Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M10M04
Numeracy Progression: Multiplicative strategies: P10, Understanding units of measurement: P10
At this level students are becoming familiar with the distinction between exact and approximate representations of values through their study of irrational numbers. A comparison can be drawn between a calculator approximating and a measuring device approximating the true value of a length, weight, or force.
Before teaching this topic, it is recommended to visit the teaching and learning focus for the previous level, which covers the calculation and interpretation of measurement errors. Students can use these calculations to identify the impact size an error may have on the accuracy of results. This should be done in practical contexts. As a class activity, students can investigate the errors produced when measuring the classroom with different devices to determine the quantity of carpet tiles required to cover the floor. A metre stick, trundle wheel, ruler, tape measure with centimetres, and one with millimetres, could be compared. How does the choice of device affect the order? A relevant and meaningful homework task could be set that requires students to replicate this process at home, to determine the number of tiles required to renovate a bathroom or kitchen. This poses the additional challenge of tiles that don’t evenly fit along the length or width of the floor/wall. Students can use their error calculations to recommend an appropriate quantity of extra tiles that should be ordered.
Explore real world examples, such as the 1999 incident in which NASA lost the Mars Climate Orbiter because of the discrepancy between a calculated and measured position. This incident illustrates the additional errors that can arise when converting between different systems of measurement. This topic offers a broad range of possibilities for creatively assessing students. For example, students may explore crosscurricular subject areas in Science, Design and Technologies and incorporate the mathematics and contexts into a short story that meaningfully features a measurement error in the plot. This allows them to demonstrate an understanding of how errors and inaccuracy make an impact in practical contexts.
Teaching and learning summary:
 Comparing the estimation of true measurements to the approximation of irrational numbers.
 Investigate the impact of errors in practical contexts.
 Conduct an experiment in class by taking the same measurement with a variety of devices.
 Examine a case study when measurement errors have had a significant impact on the outcome of an event.
Students can:
 perform a mathematical investigation to determine the impact of a measuring error in a practical context
 comment on the accuracy of results and whether they are appropriate for the given context
 explain the impact of a measuring error in a case study.
Some students may:
 not have a solid understanding of place value and/or rounding. These are foundational for this topic and may need to be explicitly revisited for some students.
 need to be refreshed on the units of measurement and how to convert between them.
 find it hard to accept that all measurements are estimates. This concept is somewhat philosophical and may clash with students’ physical interactions with the world around them.
 have forgotten how to calculate absolute and relative error from the previous level. A review of this should be the starting point for this topic. (This is new for this topic.)
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
 I am identifying the impact of measurement errors.
 I am considering the degree of accuracy required in my household machines or objects and think about examples where accuracy is important.
Why are we learning about this?
Slight miscalibrations and measurement errors can have major impacts on everyday activities in our homes. Being aware of the potential causes of error and monitoring the measuring devices we use will ensure the highest level of accuracy. This means we can see better results in the kitchen and save money on heating and cooling.
What to do
Measurement errors
 Locate all the devices in your home that take measurements. These are things like a thermostat that measures temperature and controls the heating/cooling, kitchen scales that weigh ingredients or a measuring tape to plan for renovations.
 Write down the units that each device takes measurements in (this should be the smallest unit, so scales that can weigh kilograms to one decimal point are recording measurements to the nearest 100 grams). Record this data in a table.
 Consider this general rule: the degree of accuracy is half a unit each side of the unit measure. The example of the scales above therefore is accurate to within ± 50 grams of the true weight. A measurement of 64.3kg could be as high as 65.8 Kg or as low as 63.8 Kg. In a new column on your table record the general degree of accuracy for each device.
 Add another column to comment on whether the accuracy of the devices in your home is up to the level you believe is necessary for its function. Which devices need to be more precise?
 Challenge – imagine your thermostat is in error by half a unit measure. That means the true temperature in your house is 0.5higher than the thermostat reads. How might this be affecting your monthly gas or electricity bill? Can you calculate the monthly savings you could realise if the thermostat was perfectly accurate?
Success criteria
 I can consider the measurement error household devices.
 I can consider the degree of accuracy required in my household machines or objects and think about examples where accuracy is important.
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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.

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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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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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.

How wrong?
In this lesson, students explore the importance of measurement errors by considering the ‘coastline paradox’ and realworld applications.
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Maths starters
This is a differentiated activity on rounding, using index form and making approximations for estimates.
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Experimental uncertainty and error: advice for teachers
This article is a good explanation of common errors made and their differences when taking measurements and collecting data.
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Instrument error
This article is an overview of instrument error when taking measurements and the kinds or errors that are commonly made.
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Building yard
A video resource on using maths in the building industry. Questions are posed for students to consider. The problems involve finding the shortest route between two points, ratio and proportion, area, perimeter, volume and number sequences.
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Assessment
By the end of Year 10, students can identify the impact of measurement errors on the accuracy of results.

Maths starters
This is a differentiated activity on rounding, using index form and making approximations for estimates.
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Building yard
A video resource on using maths in the building industry. Questions are posed for students to consider. The problems involve finding the shortest route between two points, ratio and proportion, area, perimeter, volume and number sequences.
Go to resource