A: While researching some ideas myself I came across the following activity at http:math.rice.edu laniuspatternsadd.html
(In figure 1. six triangles can fit in the hexagon and three in the trapezium, so one triangle is a ninth; in figure 2, the two triangles make a quarter.)
Having set pupils the problems, perhaps you could encourage them to make up some more of their own, and even introduce other shapes. This provides an interesting link between fractions and shape.
The discussions should increase not only the understanding of the properties of shapes, but also consolidate the idea that when dividing a shape into parts that create a unit fraction of that shape the pieces have to be the same area.
Q: I work with young adults who have little, if any, English and have only recently arrived in the country as refugees. Maths was never my strong point! Yesterday, I was working with a 12-year-old boy trying to teach him about English money. He finds it difficult to link the coins with their names and understand the value when it is in written form. He also doesn't seem to understand how the coins relate to each other.
A: I will make some suggestions to you, but you will need to pace them according to his ability, which can be difficult to assess when there are language issues. I am assuming that he can add and subtract.
I would begin by teaching him how to do brass rubbings of the coins. Get him to create his own, this can be done in pencil or in colours as he likes. Label them underneath with their written value, eg pound;1, 50p and as a decimal, pound;1.00, pound;0.50. Say the name of the coin with him as they are created. Get him to put them in order of value. Have some blank coloured card (makes it more interesting) and stick his brass rubbing onto the card, one for each coin, eight cards in all (I have not included the pound;5 coin as I don't think it is very common). Make another set of cards with the values written on them pound;2, pound;1, 50p, 20p, 10p, 5p, 2p, and 1p and their decimal equivalents, then a set of cards with the names of the coins in writing. Go through each of them with him, repeating the names. Shuffle the pack, show him a card and ask him what it is, if he gets it right then he keeps the card. Set a time limit and then slowly lower it. Encourage him to play the 'game' with someone else, this way he will be teaching them and learning at the same time.
Next set out a table as in the diagram shown and place some of the cards on the table. Then again set the timer and ask him to place the cards in the right places (the 50p row is completed here). Now that he knows the names and notation of the coins, he needs to learn the relationship between the coins. Give him coins of a denomination less than 10p. Then show him a 10p coin, demonstrate how you could make 10p with the coins that you have given him, for instance 5p + 2p + 2p + 1p. Write this down. Then ask him for 10p with different coins, until he has found all the arrangements. Then work with other coin relationships, until he is confident about the different ways he can make the same sum.
I was talking to someone who had to write an induction programme for Eastern children and she said the second most important part of that programme after politeness was money. When people can handle money confidently this raises their overall confidence and self-esteem.
Poetry in motion
For those holiday moments, a mathematical thought in poetry:
For the tangent divide sine by cosine
The answer provides the gradient of a line
A piece of poetry just touching a curve
An instant in time dictating the swerve
Of a ball as it smashes at a rate of knots
Another ball that the change just pots
How fast this moment in time?
Use Calculus as the tool
For this moment in pool
Calculus is the magic potion
For understanding the motion.
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 email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX