Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M6M01
Numeracy Progression: Understanding units of measurement: P8
At this level, students make connections between the metric system and decimals. The metric system is linked to the base 10 number system, in that each unit is a power of 10. The base unit represents 100 = 1 and the other units grow or decrease by powers (factors) of 10.
The standard units for length (m) can also be used for other units of measurement, such as mass, where the base unit is 1 gram (g), for example:
 1 kilogram is the same as 1 × 10^{3} = 1,000 g (one thousand times bigger)
 1 milligram (mg) is the same as 1 × 10^{3} = 1 × 1,000 = 0.001 g (one thousand times smaller).
Make explicit the connections between the metric system and decimals. Support students to recognise that the measurements 1.24 m and 124 cm are the same.
Through making explicit links to place value tables, students can be shown how to read the measurement in different ways (for example, 1.24 metres in expanded form is 1 metre + 2 decimetres + 4 centimetres). Make explicit that when using smaller units to measure (cm), the measurement will be large, as opposed to when using larger units (m), for example, 124 cm is equal to 1.24 m.
Follow a similar approach when working through conversions of units of capacity, with the base unit of 1 litre and powers of 10 used in conversions.
Teaching and learning summary:
 Make connections between the metric system and decimals.
 Model how to convert between units of measurement.
 Provide practical activities to measure length, mass and capacity.
Students:
 describe how place value and powers of 10 are linked to metric measurement conversions (i.e. know that a larger metric unit can be converted to a smaller unit through multiplication of the base 10 multiple of the smaller unit, and vice versa)
 describe links between multiplication and division of powers of 10 and measurement conversions
 use their knowledge of place value and metric naming conventions to convert between metric units of measurement
 recognise reasonableness of answers with reference to reallife examples of length, mass and capacity when undertaking conversions.
Some students may:
 get confused when converting between units. When students rely on the memorisation of rules to convert between units it can lead to misconceptions (for example, if converting from metres to centimetres and taught to move the decimal point two places to the right, students may not realise the magnitude of the units and that these units are separated by a power of 10).
 get confused with measurements that include decimals. Difficulties with decimals usually occur because place value is not used when naming numbers, and they are spelled out as separate digits (for example, zero point two five instead of 25hundredths). Students may think that the more digits a number has, the larger it is; a procedure that works for whole numbers, but not decimals.
 not fully understand the concept of mass. Many difficulties occur because of visual impressions based on everyday experiences, rather than considering concepts involved. For example, an object is light if it can be picked up; if an object floats, it must be light; the larger a box (the volume), the more it must weigh.
 not fully understand the concept of capacity and find the difference between volume and capacity difficult to understand. Use practical activities, accompanied by appropriate discussion (for example, volume as the space taken up by an object, and capacity as a measure of how much it can hold).
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 are learning how to use our knowledge of place value and metric system to convert between metric units of measurement.
Why are we learning about this?
 The metric system of measurement is the standard way of measuring. We are measuring to make sure that your clothes fit properly.
What to do

Success criteria
I can:
 make connections between the metric system and decimals
 convert between units of measurement
 select and use appropriate metric units for length
 record and display the results of my investigation.
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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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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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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.

Osprey bird dimensions
In this lesson, students investigate measurement data related to the osprey.
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Decimals: Adding and subtracting
In this lesson, students play a board game that draws on their knowledge of adding decimals to tenths, hundredths and thousandths.
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Introduction to the metric system
Students will use a mnemonic to help them recall the parts of the metric system.
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Convert me
Students explore measurement prefixes and convert between units of measurement for length, mass and capacity.
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Converting length
Students measure the length and width of the gym in metres and then convert the measurements to centimetres and kilometres.
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Stepping out
Students make estimates of stride length and use this in practical measuring tasks.
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Assessment
By the end of Year 6, students are converting between common units of length, mass and capacity.

Assessment tasks: Metric units and relationship to decimals
Use the diagnostic tasks ‘Page sections’ and ‘Decimals and measures’ to assess a student’s understanding of metric units and their relationship to decimals.
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How tall?
Use this as a guide to assess students’ proficiency in converting between common units of length, mass and capacity.
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