Thursday, February 28, 2013

Fractions With Cubes

Happy Thursday!

Man, what a week it has been! It's Thursday and today was my first day at work this week! I did however have the pleasure of visiting the doctor every day Monday through Wednesday. Oh the joys! I feel MUCH better now and was so thankful to finally feel well enough to work again! 

Moving on...  Fractions!

In my last post I blogged about making equivalent fractions and some free games from TpT. Last week my class began looking at benchmark fractions. We began with a water lab activity that you can download here. As you can see in the picture above, students used clear cups, water, food coloring and measuring cups for this activity. Using the worksheet you see, students were tasked with finding whether the 4 given fractions were closer to 0, 1/2 cup or 1 whole cup of water. The 1/2 of water and whole cup of water had food coloring added to them so we wouldn't get them mixed up (and because who doesn't like to play with food coloring?!). We had some really great discussions when students couldn't find 5/8 on their measuring cups. "Mrs. Lopez, we don't have five-eighths! We can't do that one!" Eventually someone figured out they could use one-eighth five times. Great learning experiences!

Next we transferred this information into making number lines. We put 0, 1/2 and 1 whole on the top of the line, and then 0, whatever half was and 1 whole on the bottom. For example, 0, 3/6 and 6/6--then filled in the remaining numbers in between.  It's crazy how much time students put into number lines trying to get exact spacing. It took some of my kids a little longer to grasp the concept than others, but for the most part, they can successfully tell you whether a given fraction is closer to 0, 1/2 or 1 whole.

The next day, a colleague of mine suggested using cubes to deeper their understand of benchmark fractions. Here's what we did. 

Using the cubes above, we made various fractions, figuring out how far away they were from each benchmark fraction. The students copied this simple chart into their notebooks, and filled in the answers as they were discovered. Two different colors were used--one for the numerator and another for the denominator. In order to figure out how far the fraction was from zero, students removed the numerator. In order to figure out how far it was from 1/2, they broke the denominator in half, and compared the half to the numerator, and calculated the difference. To figure out how far it was from 1 whole, students counted how many more cubes would be needed to have the same amount for the numerator as the denominator. This definitely  was a winner! Finally, we discussed how to tell which benchmark fraction was closest to the fraction given. We figured out the smallest distance was the closest, and that if there happened to be two of the smallest distances, the larger distance would be closest. For example, if you look at the chart, 3/4 is closer to one whole. 

I hope you can find this useful. Enjoy! :)

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