Today's goal was to learn how to solve linear systems by elimination. We jumped right in with the first example:
Side note: I do not actually drink coffee, unless you put a little chocolate or caramel in it. Yes, I'm one of "those" Starbucks coffee drinkers. I actually prefer tea. And I don't remember when I last ate a doughnut. I'd much rather have some dark chocolate.
A couple of years ago Sheri Walker showed me how she teaches solving systems by elimination and I kicked myself for not realizing that I needed to teach it this way sooner. I teach both my applied and academic classes using these examples as they make it all make sense. I use pictures and I find this helps certain students make the link between the words and the equations. I also wrote the equations for this first example on the white board.
We compared what was the same in both orders and concluded that the extra 2 coffees had to account for the extra $4.50. From there we could find the price of 1 coffee and then the price of 1 doughnut.
Next, a slightly more difficult example:
I was impressed by the number of students who thought to double the order. I really liked it when one student suggested adding 2 cookies to the first order as it let us discuss why we can't do that.
They worked through the 3rd example and noticed that there was more than one correct way of solving it. Some doubled the first order and tripled the second, while others did the opposite. One student multiplied the first order by 1.5. We talked about this not working in context (you can't buy half a muffin...), but clearly this student was not having any trouble making this more abstract.
Then we went over the process of solving by elimination, emphasizing that we are creating an equivalent system by multiplying one or more equations by a constant. They then practiced solving more systems which no longer had a context, and where they needed to make a choice between adding or subtracting.
I had hoped to have them work on the Oreo problem also, but that will have to be saved for tomorrow. Here is the homework I gave today.