This lesson uses the best task that I have seen to teach students about solving systems of equations using elimination. I have found students have a better understanding of elimination when presented with scenarios like the ones in Shopping for Cats and Dogs.
I begin class by having students read the first problem aloud. We work on the first problem together, and I find it exciting to see which students really connect with the problem. In my experience, students who sometimes struggle with the more rote tasks of algebra have success with this line of thinking. It is intuitive for them to think about the price difference in Question 1. I will have a student share out his/her thinking and make sure s/he highlights and explains why the difference in costs has to be due to the difference in the amount of Figaro Flakes that were purchased.
Once we have worked through Question #1 together, I have students work in small groups on the rest of the problems. I let them know that each group will be sharing out their thinking for one of the problems.
Students spend the bulk of this lesson working on Shopping for Cats and Dogs in their groups. As I circulate, I look for students who are struggling but try not to help too much! This task is really about students reasoning and making sense of the problems.
One wording issue to watch for is that sometimes students think the word "additional" means in addition to the first purchase. This happens in Question #3 for example. In this case, additional just means Carlos bought three more leashes, not 6 plus 3 more.
I might ask some of the following leading questions for students who are stuck:
I really like the share out section and discussion of today's lesson. It is exciting to have students present in their groups their understanding of the problems. I like to have different groups present each of the problems and we focus on the thinking behind their answers. Questions #4 and #5 can lead to an animated dialogue. I try to step back as much as possible and let students hash things out. I also try to make sure that students who do not have a clear understanding can get help from their peers. All of this work lays the groundwork for the next lesson where students will write each of these scenarios as a system of equations.
As a closing activity for today's lesson, I want students to summarize the strategies they used to solve these problems. I ask them to write a list of the key strategies they used to solve these problems. I might type them up and have them on the board as students come into class the next day.
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