Mathematics / Year 6 / Number and Algebra / Patterns and algebra

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

Elaborations
  • identifying and generalising number patterns
  • investigating additive and multiplicative patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern looking for patterns in the way the numbers increase/decrease
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Sequences (Number patterns),  Mathematical expressions

Interactive Resource

Sites2See: Patterns and Algebra

Selected links to a range of interactive online resources for the study of patterns and algebra in Foundation to Year 6 Mathematics.

Tablet friendly (Interactive resource)

Circus towers: square stacks

Work out how many acrobats are needed to form square-shaped human towers. Start by building a square tower with four acrobats: two acrobats in the base layer and two acrobats standing on their shoulders. Examine a table and graph of the total number of acrobats in the towers. Predict the number of acrobats needed to build ...

Interactive resource

Bridge builder: triangles 1

Build bridges by adding triangular sections. Each section is made up of three beams. Make bridges in order of increasing widths (increasing by one section each time). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build a wider span. Describe ...

Interactive resource

Bridge builder: complex squares

Build bridges by adding regular sections (each made up of three beams plus a shared beam). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build a wider span. Describe the number pattern. This learning object is the fourth in a series of five ...

Interactive resource

Bridge builder: quadrilaterals

Build bridges by adding quadrilateral sections (each made up of four beams). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build bridges with wider spans. Describe the number pattern. This learning object is the third in a series of five ...

Interactive resource

Bridge builder: triangles 2

Build bridges by adding triangular sections (each made up of three beams). Make bridges in order of increasing widths (increasing by at least one section each time). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build a wider span. Describe ...

Interactive resource

Balance the blobs: find the rule 2

Balance scales by using blobs. Using non-unit ratios, such as 3:2, 4:5 or 5:2, explore how many black blobs and white blobs balance each other. Discover the rule that balances the scales with the correct number and type of blobs. For example, 3 black blobs balance 2 white blobs. Find out how many black blobs balance 4 white ...

Interactive resource

Circus towers: rectangular prisms

Work out how many acrobats are needed to form towers in the shape of rectangular prisms. Start by building a prism with twelve acrobats: six acrobats in the base layer and six acrobats standing on their shoulders. Examine a table and graph of the total number of acrobats in the towers. Predict the number of acrobats needed ...

Interactive resource

Circus towers: triangular prisms

Work out how many acrobats are needed to form prism-shaped human towers. Start by building a triangular prism with six acrobats: three acrobats in the base layer and three acrobats standing on their shoulders. Examine a table and graph of the total number of acrobats in the towers. Predict the number of acrobats needed ...

Moving Image

Patterns, primes and Pascal's Triangle

Are you intrigued by patterns? Check out Vi Hart as she explains how to visualise patterns in prime numbers, using Ulam's Spiral. Watch as Vi creates patterns, using Pascal's Triangle to explore relationships in number. See what happens when she circles the odd numbers. What rule does she use to create the final pattern?

Teacher resource

reSolve: Real World Algebra: Chicken Box Patterns

This series of lessons explores number patterns and their rules, exploring pre-algebra ideas in a real-world setting. Students investigate how the geometric construction of chicken boxes (with toothpicks and chickpeas) is reflected in number patterns. The unit provides opportunities to expand to the more algebraic idea ...

Interactive Resource

Pattern shapes, by the Math Learning Centre - iTunes app

Use this open exploration tool to explore patterns in geometry, fractions, area and perimeter by creating your own shapes or filling in shapes. Use the text tool to annotate your representations. Great for work on fractions, symmetry and area. Free when reviewed on 12/5/2015.

Moving Image

Phi challenge

The golden ratio, Phi: fact or fallacy? What about the Fibonacci sequence? We are told this ratio and its cousin Fibonacci occur everywhere in nature. Let's see which of these claims stacks up when put to the test.

Teacher resource

Palindromic numbers

In a grade 6 mathematics class a teacher plans for, delivers and reflects on a lesson focusing on Number and Algebra. In planning the lesson, she articulates a preference for using open-ended problem-solving activities and resources that can cater for a range of abilities. In designing activities, and in selecting resources, ...

Moving Image

Spiral away with Fibonacci

Do you know the Fibonacci sequence? Learn how to draw a cool spiral as Vi Hart shows you an easy way. See how a spiral is an example of Fibonacci numbers. Vi shows examples of spirals from nature. You might be surprised at some of her examples! This is the first in a series.

Interactive resource

Visual, geometrical and numerical patterns

This interactive animated presentation includes different scenarios in which visual, geometrical and numerical patterns are identified, explained and described. Students are engaged in extending patterns; and creating and using rules to describe and extend the patterns.

Text

BBC Bitesize: linear sequences - revision

These illustrated information sheets revise the definition of a sequence and the nth term. The method of finding the rule for the nth term is extended to more complicated sequences. Highest common factors and lowest common multiples of pairs of numbers are found. This resource is one of a series of online resources from ...

Teacher resource

Top drawer teachers: fractions

This is a web page that comprehensively covers the teaching of the conceptual understanding of fractions through links to six sections. The first section covers the ‘Big ideas’ behind fractions, while the second section uses research findings to identify some common misunderstandings when learning fractions. The third explores ...

Teacher resource

TIMES Module 19: Number and Algebra: multiples, factors and powers - teacher guide

This is a 33-page guide for teachers. It introduces the concepts of primes, composites, prime factorisation, factors, multiples, odd and even numbers, the least common multiple and the highest common factor.

Teacher resource

Starting Smart: what is next in the pattern? - years 6-8

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' understanding of patterns and sequences. Students: identify, describe and extend patterns; construct tables of values; plot graphs; and develop skills to describe algebraically the relationships ...