Trying to Think Algebraically

It’s been more than six weeks since I participated in a week-long Common Core institute put on by Pearson Education. I have 21 days worth of lessons done so far for Unit 1 and have moved on to Unit 2. Unit 2 is supposed to last 4 weeks according to the ISBE Scope and Sequence and I already have an opening 3-Act math activity similar to this planned to introduce the lesson and a few direct instruction lessons planned after that for solving equations.

Now, I’m trying to create lessons and activities where students will have to write and solve equations in order to work through the task. However, it’s been tough to come up with activities outside of rates or ratios. I looked in my textbook to see what word problems/scenarios were in there and here were two of the problems I found:

book problem 2

book problem

First, question #38 is so contrived, it made me laugh as a math teacher. If Chris and Nora can determine that “Chris has saved twice the number of quarters that Nora saved plus 6 and the number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved,” they should also be able to just count the number of quarters they each have without having to write and solve an equation. Dan Meyer has a weekly “Makeover Monday” in which he takes a bad textbook question and he and his Twitter followers give the question a “makeover” to try and create a 3-Act math activity out of it. I’m not sure if this one can be saved.

When I look at question #52, it starts off looking a little better. When we go shopping as a family, there are times where we find unit prices in order to find the better deal. This is probably one of the few times my wife uses math in a real-life situation. But once I read through the entire problem, I thought, “Why would any market give you the price of apples, pumpkins, blueberries, and winter squash, but not give you the prices of potatoes or zucchini?” Also, when you are told the prices, why would the prices of potatoes be given as “$1.50 less than half the price of apples?” I’ve never seen a price list anywhere that writes prices this way.

Now I’m back to where I started, looking for situations in my life where I use algebra. I think the hard part is that I do it automatically, without thinking about inverse operations. I also have to remember that I may not be able to come up with multiple tasks/scenarios to model each standard, especially enough to last four weeks. As time goes on, I think we will all come up with one or two activities that work really well, share them with each other, and accumulate weeks worth of intriguing, engaging activities.

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2 thoughts on “Trying to Think Algebraically

  1. I agree that many “real-life” scenarios given in the texts are not at all how something would actually happen in real-life. Weak! and not at all related to how math is actually used in the real world. And I really believe that there are just certain math tools/strategies/computations that don’t have a truly relevant real-life scenario to go with it. So my philosophy is to only incorporate scenarios when it makes sense to do so and try to stay true to how problem solving really works.

    On the flip side, there could be a case made for posing a “what if” situation to a strictly abstract math concept and see if you can hook them in by engaging their curiosity. That at least ups the odds of increasing their interest.

    You will be missed at the HS Andy!!!

    1. Thanks for the comment Wendy! I always go back to my example of when Kenzie got an iTunes gift card for her birthday and wanted to buy a $14.99 movie and then was asking how many $1.29 songs she could buy. I think people do this all of the time, not realizing they are solving 1.29x+14.99=25. Also, there are a lot of activities involving systems of equations. When solving systems, you have to know how to solve an equation, so it will come up later. (I will miss you guys next year also!!)

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