Workshop 4: Multiplication, Division and Fractions

1. Workshop 4: Multiplication, Division and Fractions Presented by CW

2. Building the knowledge foundations Factor of 10 between columns Using 10 x Groups to 20 Decade Pairs to 100 X 2, x5, x10 10’s in any number Using decades Larger numbers Name columns Importance of 10 Using facts to10 10+ Doubles to 20 Count in 2’s 5’s 10’s Groups to 5 5 + Groups to 10 Doubles to 10 Counting Numerals Sequence Language Sets

3. Multiplication type problems I have 3 bags of lollies and there are 5 lollies in each bag. How many lollies have I got altogether? Can I solve the problem if I am stage 0 or stage 1? How would I solve the problem if I am stage 2 or stage 3? How could I solve the problem if I am at stage 4 and what knowledge MUST I have in my tool box?

4. The key Idea to use Skip Counting • Skip Counting like counting can be just rote learnt. • Realisation that the skip counting sequence relates to putting the same sets of numbers together and the end count measures the set and that the rote count forwards gives the result of adding the set number of objects and backwards gives the result of subtracting the set number of objects.

5. Stage 4 - 5 • Key Idea: Children are learning to use addition strategies to solve problems that could be solved by multiplication. • Multiplication as repeated addition • Commutativity of multiplication • Sharing into equal sets • Grouping, how many sets can be made.

6. Stage 5: Using known facts • 2 x doubles • 10 x place value • 5 x place value and doubles (halves)

8. Stage 5 - 6 • Children are learning to derive further multiplication facts using addition and subtraction strategies from multiplication facts they already know. • 4 x = 2 x + 2 x (doubling) • 3 x = 2 x + 1 x • 6 x = 5 x + 1 x ( or double 3 x when 3 x are known facts)

10. Not many left to learn • 7 x = 5 x + 2 x • 8 x = 5 x + 3 x or 10 x – 2 x • 9 x = 10 x – 1 x Children need to understand and be able to use the relationships between the multiplication tables. When working with bigger numbers the “tables” become the knowledge tools for multiplicative thinking in the same way as basic addition facts are the knowledge tools for additive thinking.

11. Tools in the tool box Counting Plastic tools, good to start with but not very efficient Addition and Subtraction Increasing range of more sophisticated tools Multiplication and Division The power tools. Increasingly efficient and sophisticated.

12. Fractions at ENP Why? When ? How?

13. Fractional Misconceptions • No acceptance of the existence of numbers between numbers Share 5 biscuits between 4 children …. You can’t do it!

14. Fractional Misconceptions • The numerator relates to the whole ½ is 1 shared between 2 ¼ is 1 shared between 4

15. Fractional Misconceptions • Half is a variable hence all fractions are variable ½ of 12 is 6 ½ of 8 is 4 ½ of 4 is 2……so the half keeps changing

16. Fractional Misconceptions • The symbol can be either way up • You can’t have fractions greater than 1 4 = 6 never been challenged 6 4 if fractions greater than haven’t been explored

17. Fractional Framework

18. Stage 2/3

19. Stage 4

20. Stage 5