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.

Version “WIP It’s Not Done Yet”

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

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point

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.

Relevant Sections

Book: Make it Count

Activity: Bucket Count

Activity: Calculator count (eyes closed)

Book: Teaching with Ten Frame

  • Which is Bigger (p.49) – extends to beyond 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.

Relevant Sections

Book: Make it Count

  • See AC Links Appendix
  • Counting Books/Rhymes
  • Activity: Counting Calculator

A3 Game: Walk the Dog

A3 Game: Track the T-Rex

Trust the Count

  • Make it Count: How many are there?
  • Make it Count Activity: Hungry Wombat

First Steps (p. ??)

Book: Counters in the Classroom

  • Counting and Conservation (p. 9)

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.

Relevant Sections

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

Book: Maths Games with Student Friendly Cards

  • Card Game: Snap One More
  • Card Game: Snap One Less
  • Card Game: Snap One More/One Less

Materials: School Friendly Cards

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.

Relevant Sections

Book: Counters in the Classroom

  • Number Window (p.12)

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.’

Relevant Materials

Relevant Sections

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.

Relevant Materials

Relevant Sections

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Milestone: See Subtraction, Think Addition

All related addition facts

Relevant Sections

Book: Counters in the Classroom

  • Modelling Addition (p.13, 14)

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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 =

Relevant Materials

Relevant Sections

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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’.

Relevant Materials

Relevant Sections

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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.

Relevant Materials

Relevant Sections

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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.

Relevant Materials

Relevant Sections

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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.

Relevant Sections

Book: Teaching with Tens Frames

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

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

Relevant Sections

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