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Geometry and Measurement: Position and orientation

Level 1

AO1: Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
This means students will be able to follow instructions given in distances, for example 14 steps; direction for example facing the library; and angle (turn) for example do a half turn clockwise (right). They should become proficient at following a series of instructions. Students should also be able to give instructions.

AO2: Describe their position relative to a person or object.
This means students will describe their position using positional language such as next to, in front of, behind, between, to the right/left and simple diagrams and maps. Their descriptions should become increasingly precise in terms of distance from the landmark (in steps) and location of that landmark on simple schematic maps.

Click to download a PDF of second-tier material relating to Level 1 Position and orientation (106KB)

Level 2

AO1: Create and use simple maps to show position and direction.
At Level Two students should be able to use simple schematic maps, e.g. 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 (e.g. about 12 metres) . Students should use simple co-ordinates (e.g. B5) to specify locations on schematic maps.

AO2: 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, e.g. turn right and walk about 25 metres.

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

Level 3

AO1: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
This means students will use co-ordinate systems that are used on maps to specify location and direction (e.g.Greensborough Reserve is at D1, Ruakura Road runs West-East). The scale of a map indicates distance.

map.

At Level Three students should be able to:

  1. Give the location of something using co-ordinate references, e.g. A3.
  2. Find the location of something given a co-ordinate reference, e.g. Find Daphne Street at E8.
  3. Use features of a map to describe movement that would get someone from one location to another, including distance and direction. This includes turns (right, left relative to orientation), main compass directions (N,W,S,E) and approximate distances in metres or kilometres.
  4. Follow a set of directions given in terms of turns and distances (as above) and show that path they walked on a map of the area.

Level 4

AO1: Communicate and interpret locations and directions, using compass directions, distances, and grid references.
This means students will apply their understanding of the measurement system, particularly of length and angle. This involves converting the scale on a map to actual measurements and describing direction given the orientation of North.

  1. Give or interpret the location of a feature on a map using grid references, distances and direction from a landmark, e.g. AA 24 (Street map), 536 721 (topographical map), 160m South-East of the library, Latitude 12o South, 77o East (World map), 2047km South-West of Los Angeles.
  2. Follow instructions given by others using compass directions, distances and grid references by interpreting a scale map, e.g. Travel from New Plymouth to Tauranga.

Level 5

AO1: Construct and describe simple loci.
Further detail on this Achievement Objective will be added shortly.

AO2: Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
Further detail on this Achievement Objective will be added shortly.

Level 6

AO1: Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

This means the students will be able to use algebra and graphing to find a point in common with two intersecting lines when given their equations and connect this understanding with contexts that can be modelled with simultaneous linear equations in two variables. A loci is a set of points satisfying a given condition so common examples are lines, circles and ellipses, parabolas, and hyperbolas.

They should be able to sketch the locus for a given condition and recognise when that condition meets that of a conic section, e.g. perimeter of the flight area of a jet taking off and returning to a moving aircraft carrier (ellipse). Using graphing techniques students should be able to find the point or points in common between a line (given two points) and a conic (given the condition) and describe the area bounded by common lines and conics, for example, the grazing area of a tethered animal constrained by a wall.