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Listed under:  Mathematics  >  Algebra  >  Mathematical expressions
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Linear expressions and equations: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Linear expressions and equations. Students have developed confidence from their prior learning to algebraically solve linear equations of the form ax + b = c and can represent the solution graphically. They extend this to solving pairs of simultaneous linear equations ...

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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.

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Formulate and manipulate expressions: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Formulate and manipulate expressions. Students extend the distributive law to expanding the product of two binomials (ax + b)(cx + d) and the factorisation of non-monic quadratic expressions with integer coefficients. Students practise algebraic manipulation involving ...

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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.

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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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Use variables: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Use variables. Students apply and extend their knowledge and skills of exponent laws to simplify or expand numeric and algebraic expressions and solve equations.

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Formulate and manipulate expressions: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Formulate and manipulate expressions. Students move beyond expanding and factorising linear expressions, such as 3(2x – 1) or 4x + 6, to working with monic quadratic expressions (that is, where the coefficient of the square term is 1). This involves expanding expressions ...

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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 ...

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Use variables: Year 7 – planning tool

This planning resource for Year 7 is for the topic of Use variables. Students students recognise pronumerals and variables in formulas they have been exposed to. They are presented real-life scenarios and explore the relationship between variables using algebraic notation as a representation.

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Linear expressions and equations: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Linear expressions and equations. Students build on their knowledge of the order of operations, simplifying algebraic terms and their prior knowledge of the arithmetic laws. Students will now create and rearrange linear expressions, as well as expand and factorise them.

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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 ...

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Fractions

This is a website designed for both teachers and students that addresses components of the arithmetic of fractions. It is particularly relevant for comparison and addition and subtraction of fractions with related denominators. It also contains material on finding a fraction of a quantity where the result is a whole number. ...

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Algebraic expressions

This is a website designed for both teachers and students that addresses algebraic expressions from the Australian Curriculum for year 8 students. It contains material on using simple positive and negative fractions, substitution, collecting like terms, taking products, and expanding brackets using the distributive law ...

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TIMES Module 17: Number and Algebra: the unitary method - teacher guide

This is an 18-page guide for teachers. This module introduces the idea of ratios and rates.

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Whole numbers with all four operations

This is a website designed for both teachers and students that addresses whole numbers with the four operations from the Australian Curriculum for year 6 students. It contains material on the strategies and algorithms used when adding, subtracting, multiplying and dividing whole numbers. There are pages for both teachers ...

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Addition and subtraction of fractions

This is a website designed for both teachers and students that addresses addition and subtraction of fractions. There are pages for both teachers and students. The student pages contain interactive questions for students to check their progress in the topics.

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reSolve: Algebra - Equivalence

This sequence of two lessons builds students' understanding of equivalence as balance. The equals sign is used to indicate the same value on both sides of an equation. Students develop their understanding of equivalence by looking at balancing scales with blocks of different weights. Each lesson is outlined in detail including ...

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reSolve: Polygon Pieces

This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations ...

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reSolve: Paint with Numbers

This sequence of three lessons explores ratios through the context of mixing paint. Students investigate how ratios express a multiplicative relationship between two measures and under what conditions the proportions remain constant when the numerical values of both quantities change. The lessons are outlined in detail ...

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reSolve: Quarter Cartons

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities ...