Mathematics / Year 8 / Number and Algebra / Patterns and algebra

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

Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)

Elaborations
  • applying the distributive law to the expansion of algebraic expressions using strategies such as the area model
General capabilities
  • Numeracy Numeracy
ScOT terms

Distributivity,  Mathematical expressions

Refine results by

Year level 7-8
Resource type
Learning area Mathematics
Teacher resource

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 ...

Teacher resource

reSolve: Algebra: Think of a number - Linear Equations

This lesson explores algebra by generalising results from arithmetic used in 'think of a number' games. Students connect arithmetic operations with algebraic notation and visualisations. The lesson begins with an observation made using arithmetic that students then justify and extend using algebra. The lesson is outlined ...

Moving Image

Solving equations with the distributive property

This is a video demonstration of solving a linear equation by algebraic means. In the commentary, the presenter carefully explains the step-by-step method used to solve this example, which includes use of the distributive law and collecting like terms to simplify the equation. Having found the solution, the presenter verifies ...

Teacher resource

reSolve: Algebra: Tens and Units

This sequence of lessons aims to develop understanding of algebra as generalised arithmetic. Students learn to express 2- and 3-digit numbers in a general form and use this to explain results of arithmetic operations involving numbers with their digits reversed. The task links the ideas of place value with algebraic reasoning. ...

Teacher resource

reSolve: Working with algebra

This sequence of two lessons gives students opportunities to explore and share strategies for solving algebraic problems. The lessons focus on open-ended problem solving and developing multiple approaches to solving problems algebraically such as using like terms and substitution. Students work individually and in small ...

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

Brackets

A short, animated tutorial about expanding brackets, followed by an interactive quiz.

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

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

EagleCat: linear graph

Explore the graphs of linear equations in the form y = mx + c. Observe changes to the gradient and y-intercept under various transformations. Alternately, change the equation and observe changes in the y-intercept or change the y-intercept and see how the equation changes.

Interactive resource

Mobile phone plans: find the best deal 1

Help three customers compare monthly call costs quoted by two different phone companies. Use line graphs to work out the costs for talk time, text messages and total costs. Recommend the best plan. This learning object is one in a series of six objects.

Interactive resource

Mobile phone plans: several companies

Compare monthly call costs quoted by different phone companies. Use line graphs to work out the costs for talk time, text messages, photos and total costs. Recommend the best plan. This learning object is one in a series of six objects.

Interactive resource

Biscuit factory: complex ratios

Examine a pair of gears that drives a conveyor belt to an oven, including cases where the belt gear is larger than the driver. Notice that the number of rotations for each gear depends on the gear size (number of teeth). Explore the relationship between the number of teeth and the number of rotations. Build a table to compare ...

Interactive resource

Exploring linear equations

Watch a video showing animals feeding at a zoo. See how linear equations are used to calculate daily feeding costs. For example, daily costs of meat for tigers is ($9.90 per kg x 36kg) + $10 delivery = $366.40. Adjust three variables on sliding scales to produce a given number.

Interactive resource

Mobile phone plans: peak and off-peak

Compare monthly call plans quoted by a phone company. Look at the effect of off-peak discounts. Use line graphs to work out the costs for talk time, text messages, photos and total costs. Recommend the best plan. This learning object is one in a series of six objects.

Interactive resource

Mobile phone plans: one company

Compare monthly call plans quoted by a phone company. Use line graphs to work out the costs for talk time, text messages, photos and total costs. Recommend the best plan. This learning object is one in a series of six objects.

Interactive resource

Mobile phone plans: find the best deal 2

Help three customers compare monthly call costs quoted by three different phone companies: Orbit, Presto and Kool. Use line graphs to work out the costs for talk time, text messages, photos and total costs. Recommend the best plan. This learning object is one in a series of six objects.

Interactive resource

Mobile phone plans: find the best deal 3

Help three customers compare monthly call costs quoted by three different phone companies: Dialo, Airplay and Jump. Use line graphs to work out the same company and standard rates for talk time, text messages, photos and total costs. Recommend the best plan. This learning object is one in a series of six objects.

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.

Interactive Resource

Linear Equations

An animated tutorial about solving simple linear equations, followed by an interactive quiz.