Geometric thinking

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.

This means students will focus on key characteristics of 3-dimensional models (shape and relationship of faces and surfaces, faces joining at edges and vertices) to create 2-dimensional drawings of those models. Drawings of objects can take the form of isometric projections, plan views or nets. Students should also be able to construct a model from given 2-dimensional drawings, for example build a model using interlocking cubes from the plan views below.

This means students will use geometric properties to identify classes of shapes. Classes are categories of two or three-dimensional shapes. Shapes are sorted into classes according to defined geometric properties, such as number and relationship of sides (for example equal and parallel); number and nature of angles (for example four right angles); symmetry, number, nature, and shape of faces and surfaces (for 3-dimensional shapes). Classes can be included within other classes, can intersect or be disjoint, for example all squares are rectangles or no triangles are pentagons.

This means students will explore and describe transformations. “Transformation” is a generic term used to describe actions on shapes that result in some form of pattern, usually symmetric. A reflection is the image of a shape as seen through a mirror line either inside or outside the shape, sometimes called a “flip”. A rotation is the image of the shape turned about a point either inside or outside the shape. A translation is the image of a shift of the shape along a line, and an enlargement is the image of the shape made bigger or smaller by some scale factor.

This means students will use co-ordinate systems that are used on maps to specify location and direction (for example Greensborough Reserve is at D1, Ruakura Road runs West-East). The scale of a map indicates distance.

At Level Three students should be able to:

This means students will make drawings of objects, which can take the form of plan views or nets.

This means students will be able to define the characteristics of things and use these characteristics as a basis for sorting. Plane figures are those that lie flat, so have only two dimensions. So circles, triangles, and hexagons are all 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

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.

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).