Fractions on Friday

Today was part two of comparing fractions in Prealgebra. I love fractions. I understand fractions and I desperately want kids to understand and love fractions as much as I do.

okay, I like fractions a lot, love may be a bit strong, but I do like them and I personally do not see what is so difficult with them.

But then again, I am a math teacher and what is second nature to me is not even on their radar in many cases as far as math is concerned, so where does that leave me? Right in the middle of a 20 minute diatribe about why we should convert 5 7/8 to an improper fraction…but that I should eliminate the whole number first and just compare the fraction part…blah…blah…blah…ugh, I am even bored reflecting on it.

So I tried to do this really cliche thing in a sorta kinda cool way. I tried to ask this question to get them thinking about comparing fractions and I used pizza (recently I read that this was a no-no, and I tried to find the article but couldn’t, so I had to go with it) to do this:

Image

And after a good while of discovery and recon as to what congruent and radius meant, we got down to business and it seemed to me that when it came to pizza, these kids were very aware of what makes a whole pizza a whole pizza. They could visually slice and dice the thing into thirds, fourths, sixths and eighths and had no trouble with the fact that this:

Image

ended up a raw deal for them. They could explain that if the denominators were different, the one that was bigger yielded smaller pieces and therefore was a bad trade for something with a smaller denominator (although one student pointed out that he would evaluate the trade based upon toppings, which I had to acknowledge would weigh on my own decision as well). They could even tell me how many slices you would have to divvy up each into to have a reasonable comparison. The opener was great but moving into the abstract left me with spaced out kids and a lack of flare as we reviewed the theory of finding a common denominator. The day before, they were fine, we cruised through common denoms! I have a feeling that the Friday afternoon factor weighed heavily on them, as they had success the day before with the skill, but we will see if a formal evaluation on Monday can coax the previous day’s prowess out of the Friday funk. Definitely keeping the opener for next year, unless I find that article…

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