Mathematics / Year 7 / Algebra

Curriculum content descriptions

recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown (AC9M7A01)

Elaborations
  • linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length x width as \(A\;=\;l\;\times\;w\) or using \(p\;=\;6g\;+\;b\) to describe a total of points expressed as goals (worth \(6\) points) and behinds (worth one point)
  • interpreting and using formulas obtained from other sources; for example, maximum heart rates and target heart rates for moderate exercise
  • substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage \(W\) given base wage \(b\) and overtime hours \(h\) at \(1.5\) times rate \(r\), \(W\;=\;b+1.5\times h\times r\), using values for mass \(m\) and volume \(v\) to determine density \(d\) of a substance where \(d\;=\;\frac mv\)
  • using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables
General capabilities
  • Critical and creative thinking Critical and Creative Thinking
  • Numeracy Numeracy
ScOT terms

Substitution,  Variables (Mathematics),  Equations

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

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.

Online

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.

Downloadable

Algebra: Foundation to Year 9

This comprehensive resource describes the progression of algebra-related ideas and algebraic thinking. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in algebra including teaching and cultural implications.

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 ...

Downloadable

The wide wide world of sports betting

This lesson explores the difference between perfectly predictable events (like the roll of a die) and less certain events (such as sports). Students investigate mathematically how sports bookmakers create odds to guarantee themselves a profit and pay gamblers less for a win than they deserve. The lesson is outlined in ...

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 ...

Video

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?

Video

MathXplosion, Ep 22: How to communicate numbers with Roman numerals

Explore an alternative way to communicate numbers using the anchor numbers 5 and 10 and the ancient Roman counting system based on letters. Roman numerals were used throughout Europe well into the middle ages and still appear in the names of monarchs, the production year of films, on buildings and on timepieces.

Online

reSolve: Algebra - Prisms and pyramids

This lesson engages students in investigating the relationship between the number of faces, edges and vertices of pyramids and prisms. Students construct their own 3D shapes, systematically record the properties of the shape and develop an algebraic formula to generalise the relationships discovered. The lesson is outlined ...

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 ...

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Representing Patterns - Calculate

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

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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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Algebra Tiles: Learning Sequence - Calculate

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

Video

MathXplosion, Ep 17: Develop mathematical mind-reading skills

Amaze your friends with your super mind-reading skills. Here’s a brain game you can play by asking a few questions and substituting letters for numbers! Learn to follow a specific sequence of arithmetical steps to always arrive at the same answer.

Video

Can you guess the weight of Uluru?

What is the "wisdom of a crowd"? Mathematician Lily Serna investigates a mathematical phenomenon that suggests that if you have a large enough crowd, with a broad variety of people making estimates, then the mean (average) answer of the crowd will be accurate! Find out if a crowd can guess the weight of Uluru from the ground ...

Video

My Five Cents: What is opportunity cost?

What is the true cost of buying something? Gen Fricker explains that it's more than just money. Learn about opportunity cost - what it is, why it's a helpful tool and when to use it. Simple! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Video

My Five Cents: Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Video

MathXplosion, Ep 7: The power of exponents

Have you heard of the term "exponential growth"? Growth can occur very quickly when powers are involved. See how you can use the power of two to rapidly increase the amount of anything from grain to coins!

Video

MathXplosion, Ep 50: How to use a tetrahedron to solve the tree problem

How can you place four trees exactly the same distance apart from one other? By making a model! By using miniature trees to make a model of the problem, it becomes clear that a 2D solution is impossible. We learn how objects can help us visualise the problem situation, which in this case requires a 3D solution: a tetrahedron.