Who knew there was so much to learn about teaching fractions!?

This week we had our second lesson on teaching fractions; we talked about how we could represent this idea in a ratio….

We’ve had 2 lessons on 1 unit making the ratio 2:1

We looked at a problem about the classic recess game, ‘red light, green light’. The problem provided the ground gained by each player; this information was represented through fractions. Most of the fractions had different denominators. We were expected to put these fractions in order. The important thing to note is that we were not told what sorting method to use or what order the fractions were to be in (ie. Biggest to smallest, etc.). The openness to this problem gave us the option to choose the order we wanted to use to sort our fractions, making it less restricting and easier to begin.

We then discussed our ideas as a class. Having us first solve the problems on our own ensured we had a personal understanding of the problem; having us discuss our ideas as a class provided us with ideas of other ways we could have approached the question. Some of the orders people chose were:

•       Biggest denominators first (biggest gap between numerator and denominator)
•       Smallest gap between numerator and denominator
•       Unit fractions first
•       Change all to percentages

I originally chose to start with the fraction that had the smallest gap between the numerator and denominator, thinking this was the easiest solution. However, after our group discussion I changed my mind, deciding that changing all the fractions to percentages would make it more visually appealing and much easier to sort by size. It was really helpful to go through the problem to come up with my own solution before being able to hear other peoples strategies. It allowed me to compare my strategy with those used by other students and thus come up with a final strategy that lead me to the solution in the simplest way. 

It seems as though the most important thing we learn each week is to always use open problems to provide an opportunity for each student to grasp the concepts at hand.

A good problem has a ‘wide base and a high ceiling’. It is open enough that it allows every student to start, regardless of their learning level, but it is also extendable, meaning you can add new portions for students who may finish quicker than others and still want a challenge.  A good problem has many solutions, therefore allowing each student to comprehend in their own way but then further extend their understanding through group work and group discussion.

A second activity we worked on today was discussing fractions using Tangrams. We read a children’s story about a porcelain square that shattered into 7 pieces and then had to try and remake the square using our own tangram manipulatives. A smart board demonstration assisted in showing how tangram pieces could be used to display fractions of the square.  This activity would appeal to auditory, visual and kinesthetic learners by explaining the idea of fractions through the book and then allowing students to manipulate the tangrams themselves.

We were given an allotted amount of time to make our attempt at creating the square, but not everyone was able to solve the problem before we had to move on. A separate lesson learned from this activity was to show the importance of celebrating hard work as much as we celebrate ‘success’. Teachers need to encourage their students for working hard and persevering through difficult problems in order to propel their motivation. It is important to let students know that success is attained through diligence and they should be proud of themselves for sticking with it whether they find a solution or not.