1. Our IS to reason why, NOT just invert and multiply! Representing and understanding multiplication and division of fractions Bill Jackson School No. 2 Paterson, NJ Tad Watanabe Keenesaw State University, GA

8. Meaning of Multiplication (1)

9. Meaning of Multiplication (2)

10. Representing multiplication with a model 32 64 ? X 2 X 2 X 3 X 3

11. Partitive Meaning of Division “equal share” division

12. Quotative (measurement) division

13. Fraction x Whole Number X 2 X 2

15. Generalizing the idea of multiplying a fraction by a whole number

16. Fraction ÷ Whole number ÷ 3 ÷ 3

17. Partitive division (missing multiplicand) ___ X 3 = 4/5 x 3 x 3

19. Generalizing the idea of dividing a a fraction by a whole number

20. Fraction x Fraction Mathematics for Elementary School 6A (Tokyo Shoseki) www.globaledresources.com

21. Creating the double number line model. 4/5 x 2/3 0 0 m 2 dl 4/5 1 2/3 X 2/3 X 2/3

22. multiplicand product multiplier

23. Using an area model with number line to think about the calculation

24. Using an area model with number line to think about the calculation 4 2 5 3

25. Generalizing the idea of fraction x fraction

26. Fraction ÷ Fraction X 3/4 X 3/4

27. Fraction ÷ Fraction ÷ 3/4 ÷ 3/4

28. Relating to what was learned before 2/5 ÷ 3/4 2/5 ÷ 2

29. Thinking about the calculation of 2/5 ÷ 3/4

30. Thinking about the calculation (2) 4/3 2 4 5 3

31. Generalizing the idea of invert and multiply