# Mathematics level 8 - Measurement and geometry

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## Teaching context - Choose and convert units of measurement for area and volume

At this level, students select which units of measurement would be best to measure different areas or volumes. They will also convert between area units (mm^{2}, cm^{2}, m^{2}, hectares, and km^{2}) and volume units (mm^{3}, cm^{3}, and m^{3}).

A review of linear measurement units is recommended to support student understanding of selecting appropriate units of measurement and converting area and volume units.

Students must be provided with opportunities to select an appropriate unit of measurement to measure different objects.

Give students different objects to measure (eraser, textbook, classroom door, school oval, etc.) and ask them to choose an appropriate unit of measurement before doing so and to justify their choice. This will support students understanding when they need to select an appropriate unit of measurement for area and volume.

Converting units of measurement for area and volume is often a source of confusion for students. They may have mastered converting linear units of measurement (centimetres to metres) but do not make the connection between linear (cm), area (cm squared) and volume (cm cubed) units of measurement.

Students must recognize that the conversion factors for the area are the ‘squares’ and the conversion factors for volume are the ‘cubes’ of those for the corresponding linear factors (see conversion charts below).

It is useful to show students a conversion chart for area and volume once they have been shown an example of why the conversion factors for the area are the squares and the conversion factors for volume are the cubes. Then a conversion chart can be written in their books for memory recall once they understand the concept.

An example such as: 1 metre = 100 centimetres.

It is helpful to have students ask themselves if they expect their answer to be a greater or lesser value once they convert to the new unit. This will assist students to realise if they have incorrectly applied the conversion factor and need to revisit the question.

## Teaching idea - Estimating area and volume

This activity provides students with an opportunity to determine which unit of measurement would be most appropriate to use for different areas and volumes. Use practical everyday objects around the classroom and school.

Ask students to work in pairs or groups and identify which unit of measurement they would use to measure the area or volume of the different objects below. This is a good activity for sharing with other groups to see if any debates occur over the correct measurement unit to use.

Some suggestions are:

- area of a classroom window
- area of an A4 piece of paper
- area of the oval
- volume of a pencil case
- volume of the school gym
- volume of an eraser.

Once students have had an opportunity to decide on their responses invite groups to share their ideas and justify their answers. If some groups have different ideas from others about the unit of measurement to use, ask the class if the unit of measurement decided upon will change the area or volume of the object. This can lead nicely to a discussion about the need to be able to convert between units of area and volume.

## Extension ideas

- Pre-test students on their units of measurement knowledge so high-ability students can have their curriculum compacted and extended.
- High-ability students could be asked to identify and list scenarios where two different units of measure might be needed.

Having students propose more complicated scenarios will add complexity to the task.

Last Update: 04 April 2022