Milestones: Basic Facts Addition & Subtraction

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 31-08-2019 Count on from the Larger

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

Dr Paul Swan Relevant Books & Downloadable Resources

Activity: Bucket Count

Activity: Calculator count (eyes closed)

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.

Dr Paul Swan Relevant Books & Downloadable Resources

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

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.

Dr Paul Swan Relevant Books & Downloadable Resources

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)

 

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.

Dr Paul Swan Relevant Books & Downloadable Resources

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

First Steps in Mathematics: Number

  • Understand Operations (p.20)

 

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:

Dr Paul Swan Relevant Books & Downloadable Resources

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.’

Dr Paul Swan Relevant Books & Downloadable Resources

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.

Dr Paul Swan Relevant Books & Downloadable Resources

Book: Counters in the Classroom

  • Number Window (p.12)

 

 

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.

Dr Paul Swan Relevant Books & Downloadable Resources

<Coming Soon>

<Coming Soon>

 

Milestone: See Subtraction, Think Addition

All related addition facts

Dr Paul Swan Relevant Books & Downloadable Resources

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 =

Dr Paul Swan Relevant Books & Downloadable Resources

Free Downloads

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’.

Dr Paul Swan Relevant Books & Downloadable Resources

Free A4 Game

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.

Dr Paul Swan Relevant Books & Downloadable Resources

Book: Cubes in the Classroom

  • Doubles (p. 16)

Free A4 Games

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.

Dr Paul Swan Relevant Books & Downloadable Resources

Book: Cubes in the Classroom

  • Near Doubles (p. 16)

Free A4 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.

Dr Paul Swan Relevant Books & Downloadable Resources

Book: Teaching with Tens Frames

  • Teach Bridge Ten (p.44)
  • Bridge Bingo (p.45 – 48)

Free A4 Games

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.

Relevant Materials

Dr Paul Swan Relevant Books & Downloadable Resources

Free Downloads

Consolidate

Review Year 2 content

Dr Paul Swan Relevant Books & Downloadable Resources

Free Downloads

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