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Q When teaching the area of rectangles to Year 5, should we be saying the area is found by multiplying the length by the breadth or the base by the height?

A It makes more sense to teach pupils that the area of a rectangle is the base times the height, rather than the length times the breadth or the length times the width, provided that they understand that the base, by definition, is the side that the shape sits on and the height is the perpendicular distance from the base to the tallest part of the shape. This should be taught from the beginning in primary school.

Using "base times the height" for the area of a rectangle is helpful when pupils begin to work with triangles and parallelograms as they don't have to learn a new formula. This also avoids confusing pupils at secondary school level when they are finding the volume of a prism, which is equal to the area of the end shape times its length. They don't have to think which bit should be called the length.

Q Please can you tell me how big a billion is. When I went to school it was one million million (1,000,000,000,000 or 1012), but I am now told that it is the same as the American value, that is one thousand million (1,000,000,000 or 109). Which is correct?

A Like you, I was brought up to believe that a billion was one million million. Now, however, it is generally accepted that we follow the American tradition of thinking of a billion as one thousand million. The Collins English Dictionary defines it as one thousand million, while recognising that formerly it was one million million. The American version is now accepted in business and the media, therefore also in education.

The change occurred in the UK in 1974, when it was announced by Prime Minister Harold Wilson that the American usage for a billion would apply to government statistics and papers. This definition is attributed to the French who, in the 18th century, changed the meaning of a billion from one million million to one thousand million. It was at that time that it was adopted by the Americans.

Your letter prompted me to do an internet search about the subject and I found some interesting facts. One thousand million used to be called a milliard in Britain and France. It would be an interesting exercise for students to decide whether 1,000,000,000,000 or 1,000,000,000 is a billion, and to then ask family members what they think. If the ages of the adults are given, a comparison study could be carried out. I wonder what the outcome would be? And I wonder how many people also know that a myriad is 10,000?

Q I teach in a secondary school and we have a homework club at lunchtimes for pupils to come and do their homework. During a recent session, a pupil was revising for a maths test and asked me what a translation was, but I was unable to give a very good explanation.

A A translation is one of the geometric transformations. The most common of these transformations are translation, rotation, reflection, and enlargement. Translation is moving a point or shape from one position to a new position in a straight line without turning.

The following rhyme could be used as an introduction to creating ways to remember the definitions, so that when pupils have to construct their own transformations they can check that they have included all the steps.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses. Email your questions to Mathagony Aunt at Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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