Last week I was chatting with a couple of tweeps (Mr Bayew and Mr Reddy) about my blog http://educatingmrmattock.blogspot.co.uk/2015/05/mean-average-dont-add-them-all-up-and.html and discussing ways of teaching mean - I talked about the approach I would take and thought I would outline it here.
The biggest misconception I have come across with mean calculations is the blind 'add them all up and divide by how many there are' process, with no appreciation for the information this is designed to convey. Therefore the primary goal of my approach is to reinforce the need for a total that is shared, and so my approach looks at other ways of finding the total before looking at addition. You will see kids in my class lying down in a line being measured to see how long the line is, so we can see the total length (i.e. height) of all of the pupils. Weighing is another good one; putting lots of items on a scale to find their total weight without the need to add. In true 'mastery' style we do these practically before looking at images like these:
The biggest misconception I have come across with mean calculations is the blind 'add them all up and divide by how many there are' process, with no appreciation for the information this is designed to convey. Therefore the primary goal of my approach is to reinforce the need for a total that is shared, and so my approach looks at other ways of finding the total before looking at addition. You will see kids in my class lying down in a line being measured to see how long the line is, so we can see the total length (i.e. height) of all of the pupils. Weighing is another good one; putting lots of items on a scale to find their total weight without the need to add. In true 'mastery' style we do these practically before looking at images like these:
(images courtesy of mathszone.co.uk and teachitprimary.co.uk)
On these we can talk about mean average weight of each apple or lollipop. Once I am confident that pupils understand the idea of mean, we can then look at it in reverse, i.e. if a bag of 6 apples have a mean weight of 42 grams, how much would the bag weigh? Questions like this reinforce the sharing nature of the mean average, and highlight division as the primary operation rather than addition.
Once the concept is clear, finding totals from addition just become another type of problem, rather than an integral part of the process; we can pose problems like find the mean of 5 objects of lengths 12 cm, 17 cm, 9 cm, 6 cm and 11 cm in the knowledge that pupils are already secure that the sharing of the total is the important thing, and that the adding is just there to find the total. I also like to throw in questions like "what is the mean of a group of 10 objects, 4 of which weigh 30 grams, 3 of which weigh 32 grams, 2 of which weigh 35 grams and 1 which weighs 36 grams. As a pre-cursor to mean from tables this sort of question is really nice as it shows the use of multiplication with addition to find totals, and importantly stops kids getting bogged down in lots of adding.
So do your kids a favour, teach them what the mean means!
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