NSW Syllabuses

# Mathematics K–10 - Stage 2 - Number and Algebra Patterns and Algebra

## Patterns and Algebra 1

### 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

• MA2-8NA

generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

### Content

• Students:
• Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060)
• identify and describe patterns when counting forwards or backwards by threes, fours, sixes, sevens, eights and nines from any starting point
• model, describe and then record number patterns using diagrams, words or symbols
• ask questions about how number patterns have been created and how they can be continued (Communicating)
• create and continue a variety of number patterns that increase or decrease, and describe them in more than one way
• Investigate the conditions required for a number to be even or odd and identify even and odd numbers (ACMNA051)
• model even and odd numbers of up to two digits using arrays with two rows
• compare and describe the difference between models of even numbers and models of odd numbers (Communicating)
• recognise the connection between even numbers and the multiplication facts for two (Reasoning)
• describe and generalise the conditions for a number to be even or odd
• recognise the significance of the final digit of a whole number in determining whether a given number is even or odd (Reasoning)
• identify even or odd numbers of up to four digits

### Background Information

In Stage 2, number patterns include additive patterns that increase or decrease from any starting point.

### Language

Students should be able to communicate using the following language: pattern, goes up by, goes down by, even, odd, rows, digit, multiplication facts.

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

When working towards the outcome MA2‑8NA the sub-elements (and levels) of Multiplicative strategies (MuS3-MuS6) and Number patterns and algebraic thinking (NPA4) 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.

## Patterns and Algebra 2

### 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

• MA2-8NA

generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

• ## Content

• Students:
• Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)
• complete number sentences involving addition and subtraction by calculating missing numbers,
eg find the missing numbers: $$\Box + 55 = 83$$, $$\, \Box - 15 = 19$$
• use inverse operations to complete number sentences (Problem Solving)
• justify solutions when completing number sentences (Communicating, Reasoning)
• find the missing number in a number sentence involving operations of addition or subtraction on both sides of the equals sign, eg $$8 + \Box = 6 + 7$$
• Investigate and use the properties of even and odd numbers (ACMNA071)
• investigate and generalise the result of adding, subtracting and multiplying pairs of even numbers, pairs of odd numbers, or one even and one odd number, eg even + odd = odd, odd × odd = odd
• explain why the result of a calculation is even or odd with reference to the properties of the numbers used in the calculation (Communicating, Reasoning)
• predict whether the answer to a calculation will be even or odd by using the properties of the numbers in the calculation (Reasoning)
• Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9 (ACMNA074)
• generate number patterns using multiples of 3, 4, 6, 7, 8 and 9, eg 3, 6, 9, 12, ...
• investigate visual number patterns on a number chart (Problem Solving)
• Explore and describe number patterns resulting from performing multiplication (ACMNA081)
• use the word 'term' when referring to numbers in a number pattern
• describe the position of each term in a given number pattern, eg 'The first term is 6' (Communicating)
• find a higher term in a number pattern resulting from performing multiplication, given the first few terms, eg determine the next term in the pattern 4, 8, 16, 32, 64, …
• describe how the next term in a number pattern is calculated, eg 'Each term in the pattern is double the previous term' (Communicating)
• Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)
• complete number sentences involving multiplication and division by calculating missing numbers, eg find the missing numbers: $$28 = \Box \times 7$$, $$\, 40 \div \Box = 5$$
• represent and solve multiplication and division word problems using number sentences, eg 'I buy six pens and the total cost is \$24. What is the cost of each pen?' can be represented as $$6 \times \Box = 24\,$$ or $$\,24 \div 6 = \Box$$
• discuss whether it is more appropriate to represent the problem using $$\times$$ or $$\div$$ in order to calculate the solution (Communicating, Reasoning)
• pose a word problem based on a given number sentence, eg given $$4 \times \Box = 28$$, a problem could be: 'I have 28 cans of drink and stack them into rows of 4. How many rows will there be?' (Communicating, Problem Solving, Reasoning)

### Background Information

In Stage 2, the investigation of odd and even numbers leads to understanding what happens to numbers when they are added together or multiplied together. For example, 'An odd number added to an even number always results in an odd number', 'An even number multiplied by an even number always results in an even number'.

### Language

Students should be able to communicate using the following language: pattern, term, missing number, odd, even, number sentence, is the same as, equals.

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

When working towards the outcome MA2‑8NA the sub-elements (and levels) of Additive strategies (AdS6), Multiplicative strategies (MuS4-MuS7) and Number patterns and algebraic thinking (NPA5-NPA6) 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.