Planning tool

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

1. 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.
2. 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.
3. 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.
4. 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?
5. 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.