1. 3-D and 2-D shape

Children should understand and begin to write, the following words:
shape, pattern, flat, solid, hollow, side, edge, face, straight, curved, round, circular, triangular, rectangular, pentagonal, hexagonal, octagonal, right-angled, vertex, vertices, layer, diagram, surface, point, pointed, corner, sort, make, build, draw, cube, cuboid, sphere, cone, cylinder, prism, hemi-sphere, circle, triangle, rectangle, square, pyramid, hexagon, octagon, quadrilateral, semi-circle.

In 3-D shape work, the main new concept is that of a prism. A prism is a shape that has the same cross-section and same size throughout its length. Some shapes such as cones and square based pyramids have the same shape throughout their length (ie circle and square respectively), but they are not prisms because the size of the circle or square changes as you move from one end to the other.

There are many near prisms in real life (e.g. rulers, pencils, cans, chocolate boxes, rolls of sticky tape and exercise books), although they often have a small part such as the point of a pencil which prevents it being a pure prism. Children can generally be taught to ignore these annoying parts that manufacturers will insist on adding to spoil our maths lessons!
Children should also continue to describe solid shapes with increasing definition and precision and be more able to recognise similarities and therefore be more able to classify shapes according to their properties.

In 2-D shape work, the main new concept is that of a quadrilateral. A quadrilateral is a flat shape with four straight sides. Examples that are already familiar to children are squares, rectangles, rhombuses and parallelograms (although they may not yet know the names of the more difficult ones).

They should be able to recognise more difficult properties, in particular the right angle, and be able to classify shapes according to more difficult properties.

They should also realise that some shapes belong to larger families, e.g. squares are really just a special type of rectangle and rectangles are just a special type of quadrilateral.

In year 3 children will continue to make shapes and patterns, these becoming more complex and more accurate.

3D shapes should be related to 2D representations of them, as children match familiar solids to their pictures.

Drawing round shapes such as triangles, rectangles and hexagons and then cutting them out to make repeated patterns should be encouraged. When describing the patterns created, children should be encouraged to name the shapes.

Often children will need to copy a pattern before they feel confident enough to create their own. When drawing round shapes the emphasis should be on accuracy and care, both in placing the shape in the right position and drawing round it.

2. Symmetry

Symmetry is continued in year 3. Children should use and read terms such as:
line of symmetry
mirror line
reflection

Mirrors are essential for this work so that children can see the reflection of the shape in the mirror – they often find great difficulty predicting the mirror image without this help.

Whether shapes are symmetrical can be tested using a mirror, and a line of symmetry can be drawn where the mirror has been placed.

Further practical work should be continued, developing from that covered in years 1 and 2, such as making symmetrical patterns using ink blots or paint across a folded edge.

Other symmetrical patterns can be made with cubes, sticky gummed paper, plastic shapes etc.

Children should be encouraged to find examples of pictures, signs, letters of the alphabet etc which have a line of symmetry and to make a scrapbook up of these.

Sketching the other half of a shape is very difficult, but a few examples have been included in this module. They can also create their own ‘half’ pictures and try to draw the mirror image.

3. Describe position and direction

Children should understand and be able to use in practical contexts the following words. Where possible, they should be taught to read the words.

position, over, under, underneath, above, below, on, in, outside, inside, in front, behind, beside, before, after, higher, lower, next to, opposite, between, close, far, apart, middle, centre, edge, corner, top, bottom, side, direction, left, right, up, down, forward, backwards, sideways, across, along, around, through, to, from, towards, away from, clockwise, anticlockwise, journey, route, grid, row, column, map, plan, compass point, north, south, east, west, horizontal, vertical, diagonal, descend, ascend.

In addition to describing position in terms of ‘behind’, in front of’ etc, they should now be becoming confident with describing position in an absolute sense, ie on a grid or map. They should be able to say how many squares from a zero point horizontally and vertically an object is and give these labels when appropriate (square B3, F5 etc).

They should know the difference between a column and a row. Columns are vertical (as in the old Greek buildings), rows are horizontal (imagine standing at the front of a cinema and looking out at the rows of seats).

They should understand that a diagonal goes from one corner of a grid to the opposite corner eg bottom left to top right.
They should know the directions North, South, East and West and that on a map or plan, the North direction is almost always towards the top. The North direction should, in any case, always be indicated. North and South are generally easy to remember, but most children will mix up East and West for a long time.

They should know the meaning of the words ‘ascend’ and ‘descend’.

4. Understand angle

Children should understand and use in practical contexts the following vocabulary:

slide, roll, turn, whole turn, half turn, quarter turn, angle, right angle, straight line, is a greater/smaller angle than.

Children should recognise quarter and half turns and know that a quarter turn is a right angle and that  a half turn (or straight line) is two right angles.

They should understand the directions N, S, E and W and be able to face one direction, turn a quarter or half turn and say which way they are then facing.

They should know that turning a half turn or two quarter turns results in you facing in the opposite direction.

Children should be able to sort shapes according to the number of right angles they have and be able to fold a piece of paper to give a right angle with which they may test for right angles in other shapes.

They should be able to use a template to draw right angles and test angles to see if they are smaller, equal to or larger than right angles.

Go to year 3 shape

There is a tremendous amount for children to learn in Year 2 and two shapes that we might expect to be left until later are, nevertheless, included in the Year 2 curriculum. Two such shapes are pentagons and hexagons.

A pentagon has 5 straight sides. Some pentagons have all the sides equal and this is the shape that we are most familiar with. A pentagon with equal sides is called a regular pentagon.

A hexagon has 6 straight sides, and, again, if the sides are all equal it is known as a regular hexagon.

These worksheets introduce the terms pentagon and hexagon and provide opportunities to recognise and sort them.

Go to our Year 2 Sorting shapes worksheets

Here is another in our series of shape patterns. This set of pages is slightly different from the earlier published shape pages because some of the sequences could be interpreted differently, allowing for a number of different possibilities. The important thing here is to discuss what the patterns might be and then choose one. As long as the pattern continues in sequence there are no right or wrong answers.

Shape: colour patterns 5

Learning the correct terms to compare things is vital in the Early Years and one of the most important aspects of measurement. Here we have four more great maths worksheets on maths vocabulary for young children, looking at bigger and biggest. You can find these in our Shapes and Measures section. Pick out the biggest frog and find the bigger boot! Talk about the pictures and use the terms as often as possible around the home.
Of course bigger is a comparative word and is used when comparing just two objects, whilst biggest is used when there are more than two (superlative).

Go to our resources on Bigger and Biggest

Circles, triangles, rectangles and hexagons can be bought in the shape shop. They are priced according to the number of sides. Circles cost 1p hexagons 6p etc.

What shapes can be bought for 20p?

A good challenge which uses knowledge of shape, counting money and logical thinking. There are a large number of possibilities with this and it is unlikely that all combinations that add up to 20p will be found. Nevertheless it is important to try and work in a logical way.

Shape and money challenge (2)

Today we are taking a closer look at our shape worksheets. This is a great set of four worksheets helping with recognising rectangles, triangles and circles. It’s a help to have some templates of these shapes handy to draw round and create fun pictures of your own. The robot on page 4 is a good example of what can be produced.

Talk about the shapes and the properties of them eg a triangle has three straight sides…a rectangle has 4 sides and 4 right angles. Find examples of these shapes around the house, draw them in sand etc.

Go to our Using 2D shape (2) worksheets

Don’t forget that we have some great pages which will help with recognising 2-D shapes. Your child should be able to recognise four basic shapes: circles, squares, rectangles and triangles. These maths worksheets have plenty of interesting pictures just made up of these shapes. Good extension work would be to have a selection of plastic shapes and see what kind of pictures can be made by sliding them around or placing them on top of each other. There are also lots of sticky materials available in craft stores which can be used in scrapbooks or on paper to make pictures. When playing with them don’t forget to keep calling the shapes by their correct names.

Go to the worksheets on Recognising Rectangles, Squares, Circles and Triangles

It’s time to get all the boxes out and try to sort them into types depending on their shape. Much can be done at home to help with 3-D shape work and children love to play with empty boxes; the bigger the better. It’s well worth collecting a store of boxes and much discussion can take place about them, including mathematical language of sides, edges etc.

These four pages look at matching shapes and finding the odd one out and would work really well at the same time as looking at real 3-D boxes. Don’t forget to look at the rest of our Shape and Measures pages which can be found tucked away in the Further Resources section. If you haven’t already got our 3 day trial then now’s the time.

Go to our resources on matching 3-D shapes

The fifth set of worksheets on 2D shape reinforces the earlier pages, looking at rectangles, triangles and circles. Whilst using these pages it is important to keep naming the shapes as well as asking what makes them that shape, ie the properties of the shape. All triangles have 3 sides, all rectangles have 4 sides etc.

Once again it can not be emphasised enough how important it is to have some practical apparatus – a box of plastic or card shapes is ideal. This gives children the chance to handle shapes and see first hand that if they rotate a shape it still remains the same shape. You would be surprised at the number of children who if they see a square positioned so that it is standing on a corner, or point, will not recognise it as a square and call it a diamond shape.

Go to our great 2D shape resources

Interestingly, the Primary Framework for Mathematics believes that 3D shape should be taught at the same time, if not sooner than, 2D shape. The probable reason for this is that in real life children are coming across 3D shapes all the time and will only see 2D shape occasionally in a book, or maths sheet!

These fun pages look at a variety of 3D shapes with the emphasis on comparing and matching them and to find the odd one out. No need to mention more complex names such as cuboid at this stage!

It is a good idea to have a collection of boxes, some of which are the same as each other and to look carefully at them, discuss their properties (e.g. how many sides, corners etc). Also take two boxes which are the same and turn one round and ask if they are still the same can produce interesting answers.

Go to our resources on 3D shape