This section shows examples of activities for Number (what pupils can do) and Shape and space (what schools have tried out).

Number

Year 1

Money problem

Jade buys a sticker. It costs 6p. She pays for it exactly.
(i) Which coins could she use? (There are five different ways.)
(ii) What if the sticker cost 7p? 8p? 9p? 10p?

Teachers' notes

This type of activity gives pupils the opportunity to explore different ways of combining coins to create a fixed amount. All pupils will be able to make a start on this activity. Gifted pupils will be able to take it further. The challenge is to find as many different combinations as possible, using real coins if necessary. Pupils should be encouraged to work systematically and to explain how they know that they have found all of the possible arrangements.

National Numeracy Strategy objectives

Solve simple mathematical problems ... recognise and predict from simple patterns and relationships. Suggest extensions by asking 'What if ... ?' or 'What could I try next?' (62)

Work out how to pay an exact sum using smaller coins. (68)

National curriculum programme of study reference

Ma2 1a,c,d,f,g,i, 3c, 4a

Year 2

Legs problem

Tripods have three legs. Bipods have two legs. There are 25 legs altogether. How many Tripods are there? How many Bipods? How many different answers are there?

This problem is suitable for all pupils. It is useful to encourage pupils to use a range of approaches to solve problems. This helps to cultivate flexibility of thinking. For example, some pupils may attempt this question by counting back in twos. Others will use their knowledge of multiples of 3. It is particularly useful to discuss pupils' methods. Some will apply what they know about addition to carry out a subtraction (inverse). Others may use what they know about multiplication to carry out a division (inverse). Most pupils are likely to work randomly and be satisfied when they have found one solution. Gifted pupils should be challenged to work more systematically. In this problem it is important for gifted pupils to consider whether all of the solutions have been found.

National Numeracy Strategy objectives

Choose and use appropriate operations and efficient calculation strategies to solve problems. (61)

Explain how a problem was solved. (65)

National curriculum programme of study reference

Ma2 1a,b,c,d,e,f,i, 4a,b

Shape and space

Year 2

This was a whole-class lesson with extension/enrichment activities for the more able children.

What happened

The teacher took the class into the hall. She arranged four children into a square shape and passed a rope around them to make the edges of a square. The teacher then asked the class questions such as ‘What shape have I made?’ and ‘How do you know?’ and expected the children to respond using appropriate mathematical language.

Following this, the teacher passed a rope around only three of the children to make the edges of a triangle. She asked the class to identify the shape and discuss, in pairs, what they knew about it. The teacher challenged the more able children to make at least five statements about the shape – for example, that the shape has two short sides and one longer side, one right angle, two angles smaller than a right angle, three corners.

The teacher asked the children to think about what would happen to the shape if one child (vertex) moved a little. She then constructed more shapes with the children, including irregular pentagons and hexagons, and gave the children time to identify the shapes and discuss what they knew about them. The teacher encouraged the more able children to make jottings on their own whiteboards and think about the angles within these shapes.

Later, the teacher asked the children to create different five- or six-sided shapes using pinboards and elastic bands, and to record them, with descriptions, on dotted paper. She gave the more able children two or more criteria – for example, a pentagon with no right-angled corners and one line of symmetry – and encouraged them to create shapes using their reasoning skills.

The teacher discovered that one child could use the criteria to create more than one shape. She asked the child, and her friend, to make as many different shapes as possible and then explain how they had made these shapes. The teacher challenged other more able children to use reasoning skills to create a hexagon with four right angles, and later asked them to make up their own problems by choosing two or three criteria and trying to find shapes that would fit them. The children had to explain why some of their sets of criteria did not work.

Finally, the teacher reinforced the children’s mathematical vocabulary in a class discussion of the shapes and properties. She asked the more able children to discuss their sets of criteria and the shapes they had created, and asked the other children to check that all the criteria had been met.

Solve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could I try next?’. (‘Supplement of examples’, 63)

Use the mathematical names for common 3-D and 2-D shapes. (‘Supplement of examples’, 81)

Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. (‘Supplement of examples’, 64)

Sort shapes and describe some of their features. (‘Supplement of examples’, 81)

Ma3 1a,d,e,f, 2a,b,c,d, 3c

National Literacy and Numeracy Strategies' Guidance on teaching able children. (Print copy available from DfES, order reference: LNGT.)

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