1. Secondary Mathematics Conference 21 June 2012 Welcome Engaging Level 3 Learners Viv Brown Mathematics Education Consultant vivbrown1@gmail.com

2. Aims Experience together some of the activities and resources freely available Consider why and when to use them Discuss how to adapt them for different groups Have some fun enjoying the mathematical activities!

3. Agenda Starter questions Sequence clues Standard form Circle grid NRICH Rich Starting Points for A Level

4. Engaging Level 3 Learners The activities follow the ‘Teaching is more effective when it …..’ themes from the NCETM Mathematics Matters report July 2008

5. Teaching is more effective when it …. Builds on the knowledge learners already have Exposes and discusses common misconceptions Uses higher order questioning Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work Encourages reasoning rather than ‘answer getting’ Use rich collaborative tasks Creates connections between topics both within and beyond mathematics and with the real world Uses resources, including technology, in creative and appropriate ways Confronts difficulties rather than seeks to avoid or pre-empt them Develops mathematical language through communicative activities Recognises both what has been learned and also how it has been learned NCETM, Mathematics Matters, July 2008

6. What is the same and what is different?

8. Distance from home km 5 10 15 20 25 30 35 40 10:00 11:00 12:0013:00 Time Distance from home km 5 10 15 20 25 30 35 40 10:00 11:00 12:0013:00 Time What is the same and what is different?

10. Justify each one as the odd one out in as many ways as you can

11. y = 3x + 4 2y = 6x – 7 3y + x – 4 = 0 Justify each one as the odd one out in as many ways as you can

12. y = 3x + 4 2y = 6x – 7 3y + x – 4 = 0 Trivial reasons should be valued as well as the more in depth responses. They can often give important insight into the topic. Some learners might say that there is only one that is written ‘y = …’. On its own that is a simple observation but it is fundamentally important that equations are arranged into this format when using y = mx + c.

13. Odd one Out Justify each one as the odd one out in as many ways as you can

14. Just trial and error will not usually be sufficient. Thinking Questions All questions are (or should be) thinking questions! Questions that make you stop and think and keep you thinking. Questions which explore understanding. Usually open with more than one answer. Easily accessible but often can be extended very naturally into something quite complex Require some problem solving and reasoning skills. Allow many different approaches. Encourage justification / proof.

15. Give possible equations for the sides of the rectangles. Justify your answers. Can you generalise?

16. Give possible equations for each graph. Justify your answers. Can you generalise?

17. Give a possible equation for the curve. Justify your answer. Can you generalise?

18. STEM Mathematics Network Community More examples of….. What’s the same, what’s different? Odd one out Thinking questions and Circle Grids and other activities https://www.ncetm.org.uk/community/thread/17909 View the documents in the community (red tab)

19. Circle Grids Use a set of cards and a grid enlarged onto A3 to each pair. Cover as many spaces as you can. Where it says ‘these’ you must find two cards and where it says ‘this’ you should find one card. There is more than one possible arrangement so discussion at the end should revolve around a few key points e.g. a radius box, a centre box, a positional box and a coordinate box. For each one, one pair (of learners) suggests a possible card or cards and the rest of the class discuss whether these are correct and why. As a result of this discussion learners should be able to check their own. Any that are still undecided on can be discussed by the class at the end.

20. Improving learning in mathematics http://www.nationalstemcentre.org.uk/elibrary/collection/28 2/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/collection/28 2/improving-learning-in-mathematics Departmental Workshops www.ncetm.org.uk/resources/10848 www.ncetm.org.uk/resources/10848 Maths in Work www.ncetm.org.uk/resources/11329 www.ncetm.org.uk/resources/11329 Mathematical Moments www.ncetm.org.uk/resouces/36890 www.ncetm.org.uk/resouces/36890 NRICH http://nrich.maths.org/7344 http://nrich.maths.org/7344 Rich Starting Points for A Level www.risps.co.uk www.risps.co.uk

21. www.ncetm.org.uk

22. www.ncetm.org.uk/resources/10848

23. 52 to choose from Topics Department issues Widening participation in A level www.ncetm.org.uk/resources/10848

24. Glimpses of the real world of work People who are actually ‘doing the job’ Short video clips www.ncetm.org.uk/resources/11329

25. Mathematical Moments http://tlp.excellencegateway.org.uk/tlp/stem/stem-mm.html

26. Over 70 to choose from Mathematical Moments http://tlp.excellencegateway.org.uk/tlp/stem/stem-mm.html

27. Mathematical Moments https://www.ncetm.org.uk/resources/36890 https://www.ncetm.org.uk/resources/36890

28. NRICH http://nrich.maths.org/7344http://nrich.maths.org/7344

30. Secondary Mathematics Conference 21 June 2012 Thank you Viv Brown Mathematics Education Consultant vivbrown1@gmail.com