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.