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Primary CAME

CAME stands for Cognitive Acceleration in Mathematics Education.

This was initially a secondary initiative that followed CASE (Science).

In Croydon we have been working with King's College London (click to visit their web site) on a three year programme to develop the idea of CAME with children in Years 5 and 6. This is as part of a five year longitudinal study of Numeracy funded by the Leverhulme Foundation.

The secondary CAME has shown that using this way of working have large effects on children's attainment, not just in Maths but also in English and Science. We haven't got the final data yet for the Primary CAME but the results so far look positive. David Blunkett is particularly interested in this way of working and it links with Thinking Skills at KS3.

The Primary materials are being written up into a teachers book containing the philosophy behind CAME and a set of lessons suitable for Years 5 and 6 children. These are still only draft but if you would like further details, there will be course in September 2001.

One example of a Year 6 lesson is attached.

Halving and Thirding

CAME Aims:

To develop understanding of fractions, ratio and proportion in a variety of contexts.

Resources:

	1 litre jug about half full with coloured water.
	a mug.
	15 A3 copies of Halving and Thirding notesheets 1 and 2.
	Blue Tac

Organisation:

	Near ability pairs on mixed ability tables.
	You will need to have either the final paint scenario written on the board or use notesheet 2 to remind the children.

Vocabulary:

	full empty
	half full half empty
	half of a half quarter
	halving dividing by 2
	add more
	of lots of
	times multiply

National Curriculum Reference:

	Fractions.
	Ratio and proportion.
	Number operations.

1. Whole class preparation: (about 15 mins)

	I’ve got 1/2 litre in this jug and I pour half of it into this mug. Demonstrate with a jug and a mug.
	What can you tell me about the jug or the mug? Half of a half...half take away a quarter...half divided by two....
	Emphasis the operations that children are suggesting and write the suggestions in words and numbers/symbols (i.e. "If we take half of a half we get a quarter" or "1/2 - 1/4 = 1/4"
	How could we use division to describe what has happened? Or any other operation that has been missed out.
	1/2 ¸ 2 means we divide the half in two - is this the same as halving?

2.    Paired work: (about 10 mins)

Give out notesheet 1.

Here are pictures of a bar of chocolate.

You will need to quickly shade in the pictures to show what is happening.

Going across you will need to shade half, then half again. Point out that they can only shade where the lines are, as you would break a bar of chocolate, and not make up lines of your own.

Going down you need to shade a third and then a third again.

Remind them about the recording that you did on the board for the jug and mug. You should record what is happening in words and numbers/symbols like we did before.

3.    Class discussion: (about 10 mins)

How did you decide where to draw your cut? Some children will do this intuitively by spacial awareness and others will need to count squares.

Stick notesheet 1 on the board with Blue Tac and collect feedback on a variety of descriptions for particular pictures.

What have you got to describe the top right picture? Start with contributions from the least able children.

The centre picture is described as 1/3 of a 1/2, has anyone else got a different description? 1/2 of a 1/3....1/6....6/36....

What about the bottom middle picture?...

4.    Paired Work: (about 15 mins)

Imagine that I have got 2 pots of paint in my hands. They are not full but they do have the same amount of paint. Hold up your hands pretending to hold 2 pots of paint.

One pot is blue and the other pot is yellow.

I pour half of the blue paint into the yellow paint and stir it up completely. Mime the pouring of one into the other.

Then I pour half of it back into the first tin and stir it up completely. Mime the pouring back.

Is one of the pots a darker green? Which one? Why? You should have the instructions either written on the board for the children to refer to or use notesheet 2.

5.    Class discussion: (about 10 mins)

Collect feedback, asking children to demonstrate diagrams, number explanations on the board. Let the children discuss each other’s arguments.

How much darker is it? This is quite hard and children may need help in deciding what they use as their starting point; the original amount of paint or parts of paint.