Solving Systems Using Elimination: An Intuitive Approach -- Day 1 of 2

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SWBAT solve systems of equations using elimination by using real world problems that involve prices.

Big Idea

Where is the difference in price? Students reasons through receipts in order to see the structure of solving systems using elimination.


10 minutes

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.  




30 minutes

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:

  • For Question #2, I will try to have students reflect on their work from Question #1. I might say something like, "In Question 1, he bought the same amount of Tidbits both times he went to the store. Is there any way we can make this problem look like that one?"  Here I am trying to get students to reason that if they double all of the items on the second receipt, the Lucky Licks amounts will be the same and then they can work with the difference for the other item.
  • The same strategy works for Question #3, only now students have a choice about doubling or tripling one of the purchases.
  • Question #4 can be really tricky for students.  They are trying to figure out how to deal with a return of the one of the purchases and how that plays into the price difference. I look for groups that have a solid explanation for this problem.
  • Question #5 can also be challenging for students.  Here, there none of the purchases are clear multiples of the others.  I try not to jump in here and really let students puzzle through this problem.  It can be interesting to have different students share out different ideas.  I might prompt students by asking them how they can use mathematical operations to get any of the purchases to match up. 

Discussion + Closing

10 minutes

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.


  1. Shopping for Cats and Dogs is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.