SWBAT solve systems of equations using matrices.

Use a group activity to help students make sense of solving systems with matrices.

25 minutes

Today's activity is a Carousel Activity where students will be working on problems that are on posters that are hung up around the room. Students will do all of their work on the poster so you will have a record of what students made sense of and what they still need clarification on. This activity is also collaborative, so students will be able to bounce ideas off of other members in their group. Furthermore, they will be walking around the classroom and the simple act of moving will bring a liveliness to their discussions.

The premise of the** Carousel Activity** is simple - students start at one poster and then rotate around to move to the next poster and then on to as many others that are needed. Their movement is just like that on a carousel and usually there is some reason to rotate. In this case, the reason is to work on a different aspect of the problem.

Here is the general format for this Carousel:

- Each page from this document will be printed out and posted on one of 12 (or any other multiple of 4) posters around the room. Since I do 12 posters, I will have three copies of each page and they will alternate so that it goes in the order of page 1, page 2, page 3, page 4, page 1, etc.
- Students will be put in 12 groups (2-3 students per group) and each group will start at a poster.
- Students will just do Step 1 at the first poster - writing a system to represent the problem.
- Students will rotate clockwise to the next poster when I give them the okay. Then they will only work on Step 2 - writing the system as a matrix equation.
- Students will rotate clockwise to the next poster and will just complete Step 3 - solving the matrix equation and writing down the work they did.
- Students rotate one more time and just complete Step 4 - showing work to verify that the answers given in Step 2 are the actual solutions to the system.

Because of the way the pages are staggered, students will stop at four posters so they will get exposure to every question. In this case the problems were all similar, but this is a great grouping strategy if there are different types of problems because each group can do a piece of each problem.

While they are working I will be continuously going around and watching how students work and what they are having difficulty with. I will give the okay to rotate once every group has completed each step. If there a few groups that are holding up the rotation, I will help them out or have them ask another group.

Students may have difficulty setting up the system of equations for the problem. A **hint** I give is students are stuck is to think about the production rate per hour instead of looking at how many are produced in 6 hours, for example.

25 minutes

While students are working on the Carousel activity I will be keeping track of what they are making sense of what they need more work with. When the activity is over, students will go back to their seats and I will debrief about what I noticed was really good and what things they still need work on.

For example, my students are usually good at setting up the matrix equation, but they sometimes **have difficulty **multiplying both sides of the matrix equation by the inverse in the correct order. For example, if their matrix equation is *AX = B*, students may try to set up *X *= *BA*^{-1} instead of *X *= *BA*^{-1}. Thus, they get an error message on their calculator because the dimensions will not match up.

This activity is a **formative assessment** and will give you great feedback as to whether they are understanding things or not. After you do the Carousel Activity with your class, you can make the decision whether they are ready for the assignment or if they need more direct instruction. If they do, you can start the homework assignment together as a class.

The assignment summarizes all of the work we have done with solving systems of equations with matrices. This worksheet will also get students thinking about systems of inequalities - a concept we will use when we look at linear programming in a future lesson. I talk more about this assignment in the video below.

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