Friday, 30 May 2014

Fraction kit and playing games

Fractions have always been a passion of mine. Started researching the concepts in my math part 1 AQ class and have been fascinated ever since.  I even ended up completing my Masters' of Education thesis in the subject.  Through my studies I came across fractions, Marilyn Burns' fraction kit and games.  I still haven't found something anywhere close that helps students understand fraction concepts like this kit.  

For those not familiar with it, let me tell you about it.  The kit in itself is very simple, it is five strips of paper. Each piece is to be cut to a corresponding fraction (halves, quarters, eighths, sixteenths, and a whole). 

Now you may ask yourselves how is this the best thing ever it's just a bunch of paper. It's the best thing ever because of the talk that it generates. Since finding this in my research I have done some modifications that really bring out the talk. 

First and foremost, I have them create the kits. It does you no good to create them for your students.  By them creating the strips, the students explore how fractions are division, fair sharing, why fractions are a part of a whole and many more fractional concepts.

Second, I created a context to go with the problem. As many of you know who read this blog, I truly believe in contexts. A good context makes kids think beyond arithmetic and focus on mathematical big ideas.  For this problem I tell my students a story of how I need to clean up my mom's back yard, she has a huge yard and in payment my mom buys me a large party sub. Now many students now don't know what a party sub is because they don't sell them anymore, so you may have to show them a picture: 


The students are so impressed and they can't believe that I would eat this much. Now I tell them that just before I was about to eat lunch one of my friends popped over. Now what?  This continues all the way to eights, the door bell ringing every time we figure out portion we need to cut.  For sixteenths I tell them this is what we are going to do as I really don't have sixteen friends; however by now we have really constructed a good understanding of the pattern that is happening.  Now why this context. I like this context because it is a linear model like the strips. Having the sub also means students have to think about measurement and division because technically you cannot fold a sub, as all the pieces fall out. The other part is students often will try cutting the their strips horizontally instead of vertically. Now this also brings up interesting discussions about equivalency versus congruency but this context stops that because if students cut a sub horizontally they don't really get all of the sub.

Third I don't have the students label their fractions.  When I have done this with my fours it was mainly because I didn't want them to associate a particular fraction with the strips whole. Basically, 1/2 strip is 1/2 of the kits whole not 1/2 somewhere else.  A big misconception with students thinking is that a what they learn is he only representation of a particular fraction. When you label the students don't understand that the size of the whole matters.  That 1/4 can be bigger than 1/2 depending on the size.  However, now that I am in primary I see a whole new benifit, it makes students understand what a fraction is. Why is 1/4, 1/4? While my students where playing cover-up, one of Mariyln burns fraction kit games, they asked me which fraction is 1/4? I turned it around and asked them. They then just picked a random strip up. I the. Asked them why that one? This discussion continued as students explored that the amount of pieces that we break our sub into is our denominator and the amount we use is our numerator.   If I had them label the fractions they never would have explored this concept and I would never have realized that they struggled with it.

The final change is the questions that I ask around this particular problem.  It's not just to make the stud ets create the kit but to think about the big ideas around fractions. Have a listen to my grade two class discussion on fractions:


Day 1 of our Fraction Talk



Day 2 of the Talk:





It is quite interesting the talk that can come from building these kits and the big ideas that come from it. I have played this game in junior and primary and personally I would do this for middle school as well.  In junior I start to add fifths, tenths, thirds, sixths, ninths, and twelves.  By adding these other fractions you also start to see other misconceptions of students halving strategies but for primary halving is still okay.  I hope you really try the kits and see the benefits of it in your classroom.

You can find all of my fraction research and resources on my site: Bit.ly/Soresources.  Feel free to use anything you want.