Mathematics / Year 7 / Number and Algebra / Patterns and algebra

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

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

Elaborations
  • identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention
  • moving fluently between algebraic and word representations as descriptions of the same situation
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Distributivity,  Associativity,  Commutativity,  Mathematical expressions

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Year level 7-8
Resource type
Learning area Mathematics
Interactive Resource

Multiplication of Variables

An animated tutorial that discusses expressions such as 4x, where the multiplication symbol has been omitted, and then presents a method for multiplying simple algebraic expressions.

Teacher resource

Introduction to algebra

This is a website designed for both teachers and students that addresses the introduction of algebra. It is particularly relevant for introducing the idea of the use of a variable as a way of representing numbers. There are pages for both teachers and students. The student pages contain interactive questions for students ...

Text

Mental computation

This is a website designed for both teachers and students that discusses methods of mental computation. In particular, applying the associative, commutative and distributive laws to aid mental and written computation is discussed. These are important ideas for the introduction of algebra. There are pages for both teachers ...

Interactive Resource

Expressions

An animated tutorial with a focus on collecting 'like' terms to simplify expressions. An interactive quiz is included.

Teacher resource

The laws of arithmetic and their use in algebra

This is a website designed for both teachers and students that refers to algebraic notation, the laws of arithmetic and the use of these laws in algebra from the Australian Curriculum for year 7 students. It contains material on algebraic notation, the commutative and associative laws, the use of brackets and the orders ...

Interactive Resource

Terms

An animated tutorial about terms and 'like' terms, followed by an interactive quiz.

Teacher resource

TIMES Module 23: Number and Algebra: algebraic expressions - teacher guide

This is a 25-page guide for teachers. This module introduces pronumerals and their uses. Algebraic notation is discussed. It includes substitution, adding like terms, the use of brackets, multiplying terms and using algebra to describe number patterns.

Interactive resource

Exploring algebra

Calculate a disc jockey's profit or loss when he sells records. Use algebraic notation to represent variables. For example, T = 56 + 3n (where T is total expenses and n is the number of records produced). Calculate revenue and expenses, then work out the profit or loss.

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

Circus towers: square pyramids

Work out how many acrobats are needed to form pyramid-shaped human towers. Start by building a square pyramid with five acrobats: four acrobats in the base layer and one acrobat 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 ...

Interactive resource

Circus towers: triangular towers

Work out how many acrobats are needed to form triangle-shaped human towers. Start by building a triangle with three acrobats: two acrobats in the base layer and one acrobat 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: complex pentagons

Build bridges by adding pentagonal sections (each made up of four 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 last in a series of five ...

Interactive Resource

Order of operations

This is a set of interactive questions relating to the laws of arithmetic, their usefulness in calculations, and their importance and relevance in order of operations calculations. The questions challenge and extend students' thinking about generalisations of the laws and make a link between arithmetic and algebra. The ...

Interactive Resource

Solution of simple linear equations

This is a six-page HTML resource about solving problems concerning simple linear equations. It contains five questions, three of which are interactive, and one video. The resource discusses and explains the solution of simple linear equations to reinforce the students' understanding.

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?

Interactive Resource

Substitute values into simple linear equations

This is a five-page HTML resource about solving problems concerning substitution into simple linear equations. It contains four questions, one of which is interactive, and one video. The resource discusses and explains substitution into simple linear equations to reinforce students' understanding.

Interactive Resource

Relationship between variables in context

This is a five-page HTML resource about solving problems concerning establishing relationships between variables. It contains five questions, three of which are interactive, and one video. The resource discusses and explains how to obtain relationships between variables.

Interactive Resource

Matching a formula to a given context

This is a five-page HTML resource about solving problems concerning matching formula in a given context. It contains five questions, two of which are interactive, and one video. The resource discusses and explains determining a formula to reinforce students' understanding.

Interactive Resource

Linear relations in a variety of contexts

This is a six-page HTML resource about solving problems concerning linear relations in different contexts. It contains four questions, one of which is interactive, and one video. The resource discusses and explains linear relations in a variety of contexts to reinforce the students' understanding.

Interactive resource

Exploring order of operations

Work through mathematical operations in an algorithm. Perform calculations with integers where the order of operations is important. Start with two-step operations such as 6+10x2. Move on to numerical expressions involving several operations and notation such as parentheses and indices. Solve numerical expressions quickly ...