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NSW Syllabuses

Mathematics K–10 - Stage 3 - Number and Algebra Addition and Subtraction

Addition and Subtraction 1

Outcomes

A student:

  • MA3-1WM

    describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

  • MA3-2WM

    selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

  • MA3-3WM

    gives a valid reason for supporting one possible solution over another

  • MA3-5NA

    selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

  • Students:
  • Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
  • use the term 'sum' to describe the result of adding two or more numbers, eg 'The sum of 7 and 5 is 12' L
  • add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
  • select and apply efficient mental, written and calculator strategies to solve addition and subtraction word problems, including problems involving money LICTCCT
  • interpret the words 'increase' and 'decrease' in addition and subtraction word problems, eg 'If a computer costs $1599 and its price is then decreased by $250, how much do I pay?' (Communicating, Problem Solving) L
  • record the strategy used to solve addition and subtraction word problems
  • use empty number lines to record mental strategies (Communicating, Problem Solving)
  • use selected words to describe each step of the solution process (Communicating, Problem Solving) L
  • check solutions to problems, including by using the inverse operation CCT
  • Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)
  • round numbers appropriately when obtaining estimates to numerical calculations
  • use estimation to check the reasonableness of answers to addition and subtraction calculations, eg 1438 + 129 is about 1440 + 130 CCT
  • Create simple financial plans (ACMNA106)
  • use knowledge of addition and subtraction facts to create a financial plan, such as a budget, eg organise a class celebration on a budget of $60 for all expenses PSCWE
  • record numerical data in a simple spreadsheet (Communicating) ICT
  • give reasons for selecting, prioritising and deleting items when creating a budget (Communicating, Reasoning) CCTPSCWE

Background Information

In Stage 3, mental strategies need to be continually reinforced.

Students may find recording (writing out) informal mental strategies to be more efficient than using formal written algorithms, particularly in the case of subtraction.

For example, 8000 − 673 is easier to calculate mentally than by using a formal algorithm.

Written strategies using informal mental strategies (empty number line):

The jump strategy can be used on an empty number line to count up rather than back.
Image shows a number line that jumps from 673 to 8000 to demonstrate counting up.
The answer will therefore be 7000 + 300 + 20 + 7 = 7327. Students could share possible approaches and compare them to determine the most efficient.

The difference can be shifted one unit to the left on an empty number line, so that 8000 − 673 becomes 7999 − 672, which is an easier subtraction to calculate.

The image shows number line where the difference has been shifted by one unit to the left.

Written strategies using a formal algorithm (decomposition method):

Image shows the written algorithm for 8000 minus 673 with the workings to reach the answer 7327. 

An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations.

Language

Students should be able to communicate using the following language: plus, sum, add, addition, increase, minus, the difference between, subtract, subtraction, decrease, equals, is equal to, empty number line, strategy, digit, estimate, round to, budget.

Teachers should model and use a variety of expressions for the operations of addition and subtraction, and should draw students' attention to the fact that the words used for subtraction may require the operation to be performed with the numbers in the reverse order to that in which they are stated in the question. For example, '9 take away 3' and 'reduce 9 by 3' require the operation to be performed with the numbers in the same order as they are presented in the question (ie 9 – 3). However, 'take 9 from 3', 'subtract 9 from 3' and '9 less than 3' require the operation to be performed with the numbers in the reverse order to that in which they are stated in the question (ie 3 – 9). 

National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑5NA the sub-elements (and levels) of Additive strategies (AdS7-AdS8) and Understanding money (UnM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.

Addition and Subtraction 2

Outcomes

A student:

  • MA3-1WM

    describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

  • MA3-2WM

    selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

  • MA3-3WM

    gives a valid reason for supporting one possible solution over another

  • MA3-5NA

    selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

  • Students:
  • Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)
  • solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' CCT
  • select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) LICTCCT
  • explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) CCT
  • reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) CCT
  • give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)
  • record the strategy used to solve addition and subtraction word problems L
  • use selected words to describe each step of the solution process (Communicating, Problem Solving) L

Background Information

Refer to background information in Addition and Subtraction 1.

Language

Students should be able to communicate using the following language: plus, sum, add, addition, increase, minus, the difference between, subtract, subtraction, decrease, equals, is equal to, operation, digit.

When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, eg 'amount to pay = …', 'change = …'.

Refer also to language in Addition and Subtraction 1.

National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑5NA the sub-elements (and levels) of Additive strategies (AdS8) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.