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

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

Factorise algebraic expressions by identifying numerical factors (ACMNA191)

Elaborations
  • recognising the relationship between factorising and expanding
  • identifying the greatest common divisor (highest common factor) of numeric and algebraic expressions and using a range of strategies to factorise algebraic expressions
General capabilities
  • Numeracy Numeracy
ScOT terms

Factors,  Mathematical expressions

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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 ...

Teacher resource

reSolve: Algebra: Addition Chain

This sequence of lessons explores making algebraic generalisations of sequences. Students use spreadsheets to investigate potential arithmetic relationships and then use algebra to identify and justify which relationships are generally true. The task can be used as a springboard for an in-depth exploration of the Fibonacci ...

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 ...

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

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

Biscuit factory: gears

Choose a pair of gears to drive a conveyor belt to an oven, including cases where the belt gear is larger than the driver gear. Notice that the number of rotations for each gear depends on the gear size (number of teeth). Identify the relationship between the number of teeth and the number of rotations. Choose a combination ...

Interactive resource

Squirt: three containers: level 1

Examine the relationships between capacities of containers of the same shape, but different size. Squirt liquids between three containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. Express relationships using mathematical notation such as 2a=6b=3c. ...

Interactive resource

Squirt: three containers: level 2

Examine the relationships between capacities of containers of different shapes and sizes. Squirt liquids between three containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. Express relationships using mathematical notation such as 2a=6b=3c. This learning ...

Interactive resource

Biscuit factory: two-gear system

Examine a pair of gears that drives a conveyor belt to an oven, including cases where the belt gear is larger than the driver gear. 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 by changing both ...

Assessment resource

Biscuit factory: two gears: assessment

Test your understanding of ratios by choosing two gears of different sizes according to specific criteria. Complete a pair of gears, or choose the combination of two gears, depending on how many rotations each gear must make. For example, choose a belt gear size of 10 teeth and a driver of 40 teeth to make the belt gear ...

Interactive resource

Squirt: three containers: complex proportional relationships

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. ...

Interactive resource

Biscuit factory: three-gear system

Examine a set of three gears that drives a conveyor belt to an oven. 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. Compare rotations for a range of gear sizes. Look for a pattern in the number ...

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

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

Linear Equations

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