I am sure taking my time writing my reflections for last week! Last class saw some new activities introduced to tackle the dreadful problem that is fractions. What child doesn't love fractions? Personally, I was one of those people that always hated them. I think it had something to do with improper fractions, but also because I loathe the Imperial measurement system, and fractions always remind me of that. Growing up, I always had a desire to make things---build things---and the Imperial system made sure to swiftly kill that urge. Toto, I have a feeling we're not in base ten anymore.
There were some good activities presented. Roll to Win dealt with rolling two dice twice, to get two fractions whose product was a whole number. I liked this idea in theory, but in practice I found myself rolling over and over and over and over and over. 31 times. The optimist would say that this was excellent practice in multiplying fractions, and I would hesitantly agree. The next activity, Who Walked the Furthest? was sort of self-explanatory. I found this to be a good way to practice finding common denominators and adding fractions. I put everything over 12 and away I went. I made a mistake adding (shame on me!) but my elbow partner was there to save me. And the last activity, Dollars and Decimals entailed finding all of the combinations of quarters, nickels, and dimes that you could sum to a dollar. I laid this out into a chart with each coin as a column, and then worked my way down starting with the largest number of quarters, then to the smallest. I found 29 different ways to make a dollar (this is verified by algebra.com, though I am not certain what credibility can be attached to that). I really liked this activity! I think there are many ways you can use the idea, and there is a lot of potential for people like me to fuss over whether they got them all or not. I did not however feel it was terribly relevant to the topic of fractions, and that it fell more comfortably in the category of decimals. Oh yes, I know they are the same thing, but I doubt anyone added four quarters as 1/4 + 1/4 + 1/4 + 1/4, and instead used $0.25 + $0.25 + $0.25 + $0.25. There's nothing wrong with this---I think we'd call it a strategy---but it somewhat defeated the purpose. But perhaps I liked this activity the best because it had the least to do with fractions?
In preparing for my own presentation this coming class, I read the material weeks ago. Having read it all, I had some ideas, but I had no first-hand experience directing an activity in our classroom, so I sat on it for a while to see how others approached it. I was really set on doing the integer football activity in the van de Walle text, however I think it's a little confusing. I think it's a great application of integers, but having two teams moving in two different directions, with a sign given to each, and only one team has the ball, and...and.... And it concepts get buried in trying to figure out who has possession of the ball! At least that was how I felt about it all.
With integer football out, I decided to do something based on the idea, but hopefully more straightforward. A person is standing in the middle of a number line and has to choose between two trips---one east and one west---and we'll discuss distance and time in the process. My thought was that directions are more intuitive than simple positive and negative values, and could be a physical way of showing something move up or down a number line. I think the most common statement in math next to "I hate math" is probably "when am I ever going to use this?" So I think that in showing multiplication and division of positive and negative numbers in a context will be useful. I won't say they're positive and negative, just east and west to start, and build from there. Integers are just opposite numbers after all! More on all of this once I see how it goes...
