. 2) Trigonometry(NEW to Foundation)

  20. Exact Trigonometric Values (Both Tiers)

  21. Table for Students to Learn (1)

  22. Exact Values

  23. Table for Students to Learn (2)

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

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

  26. 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]

  27. 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.

  28. Pearson ActiveTeach Question

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

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

  31. Previous GCSE Questions (1988-92)

  32. SAMs GCSE Question (2015-17)

  33. SAMs GCSE Question (2015-17)

  34. SAMs GCSE Question (2015-17)

  35. Thank you for your attentionAny Questions?

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