There is something very simple about a task which presents two numbers and simply asks “which is bigger?”. This should be done using mathematical notation, i.e. using the < > symbols. I have seen these being introduced successfully in Year 1 without any mention of crocodiles, or such similar unhelpful “stories”. But my Year 7 class still insist on calling them crocodiles and drawing teeth on them. But hey, I have bigger battles to fight…
As well as comparing 2 fractions we can put multiple fractions into order from smallest to largest. There is a significant range of difficulty in this apparently simple task.
- Comparing fractions of the same denominator
- Unitary fractions with different denominators
- Same numerator, different denominators
- Different denominators where one is a multiple of another.
- Different denominators where a common denominator needs to be found for both fractions.
Alongside all of these there may also be strategies where learners are using known facts or doing calculations to convert to decimals or percentages, e.g. 1/2=0.5, 2/5=0.4, therefore 1/2 > 2/5. That is not the intention of this task (it is of a different task here) but in the end we want learners to be able to play with all these ideas and I can’t really control, nor would I want to control, the order in which they coalesce in students’ mind.
Here is a simple set of cards that I used recently. I got the students to do the last bit of cutting to turn each strip into the 3 separate cards. I also told them that there is deliberately some space alongside the fraction to enable them to write equivalent fractions if they needed to.
I gave them out a strip at a time, the idea being that they were to “slot in” the subsequent fractions to maintain the order. The fractions are carefully chosen, so that each time they get a new strip they are having to apply the next level of reasoning. The first set are simple but this can end up quite challenging especially if they chose their own more “exotic” fractions.
It can be a bit of a hassle preparing and managing card sort exercises in the classroom. Whenever I see a resource that is created as a card sorts, I always think, could students get the same benefit by just writing in their books. But for some tasks such as this, I think it is worth it as it enables a richer discussion and the possibility for learners to easily changing their mind as they are building understanding.