1. 1

2. The sum of two numbers is 1
Question
The sum of two numbers is 1
Add together the smaller number to the square of the larger
Add together the larger number to the square of the smaller
What do you notice? 2 2 2

3. a² + b a² b a a + b² b² a² + b = a + b² a² b² 1 unit b Area = a a
Area = b a² b²
a² + b = a + b² 3 3

4. From Good to Outstanding in Functional Mathematics :
Algebra 4

5. Thinking about learning mathematics …
If only my maths teacher would ….
If only my pupils would ……. 5

6. What is good teaching and learning?6

7. Ofsted said:
The quality of teaching was the key factor influencing students’ achievement. The majority of the teaching seen was at least satisfactory in preparing students for examinations. However, in promoting a really secure understanding of mathematical ideas, in stimulating students to think for themselves and to apply their knowledge and skills in unfamiliar situations, the picture was less encouraging. In approximately half of the lessons observed, the teaching did not sufficiently encourage these important aspects of learning in mathematics.
Evaluating mathematics provision for year olds: Ofsted May 2006 7

8. And..
The best teaching gave a strong sense of the coherence of mathematical ideas; it focused on understanding mathematical concepts and developed critical thinking and reasoning. Careful questioning identified misconceptions and helped to resolve them, and positive use was made of incorrect answers to develop understanding and to encourage students to contribute. Students were challenged to think for themselves, encouraged to discuss problems and to work collaboratively. Effective use was made of information and communication technology (ICT). In contrast, teaching which presented mathematics as a collection of arbitrary rules and provided a narrow range of learning activities did not motivate students and limited their achievement. Focusing heavily on examination questions enabled students to pass examinations, but did not necessarily enable them to apply their knowledge independently in different contexts. 8

9. “All of my lessons would be graded good or better by Ofsted”
Standpoint activity
“All of my lessons would be graded good or better by Ofsted” 9

10. Moving from good to outstanding
1010

11. Self assessment …….
1111

12. 1212

13. Outstanding teaching is …………
Good teaching is …………
Outstanding teaching is …………
1313

14. 1414

15. 1515

16. 1616

17. Tactiles
1717

18. 1818