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

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

Online

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 ...

Online

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 ...

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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 ...

Downloadable

Expressions, formulas and substitution

In the lesson ‘Formulating algebraic expressions’, students were introduced to variables and forming algebraic expressions. In this lesson, students continue to develop these skills and will explore substituting values into familiar and unfamiliar formulas to determine an unknown. Students explore substitution in a range ...

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7A01A Algebra - Ochre Education

This eight lesson unit of work focuses on algebra. Students use pronumerals and variables to generalise expressions, explore substitution of pronumerals, write and interpret algebraic expressions in words and apply numerical and algebraic operations to pronumerals and expressions. The unit includes a slide show for structuring ...

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7A02A Equations - Ochre Education

This seven lesson unit of work focuses on equations. Students write algebraic equations from worded descriptions and identify solutions by inspection using addition and multiplication facts, apply numerical and arithmetic operations to numerical and algebraic equations, solve and verify solutions to equations, describe ...

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Algebra Tiles: Learning Sequence - Calculate

The following is a suggested teaching and learning sequence for using Algebra Tiles.

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The Geometry and Algebra of Honeycomb - Calculate

This integrated unit of work explores the amazing structures of honeycomb by examining the properties of regular and irregular polygons and polyhedra. Students then move on to solve problems using geometric and algebraic reasoning.

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Linear Algebra Year 7 - Calculate

The focus of this activity is to find out what students know about linear equations and what are some of the different strategies students are able to use and explain. Do students prefer to use equations or do students rely more on empty number lines?

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Representing Patterns (Year 7) - Calculate

Patterns can be represented in several ways and this unit will explore five different representations.

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Representing Patterns - Calculate

In this activity, students examine the representation of patterns, including as diagrams, charts and formulas.

Video

Algebra basics video

Use this video as a springboard to introduce algebraic thinking, and to apply that thinking to a financial context, drawing on reasoning.

Video

Algebraic equations: video and teaching guide

This video uses an everyday scenario of three people sharing a taxi ride to explore algebraic thinking, and to apply that thinking to a financial context, drawing on reasoning and mathematical modelling. Use the video with the supporting teacher guide as a springboard to explore mathematical concepts. The teacher guide ...

Interactive

Squirt: three containers

Examine the relationships between capacities of various containers. Look at three containers that may have different diameters, heights and shapes. Fill a container and squirt liquids between the containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. ...

Video

BTN: What is the GST?

The Goods and Services Tax (GST) is a tax placed on things people buy with money or things people do for money. Can you name some goods and services that have GST? What about some goods and services that don't have GST? Find out when and why the GST was first introduced.

Video

My Five Cents: Why investing can be risky

Planning to get rich quick by investing one day? Before you jump in, let Gen Fricker explain some of the risks involved with different types of investments. Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Video

Numbers Count: What are factors?

What are factors? Watch as the jelly babies in this clip show you! What are the factors of 12? How many factors does the number 11 have? Try explaining to a friend what a prime number is.

Interactive

Syllabus Bites: Revisiting proportion

This is the first in a series of Syllabus Bites related to direct and indirect proportion. Students revise the concept of ratio. They create short visual explanations showing how problems can be solved.

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Solving equations with algebra mats

In this lesson, students are introduced to solving one-variable linear expressions using a variety of concrete materials, which are related to authentic contexts to enhance their understanding.

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Using algebra tiles to solve equations

In this lesson, students use algebra tiles to solve one-variable linear equations involving multiplication and division, applying these skills in real-world contexts to enhance their understanding.