Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M10M02
Numeracy Progression: Multiplicative strategies: P10
At this level, students can read and interpret different types of scales. They understand that a logarithmic scale uses powers of 10 and how it appears on a graph. Students know when the use of such a scale is appropriate and where logarithmic scales are used for very small quantities and very large ones.
Teaching and learning summary:
 Investigate the use of different scales.
 Demonstrate how changing the scale alters a graph.
 Discuss why using different scales may be useful (changing a curve to a straight line).
 Show examples of where logarithmic scales are used (for example, Richter scale, modelling growth, pH scale).
 Show how to draw a logarithmic scale using digital technology (for example, in Excel, on a CAS calculator).
Students:
 understand what a logarithmic scale represets
 recognise, read and interpret a graph drawn using a logarithmic scale
 know when using a logarithmic scale is appropriate
 can draw a graph using a logarithmic scale.
Some students may:
 be unfamiliar with the concept of logarithms.
 not pay attention to the scale of a graph.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
 We understand that logarithms are not just on paper or computers. They are applied all around us.
 We make connections with musical tonology of a piano and logarithms.
Why are we learning about this?
To make sense of the world around us, we need to identify elements that we learn about in school. Conversely, if we know about things like logarithms at school, we can apply it to our world at home, at work and in the environment.
What to do
Tuning and ratio
 Find a keyboard or piano at school or at home. If you know how, play the C major scale. If you don't know how, start on the very middle note of the keyboard and work your way up the white notes.
 Does it sound nice?
 Go to this site on your device while sitting at the piano.
 Find middle C. Read along and work your way down using your piano to understand and make connections between sound, musical notes and logarithmic scales.
Success criteria
 I can play a C major scale and understand what a musical scale is.
 I understand that a musical scale is a logarithmic representation of frequency.
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Teaching strategies
A collection of evidencebased teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.

Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Multiple exposures
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Off the scale
This lesson introduces students to the idea of a log scale, a seemingly perplexing way to present data.
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Exponentials and logarithms
This UK resource introduces logarithms and exponential growth, with examples and questions for students to work through.
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Power match
A familiarisation and interactive activity designed to make estimates when thinking about logarmithic scales. The teacher resources show possible approaches, key questions and extension ideas.
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The laws of logarithms
This site gives guidance for teachers, provides links to online resources, and provides teaching ideas around the area of logarithms.
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Assessment
By the end of Year 10, students can interpret and use logarithmic scales representing small or large quantities or change in applied contexts.

Mixing pH
Students can make crossconnections here with chemistry and the logarithmic pH scale, which is used to describe the acidic concentrations of substances. This realworld example shows the diversity of logarithmic scales in our world.
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The laws of logarithms
Scroll down to the teaching ideas to discover a classroom activity using log scales.
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