Children should be able to use, read and write the following words:
pattern, shape, 2-D, two-dimensional, 3-D, three dimensional, line, side, edge, face, surface, base, point, angle, vertex, vertices, centre, radius, diameter, net, make, build, construct, draw, sketch,
curved, straight, regular, irregular, concave, convex, closed, open, circular, triangular, hexagonal, cylindrical, spherical, square-based, right-angled.
They should be able to name, classify and describe the following 2-D and 3-D shapes:
circle, semi-circle, triangle, equilateral triangle, isosceles triangle, quadrilateral, rectangle, oblong, square, pentagon, hexagon, heptagon, octagon, polygon, cube, cuboid, pyramid, sphere, hemisphere, cylinder, cone, prism, tetrahedron, polyhedron.
Oblong – some dictionaries and textbooks define this as another word for a rectangle, some as a rectangle that is twice as long as it is wide (in other words, two squares put next to each other).
Radius, diameter and circumference – the easy way to remember which is which, is that the shortest distance (from centre to circle) has the shortest word (radius) and the longest distance (distance around circle) has the longest word (circumference). (N.B. Strictly speaking, ‘circumference’ is not introduced until year 6, but why wait?)
Regular polygon – a shape that has all the sides the same length and all the angles the same value.
Regular polyhedron (a solid shape whose faces are polygons) has all the faces the same shape. All the edges are the same length and all the angles have the same value. (A cube is therefore a regular polyhedron, but a cuboid is not, as not all its edges are the same length.)
2. Describing and classifying 2D and 3D shapes
Children should be becoming familiar with the idea that shapes belong to groups or classes. For example, there is a group of shapes called polygons. These are flat (2-D) shapes that have straight sides. The names of many of these end in ‘agon’ such as pentagon, hexagon, heptagon, but there are other names that do not, such as square, rectangle, quadrilateral. There is a similar group of 3-D shapes (polyhedra – plural of polyhedron) that end in ‘hedron’ such as octahedron, dodecahedron, but not all names of polyhedra end this way, for example cube, cuboid and pyramid.
They also need to be aware that groups of shapes are often subsets of other shapes. For example, squares are part of the group of rectangles, rectangles are part of the group of parallelograms, cylinders and cuboids are part of the group of prisms.
Children also need to know that in a polyhedron:
the faces are flat and polygonal and surrounded by edges
an edge is a straight line between two faces
a vertex is a point where three or more edges meet
and that a polygon is a 2-D shape that is closed (i.e. no gaps in its perimeter), and has three or more sides. Also that a regular polygon has equal sides and equal angles.
They should also know the properties of isosceles and equilateral triangles.
Much of this work should initially be oral. Children need to discuss these ideas over and over again before they become established in their minds. Keep practising the language at every opportunity and watch out for geometrical shapes in everyday life (e.g. The human body can be thought of as a sphere for the head, four cylinders for the arms and legs – or eight allowing for the joints – and a larger cylinder for the torso. Houses are often cuboids with triangular prisms for roofs. Swimming pools are normally prisms.)
When sorting shapes, it is sometimes a good idea to put them on a Carroll or Venn diagram. If you do not have any plastic shapes, children may easily cut out shapes of their own.
Children need to spend time handling 3-D shapes and should be familiar with the terms ‘edge’, ‘face’ and ‘vertex’ (plural: ‘vertices’) when applied to 3-D shapes.
A range of boxes used for packaging such as chocolate boxes, tissue boxes etc, may be opened to see the nets used to construct them.
(A net is the 2-D shape that must be cut out and folded to make a 3-D shape.
Children should make 3-D shapes from suitable materials such as straws and pipe cleaners (used to join the ends) or kits designed for the purpose.
In this way, they will be able to see how many of each 2-D shape are needed as faces for a 3-D shape (Eg. six squares are needed to make a cube; a square and four isosceles triangles are needed to make a square based pyramid etc.)
Many shapes can be made from cubes. Cubes that join together are helpful here, but non-joining cubes are very useful too.
Other properties of shapes will be discovered, such as ‘the number of faces of a prism is equal to two more than the number of edges on one of the end faces’.
A pin board may be simply made by nailing panel pins or small nails into a piece of plywood approximately 24cm × 24cm.
Cut out the plywood and mark a grid of lines at 2cm intervals in both directions across the plywood. Tap in the pins at the points where the lines of the grid meet. Leave enough of the pins protruding to accommodate elastic bands.
Children should know and be able to read, write and use the following words:
Mirror line, line of symmetry, line symmetry, symmetrical, reflect,
Children should be able to draw lines of symmetry on shapes and say if a shape has no lines of symmetry.
They should look at everyday designs on advertising posters, in magazines etc and see if these have reflective symmetry, being careful not to mix this up with rotational symmetry.
They should be able to classify shapes according to the number of lines of symmetry they have (rectangle has two, square has four etc).
Children should be able to draw the reflection of a simple shape in a mirror line using tracing paper if necessary, but increasingly doing so by looking at the distances of points from the mirror line.
They should understand the concept of a translation (a simple slide) and be able to construct patterns using translation. They should be able to try to predict the patterns they will make using this idea and be able to talk about their discoveries.