1. Teaching Multiplication & Division Centre for Excellence cluster of schools Combined staff meetings NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au

2. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au In groups/pairs discuss –What does teaching Multiplication & Division look like in my classroom? –What do I already know about how students learn to multiply and divide? –Share Multiplication & Division in the classroom

3. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Counting and grouping Counting Grouping Coordinating 3

4. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Terminology Composite units a set of items are treated spatially (visually) or numerically (abstractly) as a unit

5. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au 4 groups of 3 counting grouping 4 threes coordinating 3 3 3 3 Thinking groups - not items

6. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Background notes Some students persist with counting by ones and have difficulty in progressing to grouping strategies By focusing on groups, rather than individual items, students learn to treat the groups as composite units. 6

7. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Key concepts in Multiplication and Division

8. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Teaching Key concepts In our Explicit teaching part of the lesson how do we ensure deep understanding of the concept? How do we teach concepts? What are the key ideas?

9. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au What are the key concepts in multiplication & division?  Repeated addition  Commutative property  Associative property  Inverse relationship mult/division Key concepts

10. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Repeated addition - Multiplication is a fast way of adding a series of numbers 3 + 3 + 3 + 3 = 12 (Division – repeated subtraction) Key concepts – Repeated addition

11. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Concrete  Visual  Abstract 3 + 3 + 3 + 3 = 12 4 groups of 3 = 12 Key concepts – Repeated addition x

12. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Commutative Property of Multiplication - it doesn’t matter which number is first. 3 x 4 = 12 4 x 3 = 12 Key concepts – Commutative Property 3 x 4 = 4 x 3

13. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Concrete  Visual  Abstract- 3 x 4 = 4 x 3 Key concepts – Repeated addition Key concepts – Commutative Property 

14. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Distributive Property 2 x 14 = 2 x (10 + 4) = (2 x 10) + (2 x 4) = 20 + 8 = 28 Key concepts – Distributive Property

15. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Concrete  Visual  Abstract12 x 2 = 2412 2 x Key concepts – Distributive Property

16. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Splitting the product into known parts. 8 x 7 = 7 x 7 = 49 8 x 7 = 49 + 7 8 x 7 = 56 Key concepts – Distributive Property

17. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Key concepts – Inverse relationships 3 x 4 = 1212 ÷ 3 = 4   Division start with the total items.

18. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au  Repeated addition  Commutative property  Distributive property  Inverse relationship mult/division Key concepts

19. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Deep Understanding 19 Students who understand how to coordinate composite units are able to make efficient use of known facts What is the answer to 8 x 4? 8 x 4 is the same as 4 x 8 If 5 x 8 = 40 Then 4 x 8 must equal 32 What is the answer to 9 x 3? Double 9 is 18, 18 + 2 is 20 20 + 7 is 27

20. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Concrete /Manipulatives Counters Base 10 material Pencils Blocks Egg cartons

21. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Arrays Numberline 100 chart Visuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0

22. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Visuals - Arrays Classroom tools – arrays

23. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Learning Object – The Array

24. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Learning object - Arrays: factor families

25. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Counting-On website

26. NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au Count Me In Too website