NSW Syllabuses

# Mathematics K–10 - Stage 1 - Number and Algebra Patterns and Algebra

## Patterns and Algebra 1

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-2WM

uses objects, diagrams and technology to explore mathematical problems

• MA1-8NA

creates, represents and continues a variety of patterns with numbers and objects

• Students:
• Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)
• identify and describe patterns when skip counting forwards or backwards by ones, twos, fives and tens from any starting point
• use objects to represent counting patterns (Communicating)
• investigate and solve problems based on number patterns (Problem Solving)
• represent number patterns on number lines and number charts
• recognise, copy and continue given number patterns that increase or decrease, eg
1, 2, 3, 4, …
20, 18, 16, 14, …
• describe how number patterns are made and how they can be continued (Communicating, Problem Solving)
• create, record and describe number patterns that increase or decrease
• recognise, copy and continue patterns with objects or symbols
• recognise when an error occurs in a pattern and explain what is wrong (Communicating, Problem Solving)
• create, record and describe patterns with objects or symbols
• describe a repeating pattern of objects or symbols in terms of a 'number' pattern, eg
• make connections between repeating patterns and counting, eg a 'three' pattern and skip counting by threes (Communicating, Reasoning)
• model and describe 'odd' and 'even' numbers using counters paired in two rows
• describe the pattern created by modelling odd and even numbers (Communicating)

### Background Information

Repeating patterns of objects or symbols are described using numbers that indicate the number of elements that repeat, eg A, B, C, A, B, C, … has three elements that repeat and is referred to as a 'three' pattern.

In Stage 1, students further explore additive number patterns that increase or decrease. Patterns could now include any patterns observed on a number chart and these might go beyond patterns created by counting in ones, twos, fives or tens. This links closely with the development of Whole Numbers and Multiplication and Division.

### Language

Students should be able to communicate using the following language: pattern, number line, number chart, odd, even.

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

When working towards the outcome MA1‑8NA the sub-elements (and levels) of Quantifying numbers (QuN7), Multiplicative strategies (MuS2-MuS5) and Number patterns and algebraic thinking (NPA3-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:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-2WM

uses objects, diagrams and technology to explore mathematical problems

• MA1-3WM

supports conclusions by explaining or demonstrating how answers were obtained

• MA1-8NA

creates, represents and continues a variety of patterns with numbers and objects

• Students:
• Describe patterns with numbers and identify missing elements (ACMNA035)
• describe a number pattern in words, eg 'It goes up by threes'
• determine a missing number in a number pattern, eg 3, 7, 11, __, 19, 23, 27
• describe how the missing number in a number pattern was determined (Communicating, Reasoning)
• check solutions when determining missing numbers in number patterns by repeating the process (Reasoning)
• Solve problems by using number sentences for addition or subtraction (ACMNA036)
• complete number sentences involving one operation of addition or subtraction by calculating the missing number, eg find $$\;\square$$ so that $$5 +\; \square \; = 13$$ or $$15 - \;\square \; = 9$$
• make connections between addition and related subtraction facts to at least 20 (Reasoning)
• describe how a missing number in a number sentence was calculated (Communicating, Reasoning)
• solve problems involving addition or subtraction by using number sentences
• represent a word problem as a number sentence (Communicating, Problem Solving)
• pose a word problem to represent a number sentence (Communicating, Problem Solving)

### Background Information

In Stage 1, describing number relationships and making generalisations should be encouraged when appropriate.

### Language

Students should be able to communicate using the following language: pattern, missing number, number sentence.

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

When working towards the outcome MA1‑8NA the sub-elements (and levels) of Additive strategies (AdS6) 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.