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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

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

Coordinating

Grouping

Counting

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- 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

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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Key concepts in Multiplication and Division

- 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

- Repeated addition - Multiplication is a fast way of adding a series of numbers
3 + 3 + 3 + 3 = 12

(Division – repeated subtraction)

Concrete Visual

Abstract 3 + 3 + 3 + 3 = 12

4 groups of 3 = 12

x

- 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 – Commutative Property

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

Abstract12 x 2 = 2412

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

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

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- Counters
- Base 10 material
- Pencils
- Blocks
- Egg cartons

- Arrays
- Numberline
- 100 chart

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- Classroom tools – arrays