Teaching Multiplication & Division

Teaching Multiplication & Division

Centre for Excellence cluster of schoolsCombined staff meetings

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

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

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Counting and grouping

Counting

Grouping

Coordinating

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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

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

33

3

Thinking groups - not items

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.

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NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Key concepts in Multiplication and Division

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?

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

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

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

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

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

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

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Concrete Visual

Abstract 12 x 2 = 24 12

2 x

Key concepts – Distributive Property

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

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Key concepts – Inverse relationships

3 x 4 = 12 12 ÷ 3 = 4

Division start with the total items.

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

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Deep Understanding

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• 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 8If 5 x 8 = 40Then 4 x 8 must equal 32

What is the answer to 9 x 3?Double 9 is 18,18 + 2 is 2020 + 7 is 27

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

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

• Arrays

• Numberline

• 100 chart

Visuals

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Visuals - Arrays

• Classroom tools – arrays

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Learning Object – The Array

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Learning object - Arrays: factor families

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Counting-On website

NSW Department of Education & Training

NSW Public Schools – Leading the Way www.det.nsw.edu.au

Count Me In Too website