Today we are going to focus on two types of multiplication involving matrices – multiplying a scalar by a matrix and multiplying two matrices together. Using the data from the Purrrrrfect Cat Toy Company will allow students to know what the answers to these questions should be – then we can focus on how do we use matrices to model these situations and give us the answers more efficiently.
Here is the task worksheet that I give my students. Today’s class will be structured a little differently. Instead of giving them the whole worksheet and having them go at it, I am going to have them work on only one question at a time and then we will discuss each right away. I don’t expect students to just think of matrix multiplication on their own, so if I keep it structured and controlled then students will be able to make meaning based on their intuitive knowledge of what they know.
Questions #1 – 2 focus on multiplying a scalar by a matrix. The main aspect I focus on is that the scalar is multiplied by every entry in the matrix. Also, I want them to know the notation 1.4E = N and how that translates to matrix operations. I will also have students try this on the graphing calculator so that they are familiar with using the technology.
Questions #3 – 6 get students thinking about multiplying two matrices together. Students can easily find monthly revenue in question #3, so this will serve as the check to see if they are getting the correct answer when they are multiplying matrices together on their graphing calculator. The point of these questions is just for students to brainstorm to get them thinking about these concepts – don’t stress if they are not getting the right answers right away. I had students put possibilities for the price matrix on the board and they played around with their graphing calculator to see if they could get any of them to give us the correct revenue values.
At the end of the task worksheet is a place to summarize the work that we did. In these two boxes we will summarize multiplying a scalar by a matrix and multiplying two matrices together. In these boxes I will write the different contexts that we used and the example of each. I discuss more in the video below.
I am purposely not talking about the need for the dimensions to be compatible when multiplying matrices; students will be thinking about that for their homework assignment.
Here is an assignment to get students thinking about matrix multiplication and some of the rules and procedures for it. The assignment is structured so that most students will get to thinking about the algorithm and some of its aspects. They may not completely understand the process, but they will have tomorrow’s lesson. This worksheet will be the jumping off point for tomorrow.