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

Interactive

Terms

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

Interactive

Expressions

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

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 ...

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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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Algebra Tiles: Learning Sequence - Calculate

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

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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.

Online

Finding the shortest path

In this lesson, students will experiment with different ways of creating a path between two points with algorithm design and generalizing patterns. From the patterns, they will be able to generate an algorithm for efficiently traveling through cities in a region.

Online

Formulate and manipulate expressions: Year 7 – planning tool

This planning resource for Year 7 is for the topic of Formulate and manipulate expressions. Students find unknown quantities in numerical equations involving a combination of operations.

Online

Graphs: Year 7 – planning tool

This planning resource for Year 7 is for the topic of Graphs. Students are introduced to the four-quadrant Cartesian plane. The format of the coordinates should be explained and demonstrated; coordinates do not have to be an integer value.

Online

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 ...

Online

Patterns, rules and graphs

In this lesson, students play games and learn about space and location, the Cartesian plane, pattern recognition and reductive reasoning by playing games and thinking. Students create algebraic equations to describe their strategy. Follow this lesson with Graphs: formulas and variables, though both lessons can be taught ...

Online

Formulating algebraic expressions

This lesson encompasses students’ introduction to formal algebraic concepts. Students will be introduced to the concept of variables and will explore the construction of algebraic expressions using concrete materials. Students explore a range of authentic contexts and hands-on materials in this lesson to ensure their initial ...

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. ...

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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.