Just prior to the start of the school year, I racked my brain for ways to extend my high students in mathematics. I knew because I'd taught a few of my current grade sixes in grade five and from students' reports that my class had 7-8 very advanced students in numeracy. These students typically score between 90-100% on pre-tests across all topics, with most errors resulting from lazy question reading.
Sure, almost every numeracy lesson can be modified to cater for extension students, however sometimes even those modifications do not sufficiently challenge the really high students. Often, they need to be learning completely different topics to what I teach under a regular 5/6 curriculum. For example, for the last three weeks I've been teaching place value - seeing great progress amongst my students - but for these extension students place value is virtually not in their curriculum. As students who have mastered numbers up to millions, if not billions (as useful as those are to most of us billionaires) and down to thousandths, they have really progressed to a more year 7/8-centered curriculum involving integers, Cartesian planes and operations involving decimals.
One fantastic (not free though) resource for extending these students is www.ixl.com. Unlike Mathletics and other mainstream numeracy programs, it explains to students on every single question they answer incorrectly exactly how and why they got it wrong, and strategies to use to correct it on the next question. Which is exactly what we wish we could do for our students during numeracy on every single question. For extension students studying year 7/8 topics in a 5/6 class, this is invaluable, especially when compared to text book work because the text book just provides a correct answer, not a method on how to achieve it that relates to the specific question the student erred on. Whereas, Mathletics simply kicks the kids forward to the next question with a nice, big red cross.
Sure, occasionally a student clicks on the Mathletics question mark and listens to the concept tutorial, but that isn't nearly as good quality as the www.khanacademy.org numeracy tutorials on offer for free. This site provides completely free tutorials on how to complete almost every mathematical operation under the sun, and unlike YouTube which is very unfortunately blocked by many schools, it is not.
The combination of Khan with IXL provides extension students with so much support in learning a curriculum two to three years above their formal grade level that, combined with some non-computer based extension projects and investigations, year long, consistent differentiation for my highs has become very straightforward. Especially compared to being asked the question, "What do I do now?" every numeracy lesson (which can only be solved by the 'create your own' answer so many times).
How do you extend your students in numeracy? Please comment and share (especially project and investigation work)!