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Q. In our primary school we use MathAmigo a handheld computer device for follow-up exercises. I was using this with my Year 3 class to consolidate work we were doing about ThHTU. One pupil was asked the question, via MathAmigo; "How many 10s in 6784?" She answered 8. The machine marked her wrong and told her that 678 10s was the correct answer, but, surely 8 is the correct answer as there are 8 10s in the 10s column?
A. The correct answer isn't 8 and it isn't 678, but 678.4. Your Year 3 probably haven't studied decimals or mixed numbers yet. The numeracy framework suggests for Year 3 that: "Pupils should be taught to understand the idea of remainder." This provides an opportunity to introduce the idea of remainders, the answer should be 678 10s and 4 units remaining. The question to give an answer of 8 should have been something like: "How many 10s are in the 10s column?" To get an answer of 678, the question should have been: "How many whole 10s are there in 6784?"
A lot of confusion arises in mathematics through the misuse of language. I often think it would be a good idea to tape ourselves asking pupils questions and analyse the results of their answers. Such analysis helps to understand how language can be misinterpreted. But in reality there isn't time to do that. This is why it is so important to ask learners why they give a certain response to a particular question.
A useful book for helping to understand language difficulties is one written by Eva Grauberg, Elementary Mathematics and Language Difficulties (Whurr Publishers, 1998). This isn't just useful for the early primary years, but also for those working with pupils with special educational needs as it can help identify some problems they might be having with maths which may be grounded in difficulties with language.
For details of MathAmigo go to www.mathamigo.com
Q. As a head of maths, I have been asked by senior personnel if I would like to use any of the outdoor area for maths. It would be great to be able to take pupils outside sometimes. Have you any ideas that you have used or have seen used successfully that I can put forward?
A. I am including a couple of ideas from the measures, shape and space strand. I will feature others in later columns. I also welcome more ideas from readers.
Paint a compass on the ground with the correct direction of north. This can be used in lots of different activities. Within the same large area paint the letters A, B, C, D, E, F, G with accompanying dots as markers. These can then be used for pupils to follow bearing directions on paper, or for them to create instructions of journeys that other groups have to follow.
Other groups of letters can be used in other parts of the school. Then bearings instructions could be given to groups of pupils starting in different positions around the school. I would include some journeys that require knowledge of just the compass points as well. This space could be used for the visiting Year 6 as part of a maths trail with problems to solve left at each location.
One activity that my pupils really enjoyed was as an introduction to exterior angle properties of 2D shapes. I chalked different regular shapes around the playground before the lesson, eg equilateral triangle, square, pentagon, hexagon, and an octagon, each side extended with a dotted line.
Label one vertex with an "A" (the start letter). One member of the group stands in the centre, the rest of the group, in turn, has to stand on the "start letter" facing along the direction of the first side. They have to work out the instructions (the amount of turn in degrees and how many centimetres translation) to the next vertex. This is repeated until they are back at the start. They record their answers on a worksheet.
Depending on the ability of the group they quickly find that they turn through the same number of degrees at each vertex, the person in the centre would have turned through 360o.
Back in class the term exterior angle is introduced. You can discuss why the exterior angles of a shape sum to 360o and the angle properties of irregular shapes can then be investigated.