1. TEACHING FRACTIONS FOR MASTERY IN KS3 A lesson given in November 2015 by a Shanghai teacher to a year 8 class at a secondary comprehensive school in Devon

2. 分数的除法（ 1 ） ------ 倒数

3. Exercise 1:Calculate

4. Exercise 2:Fill in the blanks

5. Observation & Conclusion  If the numerator and denominator of two fractions are inverted, then their product is 1. Please observe the table, what conclusion can you get?

6. Reciprocal 倒数 Definition If the product of number A and B is 1, then A is the reciprocal of B.

7. Exercise 3:Draw a line to connect the reciprocal from the left to the right.

8. Exercise 4: （ 1 ） Find the reciprocal of the following fractions and conclude the solution. Reverse the numerator and denominator Change integer a to a/1 first Change a mixed number to improper fraction （ 2 ） Find the reciprocal of integers and conclude the solution (3) Find the reciprocal of mixed fractions and conclude the solution

9. Exercise 5: Say a number and pick a friend to say the reciprocal of the number. Game time

10. Exercise 6:True or false. (1)If the product of number A and B is 1, then A is the reciprocal of B. (2)If C is the reciprocal of D, then the product of C and D is 1. (3)The reciprocal of is. (4)Each number has a reciprocal. (5)No number has a reciprocal which is exactly itself. ( )

11. Conclusion The reciprocal of is. Zero does not have a reciprocal because no real number multiplied by 0 produces 1.(the product of any number with zero is zero) In positive numbers, only one number has a reciprocal which is exactly itself, 1.

12. Reciprocal & Division Exercise 7:Change the multiplication to division. If 1 is divided by a number （ ）, the quotient is the reciprocal of this number.

13. Summary Reciprocal Definition Reciprocal of a fraction Reciprocal of an integer Reciprocal of a mixed fraction Some other conclusions Relationship between Reciprocal & Division

14. Exercise 8:Calculate End of lesson

15. I did not see the next lesson, but the next slide shows how this knowledge of reciprocals and of multiplying fractions is developed into dividing by fractions in the Shanghai textbook.

17. The result would then be generalised to:

18. Division by fractions is taught not as an arbitrary rule: ‘When dividing by a fraction, turn it upside down and multiply.’ Instead, it is derived as a logical consequence of pupils’ understanding of multiplication, division and reciprocals, systematically developed in earlier lessons.