Today is the last day of finals. I gave my regular-level Algebra class the final section of their final exam today, a “Choose 3 of 7” component.

Question 2 asked students to “Order the numbers 3/7, 0.75, 1/7 and 3/5 in ascending order, and explain how you arrived at your answer.”

I forgot to remind them that they can’t use decimals. When we spent so much time teaching fractions earlier in the year, we emphasized that our students needed to be able to work with fractions *as fractions*. That was the only way to get credit and we worked really hard on it. We felt like it worked, but that was ages ago.

The first question I graded was, “I switched them all to decimals to make it easier, then I ordered them.” Oh, NO. I forgot to say something, they’re all going to do it wrong, I can’t give them credit for that.

And then I kept reading.

This was a CHOICE exam. No one HAD to do fractions. And a third of them did (Ok, to be fair, the kid with a 90.03 chose all 7–better safe than sorry I guess.)

But I read answers like these, with no reminders about decimals:

*I arrived at my answer by looking at the fractions and seeing the amount of shares they needed to accomplish a whole and I took the one fraction who the most shares…*

*I turned .75 into 75 and put it over 100 it gave 3/4, which is bigger than the other fractions. 1/7 & 3/7 have the same size but different shares and 3/5 is bigger than 1/7 and 3/7*

For a topic dating back to October, I am so pleased with these answers. I think we managed to change at least some of our students attitudes towards fractions, and lead them to actual understanding of what they’re doing.

I hope to be able to do even more with this next year. Anyone interested in collaborating? My sister is teaching fractions to adults again this summer….

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