Geometry and Measurement: Shape
Level 1
AO1: Sort objects by their appearance. This means students will classify or sort objects by their characteristics. These characteristics include shape, size, colour, texture, weight, and temperature. Students should be able to justify why they have sorted objects in the way they have and be encouraged to develop increasingly sophisticated classifications such as colour and size.
Click to download a PDF of second-tier material relating to Level 1 Shape (79KB)
Level 2
AO1: 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, e.g. "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.
AO2: 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, e.g. 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, e.g. nets for cubes.
Click to download a PDF of second-tier material relating to Level 2 Shape (83KB)
Level 3
AO1: Classify plane shapes and prisms by their spatial features. This means students will be able to classify is 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. At Level Three students should be able to classify plane shapes by the following characteristics, number of sides and angles, e.g. all triangles have three sides, parallel or non-parallel sides, e.g. a trapezium has one pair of parallel sides, equal or unequal side length, angle size (less than, equal to, greater than a right angle), lines of mirror symmetry and order of rotational symmetry (e.g. A square maps onto itself four times in a full turn). Prisms are solid shapes that have a fixed cross-section. A loaf of bread can be seen as a rectangular prism since the slices are the same rectangle. So prisms are classified by their cross-section, e.g. a triangular prism has triangular cross-sections. In this way a cylinder can be seen as a type of prism though its cross-section is a circle. .
AO2: Represent objects with drawings and models. This means students will make drawings of objects can take the form of isometric projections, plan views or nets.
Note that a net is a flat shape that folds to form a solid. Many different nets form the same solid, e.g. there are eleven different nets that form a cube. At Level Three students need to create two-dimensional drawings of three-dimensional models, as above, and be able to recreate the model when given another person’s drawings of it. Models may be built with interlocking cubes, plasticine, connecting geometric shapes or other materials, e.g.toothpicks and plasticine.
Click to download a PDF of second-tier material relating to Level 3 Shape (95KB)
Level 4
AO1: Identify classes of two- and three-dimensional shapes by their geometric properties.
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 (e.g. equal and parallel); number and nature of angles (e.g. 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, e.g. all squares are rectangles or No triangles are pentagons. At Level Four students should be familiar with:
- Classes of polygons defined by the number of sides; triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides),...octagons (8 sides),...
- Classes of 3-dimensional shapes defined by the nature of faces and surfaces; prisms (constant cross-section) and cylinders, pyramids and cones, regular polyhedral (identical faces).
- Classes of 2-dimensional closed curves and their 3-dimensional equivalents by rotation; circles and spheres, ellipses and ellipsoids.
- Sub-classes that are included within classes; squares within rectangles, rectangles within parallelograms, parallelograms within quadrilaterals, circles within ellipses, cubes within rectangular prisms.
- Classes that are disjoint, scalene and isosceles triangles, prisms and pyramids.
AO2: Relate three-dimensional models to two-dimensional representations, and vice versa.
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, e.g. build a model using interlocking cubes from the plan views below.
Students should be able to create nets for simple polyhedral and closed surfaces by visualising the “unwrapping” of those solids, e.g. the net for a dodecahedron.
Level 5
AO1: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties. Further detail on this Achievement Objective will be added shortly.
AO2: Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations. Further detail on this Achievement Objective will be added shortly.
Level 6
AO1: Deduce and apply the angle properties related to circles.
This means students will know and apply the sum of interior angles of a triangle (180°) and the angle between a radius and tangent (90°) to deduce the angle properties related to circles.
The angle properties of circles expected are:
- Angle at centre to any chord is twice the angle at circumference.
- Angles at the circumference to any chord are equal. .
- Angle between a chord and a tangent equals the angle in the opposite segment. .
- For a triangle in a semi-circle the angle at circumference equals 90?..
- Opposite angles in a cyclic quadrilateral add to 360?. .
Students are expected to connect at least two of these properties to find unknown angles in a given problem and to communicate their reasoning, citing the angle properties used.
AO2: Recognise when shapes are similar and use proportional reasoning to find an unknown length.
This means students will know what properties of shapes are conserved as they are enlarged (or reduced) to scale. In particular this refers to angles and the ratios of side lengths within a figure and between a figure and its enlargement. They should also apply knowledge that area increases by the square of the scale factor and volume increases by the cube of the scale factor. Students should solve problems in which they find unknown lengths of shapes that are both regular and irregular. For example: Given that the ellipses are similar, find the unknown length of the major axis.
Given the rectangles are similar find the values of c and d.
AO3: Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.
This means students will , given the required measurements, be able to connect trigonometric ratios (sine, cosine or tangent) in two dimensions with the demands of three dimensional problems, usually applying Pythagoras’ theorem in two or three dimensions in doing so. The problems should involve finding either an unknown length or angle. For example, find the angle <abc and the length of the line bc.
This objective also applies to problems where points are described using co-ordinates in two dimensions (four quadrants). For example, a triangle has corners at (2,3), (1,7), and (5,5). Find the lengths of its sides.
