Maths - Liquid refreshment
Division is not a favourite mathematical topic for many students. It seems we are far happier counting up than sharing out. So, if dividing by lovely whole numbers bamboozles youngsters, you can imagine the nightmare that occurs when the divisor is a decimal.
For the example above, I have seen answers of one ("Anything divided by one is one"), 0.5 ("One divided by anything equals itself") and even 17 ("Dunno, sir, I just guessed").
What's the solution?
Often in mathematics, the solution to common mistakes and misconceptions can be found by relating the problem to real life. That is all well and good when talking about sharing 24 cakes equally between 6 people, but things are not so conceptually straightforward when one cake is somehow to be split between half a person (perhaps the other half is on a diet).
However, there is one scenario that may make sense to your pupils. Imagine you have a big 6-litre jug full of Vimto. How many 2-litre bottles can you fill? Easy, it's 3, so 6 divided by 2 = 3. OK, so how about if you have only a 1-litre jug; how many 2-litre bottles can you fill? Hmmm, well you can probably fill only half of one, so 1 divided by 2 = 0.5. And now it's crunch time: if we still had a 1-litre jug, but this time we have 0.5-litre bottles, how many could we fill? The only answer that makes sense is two, so 1 divided by 0.5 = 2. And if there is still any doubt, off to the supermarket you go to physically prove it.
Once students have accepted that it is possible to divide something and end up with an answer that is a larger number than the one they started with, their minds are more open to cracking this particularly tricky topic - and you, the teacher, can begin to introduce more efficient techniques.
Craig Barton is an advanced skills teacher from Thornleigh Salesian College, Bolton. He is also the creator of www.mrbartonmaths.com and the TES subject adviser for secondary maths. He can be found on Twitter at @TESMaths.
Delight your Year 7s with decimals using CIMT's dividing lesson plans, activities and revision questions.
For division of decimals and more, see Craig Barton's Tarsia collection, turning all sorts of number problems into games.
For a bright, easy presentation for lower-ability students, Manoj Mistry goes through decimal division step by step.
Find all links and resources at www.tes.co.ukresources028
From the forums
Is the head of maths role in a large secondary one of the most demanding positions in education? That's the debate going on in the TES Maths forum.