• “What changes and what stays the same?“ Janet Ainley (ATM 2010) This article (free to ATM members) discusses the lack of challenge and progression in the ‘old’ curriculum and offers some suggestions for interesting activities, which support pupils learning fundamental geometric ideas.

Activity set A

Give the children opportunities to arrange objects, such as shapes, base 10 equipment and counters in a variety of patterns. They could work with a partner. One child makes a pattern and the other child needs to predict what the next five objects in that pattern will be and give a reason for their thinking. Doing this with shapes enables the children to rehearse shape names and also their properties. If they do this with the cubes and 10 sticks from a set of base 10 equipment, they could make number patterns. For example:

You could give pairs of children different coloured counters. One child makes a random pattern using around five counters. Encourage them to make patterns that don’t simply go in a straight line. Their partner then repeats this pattern. They continue until they run out of the colours needed to continue. They could then record their pattern on paper.

You could give the children squared paper, ask them to fold it in half and then to create a pattern by colouring in different squares on one side of the paper. They then give it to a partner who recreates the pattern as a reflection of the first. This makes a great link to symmetry.

You might like to explore Polly Plug Pattern from Nrich with the children. It gives them the opportunity to make and describe patterns. The challenge of extending a pattern allows the children to be creative and you may observe use of symmetry, rotations, enlargements and/or translations, even if the children themselves are not yet familiar with these mathematical terms.

Activity set B

You could explore direction and movement by asking the children to suggest things that move and how they do this. Ideas could include cars, airplanes, balloons, writing with a pencil.

You could ask them to draw a Formula 1 type track with several twists and turns in it. They could then take a toy car and move it around their track, describing to a friend the different directions they take. Encourage them to talk in terms of quarter, half, three quarter turns in clockwise and anti-clockwise directions and movements in a straight line.

You could ask then to work with a partner and give each other a task to do in slow motion, for example, sharpen a pencil, rub out a pencil mark, open a book. They take it in turns to observe each other and record the movements and directions of turn they make. They may well be surprised at the results!

You might like to explore Turning Man from Nrich This is intended to help children who are confident about turning themselves a quarter or half turn, but find it difficult to relate this to quarter or half turns in a picture or diagram. The activity is a ‘halfway house’ between the two.

Coloured Squares from Nrich gives children the chance to become more familiar with everyday words which describe position. It also requires them to work in a systematic way.

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

order and arrange combinations of mathematical objects in patterns

• Describe the patterns in sequences and predict what comes next in the sequence and continue the pattern.

use mathematical vocabulary to describe position, direction and movement including distinguishing between rotation as a turn and in terms of right angles for quarter, half and three- quarter turns (clockwise and anti-clockwise), and movement in a straight line

• Recognise whole, half and quarter turns. They describe turns and give and follow instructions to turn. For example, they give instructions to a friend to follow a route around the playground. They make and draw half and quarter turns from the same starting point using, for example, two geostrips.

Use the grid to help you complete this table.

trees	B2
slide
seesaw
	A3

Watch me as I rotate (turn) this picture of a clown.

(Rotate the clown smoothly and continuously through a full turn, keeping it facing the children at all times.)

Which of the pictures shows what the clown will look like if I rotate (turn) my picture a half turn?

Tick the picture

(Do not rotate your picture this time)

• The video ‘Where’s Shrompy’, is a very simple one which demonstrates how to use a rhyme and develop hand signals to describe simple positions. You could adapt the words and actions to include any vocabulary you wish.