# Elaborations on Level Two: Geometry and Measurement

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

### Measurement

GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.

This means students will recognise that the attributes length, area, volume and capacity, and weight can be measured. At Level Two students are expected to recognise that measurement units are countable and therefore able to be partitioned and recombined in the same way as other units of one. For example, if an 8 unit length is cut from a 14 unit long strip the remainder will measure 6 units. Units of measure have other characteristics including being a part of the attribute they measure and uniformity (same size). When measuring, the units need to fill a length, space, time etc, with no gaps or overlaps (this is known as tiling). Students should create measurement devices, for example rulers, rod towers, scales, to quantify the attributes of objects in numbers of units. In doing so they should develop an understanding that the marks on a linear scale show the endpoint of units and that scales always have a baseline (zero). Less tangible attributes such as turn (angle), temperature and time should also be measured. While the focus at Level Two is on students’ understanding the role of units in measurement it is also expected that students will encounter simple standard measures such as metres, centimetres, kilometres, minutes, seconds, kilograms, litres, etc, through using everyday measurement instruments. Supporting teaching resources.

GM2-2: Partition and/or combine like measures and communicate them, using numbers and units.

This means students will perform and communicate calculations involving like measures. Like measures involve the same units for the same attribute. This allows the result of joining or separating units to be anticipated using additive number strategies. For example, a box has a volume of 36 cubes. If a 3 by 4 cube layer is put in the empty box then there will be space for 36 – 12 = 24 more cubes. At Level Two students should be able to use numbers and common symbols to communicate measurement results, for example my lunchbox holds 60 cubes. I took 13 minutes to walk home. My pencil is 14 cm long. I weigh 26 kg. Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 2 Measurement (119KB)

### Shape

GM2-3: Sort objects by their spatial features, with justification.

This means students will sort objects by selecting an attribute or attributes by which to classify items and allocating the items into groups by commonality of that attribute. At Level Two students should be able to find their own system to classify items, using attributes like shape, colour, size, texture, thickness, material, purpose, etc and justify their allocation of items into categories, for example "all of these shapes have three sides". In doing so students should develop geometric language for attributes such as "side", "corner", "centre", "face", "edge", "curved", "straight", "larger", "smaller", etc. Supporting teaching resources.

GM2-4: Identify and describe the plane shapes found in objects.

This means students will be able to identify plane (flat) shapes in objects and structures around them and consider why the given shape is suitable for its purpose, for example wheels are circular so they roll freely, floors are usually rectangles because they are easier to build and things fit efficiently, etc. They should consider how three dimensional objects are built from flat shapes through pulling packets apart and constructing solids of their own, for example nets for cubes. Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 2 Shape (83KB)

### Position and orientation

GM2-5: Create and use simple maps to show position and direction.

At Level Two students should be able to use simple schematic maps, for example plans of their school, road maps of their local area. This involves finding their current position on a map by connecting landmarks they can see with locations on the map. Similarly it involves finding the place that matches a given point on the map and describing how they would move from one point to another. Descriptions of movement should include features such as main compass directions (N, S, E, W), half and quarter turns, and approximate distances in whole numbers of metres (for example about 12 metres). Students should use simple co-ordinates (for example B5) to specify locations on schematic maps. Supporting teaching resources.

GM2-6: Describe different views and pathways from locations on a map.

This objective requires students to see schematic maps as a two dimensional representation of the real world. By looking at a map students should be able to anticipate landmarks they will see from a given location and in which direction (N, S, E, W) those landmarks will be seen. From a map they should give a set of directions, using distances in whole numbers of metres and quarter/half turns, that will take a person from one position on the map to another,  turn right and walk about 25 metres. Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 2 Position and orientation (126KB)

### Transformation

GM2-7: Predict and communicate the results of translations, reflections, and rotations on plane shapes.

This means students will experience physically moving shapes so that they can predict the location and orientation of the shape after it has been translated, reflected or rotated, for example draw/show what this shape will look like if I give it a half turn about its centre. Students should be able to identify how many mirror lines a shape has that maps it onto itself, for example a square has four mirror lines. Translations are images of a shape as it is shifted along a line, for example ... Reflections are images of a shape as it is reflected in a mirror (sometimes called a flip), for example Note that the line may be outside the object or within it. Rotations are images of a shape as it is turned about a point outside or within it, for example . Supporting teaching resources.