Teaching Multiplication & Division Centre for Excellence cluster of schools Combined staff meetings NSW Department of Education & Training NSW Public Schools – Leading the Way

NSW Department of Education & Training NSW Public Schools – Leading the Way 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

NSW Department of Education & Training NSW Public Schools – Leading the Way Counting and grouping Counting Grouping Coordinating 3

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

NSW Department of Education & Training NSW Public Schools – Leading the Way 4 groups of 3 counting grouping 4 threes coordinating Thinking groups - not items

NSW Department of Education & Training NSW Public Schools – Leading the Way 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

NSW Department of Education & Training NSW Public Schools – Leading the Way Key concepts in Multiplication and Division

NSW Department of Education & Training NSW Public Schools – Leading the Way 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?

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

NSW Department of Education & Training NSW Public Schools – Leading the Way Repeated addition - Multiplication is a fast way of adding a series of numbers = 12 (Division – repeated subtraction) Key concepts – Repeated addition

NSW Department of Education & Training NSW Public Schools – Leading the Way Concrete  Visual  Abstract = 12 4 groups of 3 = 12 Key concepts – Repeated addition x

NSW Department of Education & Training NSW Public Schools – Leading the Way 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

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

NSW Department of Education & Training NSW Public Schools – Leading the Way Distributive Property 2 x 14 = 2 x (10 + 4) = (2 x 10) + (2 x 4) = = 28 Key concepts – Distributive Property

NSW Department of Education & Training NSW Public Schools – Leading the Way Concrete  Visual  Abstract12 x 2 = x Key concepts – Distributive Property

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

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

NSW Department of Education & Training NSW Public Schools – Leading the Way  Repeated addition  Commutative property  Distributive property  Inverse relationship mult/division Key concepts

NSW Department of Education & Training NSW Public Schools – Leading the Way 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, is is 27

NSW Department of Education & Training NSW Public Schools – Leading the Way Concrete /Manipulatives Counters Base 10 material Pencils Blocks Egg cartons

NSW Department of Education & Training NSW Public Schools – Leading the Way Arrays Numberline 100 chart Visuals

NSW Department of Education & Training NSW Public Schools – Leading the Way Visuals - Arrays Classroom tools – arrays

NSW Department of Education & Training NSW Public Schools – Leading the Way Learning Object – The Array

NSW Department of Education & Training NSW Public Schools – Leading the Way Learning object - Arrays: factor families

NSW Department of Education & Training NSW Public Schools – Leading the Way Counting-On website

NSW Department of Education & Training NSW Public Schools – Leading the Way Count Me In Too website