The fourth graders have been getting a workout with fractions. They spent some time using fraction tiles to build highways and number lines, a project I describe
here. In order to help the kids understand how to decompose fractions and mixed numbers, and express them as sums of unit fractions and as products of whole numbers and unit fractions (if you don't believe this is really something a fourth grader needs to know, it's 4.NF.B.3a and b and 4.NF.B.4a) we decided to let them explore with
fraction towers.

First we let them play around with the tower pieces. We compared them to the tiles, which were used during the highway sign project. This was a perfect opportunity to hammer home the idea that the fractions were meaningful only in relation to their respective wholes. 

Our idea was to let them build towers using the same color pieces (unit fractions)... 

...then swap out and make a mixed number equivalent. This student showed how 7 sixths is equivalent to 1 whole and 1 sixth.


Both towers needed to be drawn and labeled.

Rather then using a horizontal number line, like we did in the highway sign project, we thought a vertical number line provided a better representation.

Describing towers using number models. 
This activity will not revolutionize the profession. But there was something about seeing the improper fraction tower next to the mixed number tower next to the number line that made me happy. It seemed that snapping the pieces together screamed
addition more than putting tiles together. And I had a few other ideas, but not enough time (what else is new), including:
 separating the pictures from the number models and have the kids work on matching them up
 taping several pieces of paper together to allow for really big towers
And towers made me think about castles and forts, and
Fawn and Andrew's Hotel Snap project. I wish that the pieces could snap on more than just top and bottom so the kids could use them to build something other than towers and then calculate the "value" of their structures. Anyone from Lakeshore listening?
Joe, I've had that exact same feeling of happiness lately, seeing number lines and fraction blocks or strips together. It seems like such a powerful way to make sense of mixed numbers, adding fractions, and more. Really brings the idea of building fractions from unit fractions AND fractions as points on the number line to life together.
ReplyDeleteI've been playing around with games that take advantage of this representation here: http://mathforum.org/blogs/max/gameswithfractionstripsandfractioncards/. I'd be curious if any of them are interesting to you/your students. I'm also going to link to this blog post from there.
Thanks!
Max
Thanks Max. We find fractions to be the most problematic of all the concepts we teach, and are always looking for different approaches, strategies, and activities. I will take look at the games and give them a go. And thanks also for all your work at The Math Forum.
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