NSW Syllabuses

# Mathematics K–10 - Stage 2 - Number and Algebra Addition and Subtraction

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM

selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

### Content

• Students:
• Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
• add three or more single-digit numbers
• model and apply the associative property of addition to aid mental computation, eg 2 + 3 + 8 = 2 + 8 + 3 = 10 + 3 = 13
• apply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers, including:
• the jump strategy on an empty number line, eg 823 + 56: 823 + 50 = 873, 873 + 6 = 879
• the split strategy, eg 23 + 35: 20 + 30 + 3 + 5 = 58
• the compensation strategy, eg 63 + 29: 63 + 30 = 93, subtract 1 to obtain 92
• using patterns to extend number facts, eg 500 – 200: 5 – 2 = 3, so 500 – 200 = 300
• bridging the decades, eg 34 + 26: 34 + 6 = 40, 40 + 20 = 60
• changing the order of addends to form multiples of 10, eg 16 + 8 + 4: add 16 to 4 first
• using place value to partition numbers, eg 2500 + 670: 2500 + 600 + 70 = 3170
• partitioning numbers in non-standard forms, eg 500 + 670: 670 = 500 + 170, so 500 + 670 = 500 + 500 + 170, which is 1000 + 170 = 1170
• choose and apply efficient strategies for addition and subtraction (Problem Solving)
• discuss and compare different methods of addition and subtraction (Communicating)
• use concrete materials to model the addition and subtraction of two or more numbers, with and without trading, and record the method used
• select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to four digits
• give a reasonable estimate for a problem, explain how the estimate was obtained, and check the solution (Communicating, Reasoning)
• use the equals sign to record equivalent number sentences involving addition and subtraction and so to mean 'is the same as', rather than to mean to perform an operation, eg 32 – 13 = 30 – 11
• check given number sentences to determine if they are true or false and explain why,
eg 'Is 39 – 12 = 15 + 11 true? Why or why not?' (Communicating, Reasoning)
• Recognise and explain the connection between addition and subtraction (ACMNA054)
• demonstrate how addition and subtraction are inverse operations
• explain and check solutions to problems, including by using the inverse operation
• Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)
• calculate equivalent amounts of money using different denominations, eg 70 cents can be made up of three 20-cent coins and a 10-cent coin, or two 20-cent coins and three 10-cent coins, etc
• perform simple calculations with money, including finding change, and round to the nearest five cents
• calculate mentally to give change

### Background Information

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.

In Stage 2, it is important that students apply and extend their repertoire of mental strategies for addition and subtraction. The use of concrete materials to model the addition and subtraction of two or more numbers, with and without trading, is intended to provide a foundation for the introduction of the formal algorithm in Addition and Subtraction 2.

One-cent and two-cent coins were withdrawn by the Australian Government in 1990. Prices can still be expressed in one-cent increments, but the final bill is rounded to the nearest five cents (except for electronic transactions), eg

$5.36,$5.37 round to $5.35$5.38, $5.39,$5.41, $5.42 round to$5.40
$5.43,$5.44 round to \$5.45.

### Language

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

Students need to understand the different uses for the = sign, eg 4 + 1 = 5, where the = sign indicates that the right side of the number sentence contains 'the answer' and should be read to mean 'equals', compared to a statement of equality such as 4 + 1 = 3 + 2, where the = sign should be read to mean 'is the same as'.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑5NA the sub-elements (and levels) of Quantifying numbers (QuN9-QuN10), Additive strategies (AdS6-AdS8), Understanding money (UnM4-UnM7) and Number patterns and algebraic thinking (NPA4-NPA5) 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.

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM

selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

### Content

• Students:
• Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
• select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to and including five digits, eg 159 + 23: 'I added 20 to 159 to get 179, then I added 3 more to get 182', or use an empty number line:
• pose simple addition and subtraction problems and apply appropriate strategies to solve them (Communicating, Problem Solving)
• use a formal written algorithm to record addition and subtraction calculations involving two-, three-, four- and five-digit numbers, eg

• solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)
• solve addition and subtraction problems involving money, with and without the use of digital technologies
• use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving)
• reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning)
• calculate change and round to the nearest five cents
• use estimation to check the reasonableness of solutions to addition and subtraction problems, including those involving money

### Background Information

Students should be encouraged to estimate answers before attempting to solve problems in concrete or symbolic form. There is still a need to emphasise mental computation, even though students can now use a formal written method.

When developing a formal written algorithm, it will be necessary to sequence the examples to cover the range of possibilities, which include questions without trading, questions with trading in one or more places, and questions with one or more zeros in the first number.

This example shows a suitable layout for the decomposition method:

### Language

Students should be able to communicate using the following language: plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, empty number line, strategy, digit, estimate, round to, change (noun, in transactions of money).

Word problems requiring subtraction usually fall into two types − either 'take away' or 'comparison'.

Take away – How many remain after some are removed?
eg 'I have 30 apples in a box and give away 12. How many apples do I have left in the box?'

Comparison – How many more need to be added to a group? What is the difference between two groups?
eg 'I have 18 apples. How many more apples do I need to have 30 apples in total?', 'Mary has 30 apples and I have 12 apples. How many more apples than me does Mary have?'

Students need to be able to translate from these different language contexts into a subtraction calculation.

The word 'difference' has a specific meaning in a subtraction context. Difficulties could arise for some students with phrasing in relation to subtraction problems, eg '10 take away 9' should give a response different from that for '10 was taken away from 9'.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑5NA the sub-elements (and levels) of Quantifying numbers (QuN10-QuN11), Additive strategies (AdS7-AdS8), Understanding money (UnM4-UnM7) and Number patterns and algebraic thinking (NPA5) 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.