I’ve been trying to figure out how to ‘show’ fractions better so that students understand the concept that the denominator is how many bits the whole is split into (aka how big a slice of cake you get….) and the numerator is how many bits you have. That’s why you don’t change the denominator when you add, because adding more ‘slices’ doesn’t change the size of the slices, just how many you have! It’s also why you need common denominators to add fractions etc. I’m also planning to use my little resource to show things like why 1/2 x 1/3 is 1/6 (you chop it in two, then chop each bit into 3, so there are 6 bits!).
This may be very obvious to you, but I’d never found a really good way to show it to students.
I recently found a great site: http://www.crewtonramoneshouseofmath.com that shows the use of manipulatives to teach loads of stuff, particularly the basic operations, and a load of really cool algebra stuff, like polynomials! He uses ‘disguises’ – cos fractions like to pretend to be other fractions – to show things like equivalence etc. The videos are well worth a look, and I’m planning on buying some of the Mortensen blocks for use with our Y7s and lower ability sets next year.
You will probably spot the link between the fraction ‘disguises’ and what I’ve done with this little interactive resource.
I hope you find it useful.
Here is the link – it’s found on the ‘teacher tools’ page of http://www.ilovemathsgames.com.
What with the meeting I’ve just been to about the new GCSE curriculum, and the lesson study project I’m now involved in, problem solving is currently very much on my mind.
In light of that, and having seen a fab lesson done by Rachael Horsman (http://rachaelhorsmanmaths.wordpress.com), I had a lightbulb moment earlier.
My plan is to collect a bunch of ‘Big Fat Questions’. The kind of questions that will keep an enquiring mind engaged for a lesson or two. Things like ‘182,000 acts auditioned for the X-Factor last year. How long did the auditions take?’ (totally stolen from Rachael….), or ‘how many times a year do we blink?’.
The aim is then to use these for Y7, 8 & 9 next year, on a regular basis, so that they are INDEPENDENT, RESILIENT, mathematical thinkers, not just mindless robots trained to follow algorithms. I’d like them to think about assumptions, and variables, and how to formulate a mathematical representation of a problem. I’d like them to learn to really think through how to work stuff out, without prompting. I’d like them to learn to answer their own questions. I’d like them to start asking me WHY the algorithms work…..
I may even try it occasionally with Y10 and 11…!!
It would be really very awesome if you would like to donate any Big Fat Questions you may have here on my google doc.
(The direct link for those of you that would like to not have to go via my blog each time is tiny.cc/BigFatQuestions.)