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Check the ACARA website for the most up-to-date Curriculum, as well as your state curriculum if needed.
Recent Changes
Version 1.1 31-08-2019 Count on from the Larger
Milestones: Basic Facts Addition & Subtraction
For your classroom
Basic Facts: Addition and Subtraction Milestones Sheet
Once the foundation for counting has been set, building fluency for Basic Facts follows. The Basic Facts Milestones provide yearly links to the Australian Mathematics Curriculum from Foundation to Year 2.
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.
The sound understanding of Basic Facts mental strategies is an integral part in the development of a students’ mental computation ability. Having a whole school approach is essential and the Milestones suite of resources provides a platform for schools to work from.
Even if you don’t adopt the Milestones steps, you can make use of the linked materials.
Foundation
Milestone 1
ACMNA001, ACMNA002
Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point
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Activity: Bucket Count
Activity: Calculator count (eyes closed)
POP Games
- Sequences to 10
- Sequences to 20
Other Materials
Ability to Identify the Larger Number
Links may be made to moves along a track. A roll of 4 moves further than a roll of 3.
Materials such as dominoes and cubes may be used to model this.
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Book: Make it Count
Activity: Bucket Count
Activity: Calculator count (eyes closed)
Book: Teaching with Ten Frames
- Which is Bigger (p.49) – extends to beyond 20.
POP Games
- Sequences to 10
- Sequences to 20
The Counting Principles
No Curriculum Link
How to Count:
- Know the number names in order.
- One to one matching.
- The last name spoken in the count represents the total of the set (cardinality).
What to Count:
- Order irrelevance: the count can start anywhere.
- Abstraction: children will at first only count objects that are similar. Later they will count collections of different objects and later still, unseen objects.
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Book: Make it Count
- See AC Links Appendix
- Counting Books/Rhymes
- Activity: Counting Calculator
Make it Count Section: Trust the Count
- Activity: How many are there?
- Activity: Hungry Wombat
A3 Game: Walk the Dog
A3 Game: Track the T-Rex
Book: Counters in the Classroom
- Counting and Conservation (p. 9)
Other Materials
First Steps in Mathematics: Number
- Understand Whole and Decimal Numbers (p.12)
- Trust the Count (p. 13)
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Year 1
Year 1 Prerequisites
ACMNA015
Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts.
Explore links between addition and subtraction.
Make use of the commutative property to apply the Count on from the Larger Number strategy
e.g. 7 + 2 is the same as 2 + 7.
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Content:
- Partitioning
- Part Part Whole
- Addition Strategy 1:
- Count on from the larger number 1, 2, 3 or 0
- Rearrange parts to link to subtraction.
- Count Back 1, 2, 3 or 0.
Book: Counters in the Classroom
- Shake and Spill
- Number Window (p. 9)
- Partitioning Games (p. 10)
- Partioning Board (p. 11)
- Modelling Addition (p. 13, 14)
A4 Games (Free Download):
- A4 Game: Count on from the larger
- A4 Game: Count on + 1
- A4 Game: Count on + 2
- A4 Game: Count Back 1
Book: Make it Count
- Activity: Frog Across the Water
- Activity: Snap and Count On
Book: Card Capers
- Card Game: Snap One More
- Card Game: Snap One Less
- Card Game: Snap One More/One Less
Materials: School Friendly Cards
Other Materials
Milestone: Count on from the Larger Number by 1, 2, 3 & 0
Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts.
Count on:
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Book: Card Capers
- Card Game: Snap One More (p. )
- Card Game: Snap One Less (p. )
- Card Game: Snap One More/One Less (p. )
- Card Game: Snap Two More/Two Less (p. )
Book: Make it Count
- Frog Across the Water (p. 75 )
- Snap and Count On (p. 77)
Milestone: Addition Property of Zero
See ‘Count on from the Larger Number: By 0’
The Addition Property of Zero states that a number will not change when 0 is added to it (see the green shaded numbers in the above addition grid). Essentially this is using the strategy ‘Count on from the Larger Number, by 0.’
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Milestone: Commutative Property
Once a fact is learned, the turn around fact should be known too.
Numbers may be added in any order without affecting the result (sum) e.g. 4 + 1 = 1 + 4. This means that if you learn one fact you get one free. In effect you are rearranging parts.
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Book: Counters in the Classroom
- Number Window (p.12)
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Milestone: Count Back (Subtraction) by 1, 2, 3 or 0
Related to count on by 1, 2 and 3: e.g. 1 – 1, 2 – 1, 3 – 1...
Counting back is similar to counting forward by 1,2,3,0. Some students experience difficulty counting back across the decade. Begin counting back one.
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<Coming Soon>
<Coming Soon>
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Milestone: See Subtraction, Think Addition
All related addition facts
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Book: Counters in the Classroom
- Modelling Addition (p.13, 14)
Year 2
Year 2 Prerequisites
Yr 2 ACMNA030, Yr 2 ACMNA029
Yr 2 ACMNA030: Solve simple addition and subtraction problems using a range of efficient mental … strategies.
Yr 2 ACMNA029: Explore the connection between addition and subtraction.
Fact Families: Link addition and subtraction facts: learn one fact get 5 free. For example:
Review all Count on from the Larger Number facts.
7 + 2 = 9 | 7 + = 9 | 9 – 2 = _
2 + 7 = 9 | _ + 2 = 9 | 9 – 7 =
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Use Part-Part-Whole cards
Build to Ten
This strategy accounts for 3 new facts (6 + 4, 5 + 5, 4 + 6) and revision of 6 facts.
Teaching Tools:
Ten frames are an ideal tool for teaching the ‘ten facts’.
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Free A4 Game
Build To (In the Dr Paul Swan Game Pack)
Doubles
This strategy accounts for 6 new facts (4 + 4, 5 +5, 6 + 6, 7 + 7, 8 + 8, 9 + 9) and revision of four facts (0 + 0, 1 + 1, 2 + 2, 3 + 3). The associated subtraction facts for the doubles equal zero, e.g. 4 – 4 = 0.
Teaching Tools:
Cubes in two colours may be used to model this strategy.
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Book: Cubes in the Classroom
- Doubles (p. 16)
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Free A4 Games
- Doubles Game
- Double Dominoes 6
- Double Dominoes 9
Free A4 Games
- Double Up
- Double Double Up
- Double Double Double Up
Near Doubles
Students will need to know their doubles facts and then make an adjustment to the calculation and compensate for it. For example
6 + 7 is 6 + 6 and one more or 7 + 7 take one. The associated subtraction facts all have a difference of one, e.g. 5 – 4 = 1.
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Book: Cubes in the Classroom
- Near Doubles (p. 16)
Free A4 Games
- All Doubles Games
Bridge Ten
This strategy accounts for 18 new facts. If students understand the commutative property then 9 facts (7+4, 7+5, 8+4, 8+5, 8+6, 9+4, 9+5, 9+6, 9+7). The 9+ facts can be tackled first then the 8+ facts and so on.
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Book: Teaching with Tens Frames
- Teach Bridge Ten (p.44)
- Bridge Bingo (p.45 – 48)
Free A4 Games
- Nine and Nine Plus
- Eight and Eight Plus
Leading into Year 3...
Yr 3 ACMNA055: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation.
Yr 3 ACMNA054: Recognise and explain the connection between addition and subtraction. Link via part part whole thinking.
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Flash Cards
Consolidate
Review Year 2 content
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Flash Cards and Part Part Whole Cards