1. September 2015 - Shanghai Teacher Exchange Programme

2. The story so far….. In September 2015 70 maths teachers from across the country travelled to Shanghai. In November 2015 70 primary and secondary teachers from Shanghai travelled to the UK to teach maths to English students.

3. Pre-conceptions The teachers will be much better than me The students will behave impeccably All the children will be really clever.

4. UKChina Teachers in the UK have a broader depth of expertise. Highly experienced in the curriculum structure Teach approx. 170 students Teach approx. 50 students Differentiation for abilities in a class Struggled to plan lessons for low ability set SEN provisionNone Once a fortnight?Same day marking Intervention….Everyone expected to keep up with the pace. Same day intervention not seen.

5. Organisation in China

6. Organisation…. The Curriculum is planned small objective by small objective. It links together primary, middle and secondary curriculums so that there are no gaps. The curriculum is stable. Teachers are trained using the curriculum. Everyone teaches the same method…but other methods are explored

7. It’s a team effort… Lessons are planned by more than one teacher The lesson belongs to the whole department Lessons are observed by other teachers and refinements are made to the plan. It is always the teaching and the lesson plan that is being judged and never the teacher

8. TRG’s occur in school and at district level Text books support the lesson. Every pupil had his own book. There was no copying from the board

9. Topic Progression

10. On your tables….. Discuss how you would teach a sequence of lessons up to and including adding fractions.

11. This is how the Chinese would do it… 1.Prime and composite numbers 2. HCF 3. LCM 4. Exact division 5. Proper, improper and mixed fractions 6. Comparing fractions 7. Equivalent fractions 8. Reduction to simplest form 9. Finding a common denominator 10. Adding and subtracting fractions.

12. Part I Prime number & Composite number

13. Challenge 1 : Both a and b are prime numbers. If a+b=9 ， a × b=_________ 。

14. What is a factor?  Rigorous definitions

15. True or false a) 36 is a factor of 72 b) 34 is a factor of 17 c) 5 is a factor of 20 d) 5 is a factor of 0.5 e) 3 is a factor of 18 f) 38 is a factor of 19 g) 4 is a factor of 0.2 h) 3 is a factor of 17 The concept and the non- concept Conceptual variation

16. Listing Factors  In pairs Factors of 18  1 & 18  2 & 9  3 & 6

17. Write down all the factors of 16

18. Write down all the factors of 13

19. Concept Concept 1 Prime number: A prime number (or a prime) has exactly two factors, one and itself. Composite number:A composite number (or a composite) has more than two factors.

20. Ex 1: List the numbers from 1-10 which are:  (1) Odd numbers:  (2) Even numbers:  (3) Prime numbers:  (4) Composite numbers: 1, 3, 5, 7, 9 2, 4, 6, 8,10 2, 3, 5, 7 4, 6, 8, 9,10

21. Ex2:Prime or Composite, why?  (1) 27  (2) 29  (3) 35  (4) 37 The factors of 27 are 1,3,9,27 Composite The factors of 29 are 1,29 Prime The factors of 35 are 1,5,7,35 The factors of 37 are 1,37 Composite Prime

22.  By examining the number of factors of a number you can determine whether the number is prime or composite?

23. 1  Is 1 a prime or a composite number?

24. 11, 21, 31, 41, 51, 61, 71, 81,91 Prime Composite

25. Of the positive integers, 1 is  A) the smallest odd number  B) the smallest even number  C) the smallest prime number  D) the smallest integer Plan for misconceptions

26. Of the positive integers, 4, is  A) the smallest odd number  B) the smallest even number  C) the smallest prime number  D) the smallest composite number

27. What if a factor is also a prime number? 

28. Find all the prime factors of 48 2 48 2 24 2 12 2 6 3 48= 2x2x2x2x3

29. 5 35 2 60 7 2 30 3 15 35=5x7 5 60=2x2x3x5

30. Which of the following shows 24 written as a product of prime factors?  A) 24=2x3x4 B) 24=2x2x2x3  C) 24=1x2x2x2x3 D) 24=2x2x6

31. Shanghai Lesson Structure Review/recap of previous lesson Introduction of key concept Definitions of key concepts with rigorous mathematical language Conceptual variation Procedural variation –use of different methods Student solutions analysed Step by step instructions A more challenging problem that requires application of the concept

32. What number should be added to the denominator of, when 4 is added to the numerator so that the fraction remains the same value ?

33. TRG - Angles on straight lines