Q) Some of my Year 7 group find it difficult to make conversions from one set of metric units to another. They just seem to guess when to multiply or divide by multiples of 10, not taking into account the relative size that the measure they have written refers to. Have you any ideas that might help?
A) Part of the problem pupils have with conversions in metric units is that they haven't really understood the relationship between the language and the maths. The language provides the building blocks, as the prefixes determine the multiplicative element of the conversion. The metric prefixes are highlighted in blue for the metre as the basic metric unit. So, in the case of metres, we have:
* kilometre = 1000 metres (kilo = 1000)
* hectometre = 100 metres (hecto = 100)
* decametre = 10 metres (deca = 10)
* metre (no prefix, this is the basic unit)
* decimetre (1Z10 of a metre, deci = 1Z10)
* centimetre = 1Z100 of a metre (centi = 1Z100)
* millimetre = 1Z1000 of a metre (milli = 1Z1000) The prefixes will then work for the other basic units. So a millilitre is 1Z1000 of a litre and a milligram is 1Z1000 of a gram.
Having established the language, it is good to relate the conversion to concrete objects that act as points of reference. The most common object that they carry around is their 30cm ruler. Using this as a beginning, write "1cm" on the board, followed by " = ?mm". Then ask them how many millimetres are in a centimetre.
They can look at their rulers to help them remember that 1cm is 10mm. This then becomes a good point of reference for them when they are under test conditions.
Ask the question: What sum will take us from 1 to 10? (We are looking for x 10.) Put this on the board.
Then ask: "What sum will take us from 10 to 1?" (We are looking for V 10).
Draw this on the board.
Reinforce the idea (following the diagram with your finger) that to go from centimetres to milllimetres we multiply by 10, and to go from millimetres to centimetres we divide by 10. This is a diagram they can set up themselves by asking themselves the same questions.
Assume the instruction is to change 24cm to millimetres. Write 24cm under "cm" and ask which arrow to follow. Followed correctly, the top arrow leads to 24 x 10 = 240, so 24cm = 240mm. These diagrams can be repeated for metres to centimetres, and so on. The diagram helps pupils choose the operation (a self-created crib sheet).
Public maths: the alcohol challenge How likely are we to have pupils in our classrooms who have been drinking before or during a school day? Do we know how prevalent this problem is? Research shows there is a relationship between reduced efficiency in cognitive tasks and the amount of alcohol consumed. Alcohol is part of popular culture for 95 per cent of the population.
There is a lot of information related to alcohol that is conveyed through maths and statistics, which can be difficult for the "maths unhappy" to interpret in a meaningful way. Hence "Public maths: the alcohol challenge" is born. This is a new project which aims to engage the general public in maths by looking at issues related to alcohol consumption. Binge drinking is an issue for young people in today's society. Knowledge and understanding of the relevant facts may lead to responsible drinking.
The first interactive show, "How much is too much?", is generously supported by the Drinkaware Trust. The audience will participate through hand-held "Qwizdom" voting units, which allow responses to be communicated anonymously.
These will enable us to create a snapshot of the audience's perceptions of alcohol. The audience will take part as teams, using their combined mathematical skills.
The aim is to enhance knowledge of the industry and issues through fun maths questions. We will equip the audience with the mathematical, scientific and social facts that will enable students to have a rounded view of alcohol consumption.
* Wendy will present this event on July 14 in the Faraday lecture theatre at the Royal Institution of Great Britain. The target audience is 11 to 16-year-olds and entry is free. Further details at: www.rigb.orginsideout