Q) Can you recommend a source of games and investigations on fractions, decimals and percentages that is suitable for secondary pupils who need lots of practice using parts of numbers? In our learning support department, pupils are diagnosed and assessed informally by talking to them and to their teachers. We are considering whether we should use a formal method. Can you recommend one or do you think the informal approach is satisfactory?
A) Pupils really need to know about these equivalences and games are a good way to practise them. There are many games on the market and some on the internet are free. I found several using the search string "fractions decimals and percentages using parts". Once you've found good resources you can keep a link to them in a Word document. If you keep this in a common place on the network then it can develop into a useful collection.
I also created a very simple game for the most common equivalents. Make a set of cards, four for each set, as shown for a 10th, with each type in a different colour. I begin with a few sets and build it up until the pupils are confidently sorting the sets of cards to their matching equivalents.
Pupils have found this great fun when working as teams and racing each other.
These games need to be grounded in an understanding of how each is equivalent. This can be done using a 100 square or an equivalence number line - a good example is at www.ictgames.comequivalence.html.
To use the 100 square, remind them that percentage means "out of 100".
Begin with 10 shaded squares; ask them what percentage this is: 10%, equivalent to 10100. Show them that there are 10 strips of 10% in the 100 square so that 10% is in fact also 110.
To show this as a decimal your pupils need to understand place value, so represent this as shown. Ask them to look at the equivalences and see if they can describe the pattern. I have found they quickly recognise the relationship between the percentage and the decimal. A pdf of the cards and an interactive 100 square can be found at www.mathagonyaunt.co.uk
An interactive multilevel game can be found at www.bbc.co.ukskillswisenumbersfractiondecimalpercentagecomparingdecimal spercentagesgame.shtml
There's a really nice one based on a number line at www.ictgames.comequivalence.html A great game for two, using a fraction wall, is available at the American Standards site standards.nctm.orgdocumenteexampleschap55.1
Pupils assessed via formal testing may make mistakes. Some maths departments have regular assessments. Reviewing scripts from these will tell you a lot about some of the difficulties your supported pupils are having. I would focus on these in the first instance. The formal test will often pick up things like reversal of digits or miscopying, which can lead to incorrect solutions and are not concept related. Identifying these means you can help pupils develop strategies for checking for such mistakes. They also serve as a way of raising their self-esteem and confidence in their abilities: often when they understand a topic but get answers wrong they feel confused and may think they are stupid, which is not the case. To use any formal testing you would need to have an idea of what you are testing for. the National Foundation for Educational Research has a number of tests that are standardised on large samples. This will give you an idea of pupils' weaker areas. Informal discussion should also take place with pupil, teacher and parent.
Q) Can you suggest a quick, catchy mental starter that would be suitable for a lower set?
A) Maths tricks can be fun as a starter. Squaring a two-digit number that ends in 5 is a nice one. The answer will always end in 25. Have a look at 45 x 45: the end of the number is 25; to find the first part of the answer add 1 to 4 and then multiply by 4 (= 20); write this number in front of 25: the answer is 2025. Try 65 x 65, giving 4225 (7 x 6 = 42).
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 firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX