Milestones: Basic Facts Multiplication & Division
For your classroom
Getting started
Check the ACARA website for the most up-to-date Curriculum, as well as your state curriculum if needed.
Recent Changes
Version: 1.1 | Updated October 29 2019 | updated Arrays Game Milestones Edition. Please redownload.
Version: 1.0 | Updated October 23 2019 | First release
Basic Facts: Multiplication & Division Milestones Sheet
The Milestones provide a default position for schools to adopt a whole school approach for the development of properties and mental strategies associated with basic facts.
Even if you don’t adopt the Milestones steps, you can make use of the linked materials.
The Multiplication and Division Milestones have been designed such that the students learn the tables from easiest to hardest. Along the way on the easier tables they will pick up most of the harder tables “for free”, reducing the load later on.
Year 2
Year 2 Prerequisites
Yr 2 ACMNA031: Recognise and represent multiplication as repeated addition, groups and arrays.
Yr 2 ACMNA032: Recognise and represent division as grouping into equal sets and solve simple problems using these representations.
Also Revisit:
– Groups
– Commutative Property of Multiplication
– Arrays
– Repeated Addition
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Year 3
Year 3 Prerequisites
Yr 3 ACMNA056: Recall multiplication facts of two, three, five and ten and related division facts.
Relevant Materials
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Dr Paul Swan Relevant Books & Downloadable Resources
Books
Dice Dilemmas: Mary’s Game (pp. 20)
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Multiplication Properties
Multiplication Property of Zero
Multiplication Property of One
Commutative Property of Multiplication
Any number multiplied by zero is zero. This can be illustrated through arrays. It is impossible to draw an array n x 0 or 0 x n.
This pattern needs to be made explicit.
Any number multiplied by one is itself (n x 1 = n).
This pattern needs to be made explicit.
Numbers may be multiplied in any order without affecting the product.
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Books
Tackling Tables pp. 10,11
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x2 Facts
Link the doubles addition facts learned in Year 2 to the x2 facts.
Introduce vocabulary such as double.
Teaching Tools:
Joining two sets of Unifix cubes of different colours will help make the links.
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Books
Tackling Tables pp. 39
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x10 Facts
Pattern: End digit is zero. Double the fives facts.
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Books
Tackling Tables pp. 24, 25
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x5 Facts
Pattern: End digit is zero or five. Half the tens facts.
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Books
Tackling Tables pp. 42
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x3 Facts
Use known facts to derive new facts
e.g.
Use 6 x 2 = 12 to work out 6 x 3.
6 x 3 = (6 x 2) + 6.
Relevant Materials
Dr Paul Swan Relevant Books & Downloadable Resources
Books
Tackling Tables pp. 40
Free Downloads
Year 4
Year 4 Prerequisites
Review facts learned in Year 3:
Multiplication Property of Zero (x0) facts,
Multiplication Property of One (x1) facts,
Commutative Property of Multiplication (2 x 3 = 3 x 2),
x2 facts,
x10 facts,
x5 facts
x3 facts
By the end of Yr 4: ACMNA075: Recall multiplication facts up to 10 × 10 and related division facts.
The grid shows the remaining facts to be learned.
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x9 Facts
Show the pattern on a Number Grid.
Relate to 10 facts: e.g. 3 x 9 = (3 x 10) – 3
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Books
Tackling Tables pp. 46
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Doubling
x 4 facts are double x 2 facts, Similarly, x8 is Double x4
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Books
Tackling Tables pp. 16
Dice Games for Tables (Entire book)
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x4 Facts
Revise the 2x facts.
Link x 2 facts to x 4 facts.
(Doubling Strategy)
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Dr Paul Swan Relevant Books & Downloadable Resources
Books
Tackling Tables (pp. 41)
Dice Games for Tables (pp. 17-24)
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x8 Facts
Link x 4 facts to x 8 facts. (Doubling Strategy)
or
Link x 2 facts to x 8 facts using double-double strategy.
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Dr Paul Swan Relevant Books & Downloadable Resources
Books
Tackling Tables (pp. 45)
Dice Games for Tables (pp. 25-28)
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x6 Facts
Link x 3 facts to x 6 facts.
(Doubling Strategy).
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Books
Tackling Tables (pp. 43)
Dice Games for Tables (pp. 29-33)
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x7 Facts
Last fact to learn (7 x 7).
This is a natural opportunity to point out the square numbers already learned (square numbers are covered in year 6).
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Books
Tackling Tables (pp. 44)
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Division Facts
Relate division to multiplication. e.g. show that: 4 x 3 = 12, 3 x 4 = 12
12 ÷ 3 = 4, 12 ÷ 4 = 3
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Dr Paul Swan Relevant Books & Downloadable Resources
Books
Tackling Tables (pp. 44)
Check the Clues 2 ( )
Pocket Dice Book B (Diviso Game )
Pocket Dice Book C ( )
Dice Dazzlers ( )
Games
Mining Boom
Race Car Rally
Multispin (Multiplication 2-9)
Spindiv (Division 2-9)
Division Decision
Free Downloads
Halving
Relate back to doubling
Divide by 4: halve and halve again (÷2, ÷ 2).
Divide by 8: halve, halve and halve again (÷ 2, ÷ 2, ÷ 2).
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Dr Paul Swan Relevant Books & Downloadable Resources
Books
Tackling Tables pp. 16
Dice Games for Tables (Entire book)
Free Downloads
Multiplication Facts Consolidation
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Year 5
Continued Practise of Multiplication and Division Facts
Start of Year 5: An opportunity to review all basic multiplication and division facts to maintain recall
Yr 5 ACMNA098: Identify and describe factors and multiples of whole numbers and use them to solve problems.
Factors and Multiples.
Apply Simple Divisibility Tests.
Yr 5 ACMNA101: Solve problems involving division by a one digit number, …
Review all basic division facts.
Factors
For example,18 not just linked to one fact of 6×3 but has factors of 1, 2, 3, 6, 9 and 18.
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Dr Paul Swan Relevant Books & Downloadable Resources
Pocket Dice Book C
- Diviso Remainder pp.22-24
Games
Mining Boom
Race Car Rally
Multispin (Multiplication 2-9)
Spindiv (Division 2-9)
Division Decision
Free Downloads
Year 6
Fraction of a Quantity
Yr 6 ACMNA127: Find a simple fraction of a quantity where the result is a whole number …
Link to known multiplication and division facts.
3 x 4 = 12
4 x 3 = 12
12 ÷ 4 = 3
12 ÷ 3 = 4
1/3 of 12 = 4
1/4 of 12 = 3
Relevant Materials
Dr Paul Swan Relevant Books & Downloadable Resources
Books
Pocket Dice Book C
- Fraction Of (pp.39-43)
Developing a Conceptual Understanding of Fractions
- pp. 62-72
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Fraction of a Quantity Games: