Teaching Multiplication & Division
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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. Multiplication & Division in the classroom . In groups/pairs discuss

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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


Multiplication division in the classroom
Multiplication & Division in the classroom

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


Counting and grouping
Counting and grouping

Coordinating

Grouping

Counting

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Terminology
Terminology

  • Composite units

    a set of items are treated spatially (visually) or numerically (abstractly)

    as a unit


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Thinking groups - not items

4 groups of 3

counting grouping

4 threes

coordinating


Background notes
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


Key concepts in multiplication and division

Key concepts in Multiplication and Division


Teaching key concepts
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?


Key concepts

What are the key concepts in multiplication & division?

  • Repeated addition

  • Commutative property

  • Associative property

  • Inverse relationship mult/division


Key concepts repeated addition
Key concepts – Repeated addition

  • Repeated addition - Multiplication is a fast way of adding a series of numbers

    3 + 3 + 3 + 3 = 12

    (Division – repeated subtraction)


Key concepts repeated addition1
Key concepts – Repeated addition

Concrete  Visual 

Abstract 3 + 3 + 3 + 3 = 12

4 groups of 3 = 12

x


Key concepts commutative property
Key concepts – Commutative Property

  • Commutative Property of Multiplication - it doesn’t matter which number is first.

    3 x 4 = 12

    4 x 3 = 12

3 x 4 = 4 x 3


Key concepts repeated addition2

Key concepts – Commutative Property

Key concepts – Repeated addition

Concrete  Visual 

Abstract - 3 x 4 = 4 x 3


Key concepts – Distributive Property

Distributive Property

2 x 14 = 2 x (10 + 4)

= (2 x 10) + (2 x 4)

= 20 + 8

= 28


Key concepts – Distributive Property

Concrete  Visual 

Abstract 12 x 2 = 24 12

2 x


Key concepts – Distributive Property

Splitting the product into known parts.

8 x 7 = 7 x 7 = 49

8 x 7 = 49 + 7

8 x 7 = 56


Key concepts – Inverse relationships

3 x 4 = 12

12 ÷ 3 = 4

Division start with the total items.


Key concepts

  • Repeated addition

  • Commutative property

  • Distributive property

  • Inverse relationship mult/division


Deep understanding
Deep Understanding

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

19


Concrete manipulatives
Concrete /Manipulatives

  • Counters

  • Base 10 material

  • Pencils

  • Blocks

  • Egg cartons


Visuals
Visuals

  • Arrays

  • Numberline

  • 100 chart

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Visuals arrays
Visuals - Arrays

  • Classroom tools – arrays






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