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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

Content

  • 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) CCT
  • 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) CCT
  • 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)  CCT
  • create, record and describe patterns with objects or symbols
  • describe a repeating pattern of objects or symbols in terms of a 'number' pattern, eg 
    Image shows 3 shape patterns; the first depicts a ‘two’ pattern, the other two a ‘three’ pattern. L
  • 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.

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

Content

  • Students:
  • Describe patterns with numbers and identify missing elements (ACMNA035) L
  • describe a number pattern in words, eg 'It goes up by threes' L
  • determine a missing number in a number pattern, eg 3, 7, 11, __, 19, 23, 27 CCT
  • 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) CCT
  • describe how a missing number in a number sentence was calculated (Communicating, Reasoning) CCT
  • solve problems involving addition or subtraction by using number sentences L
  • represent a word problem as a number sentence (Communicating, Problem Solving) L
  • pose a word problem to represent a number sentence (Communicating, Problem Solving) L

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.