After working with trigonometry for the last few units, we are going to switch gears and work with something completely different – matrices. I won’t tell my students too much about them at first. We will be exploring Matrices for the next few days. However, I do think it is important to let them know that we will be working with something different than trigonometry.
I chose these introductory matrix tasks because I can give them to the class with no preface. As students work and we discuss their work, we will pick up important information about working with matrices.
I decided to introduce matrices using a rather large data set since that is primarily the advantage to using them – Matrices allow us to perform many operations very quickly. I also chose a context that we can revisit throughout the unit. The Purrrrrfect Cat Toy Company will be used as we explore other matrix topics.
I give my students these tasks and have them work on them with their table groups for 10-15 minutes. While circulating around the room I will make note of the conversations they are having and what their struggles are. I will pay particularly close attention to whether or not they can interpret these matrices correctly. Even really young students can add matrices, but it will be more important for students to understand what these matrices mean in the context of this problem.
I usually make the decision whether to go over questions #1a through #1d based on what I observe; usually I find that it is not necessary. It is a good idea to discuss #1e to see what they already know about matrices. I find that matrices are a polarizing topic in my classroom – some students know a lot while other students know very little. It is helpful to assess this informally at the start of the unit.
Question 2 is the heart of this worksheet – seeing whether or not students can add matrices and make sense of their meaning. I will choose a group that completed this correctly and have them share their thinking. It is important to get at the meaning of E + W as the total sales for both regions.
When discussing the dimensions of the matrix E + W, students may list them as 3 by 12 or 12 by 3. I establish the norm of rows by columns so that we are consistent with the way math texts describe matrices. When we discuss why E + W has the dimensions of 3 by 12, I want students to think about that the context – if we are adding the sales of the East and West regions, we are not adding any additional months and we are not adding any additional products. Thus, the dimensions will still be 3 by 12. We can generalize to say that with matrix addition the dimensions must always match up and the sum will have the same dimensions.
Technology has to be an important part of this unit since it will allow us to perform matrix operations very quickly. I lay the foundation for this today by showing students how to enter the matrices on the calculator and how to add two matrices. Here is an online matrix calculator that student can use if they do not have a graphing calculator. Unfortunately, the online calculator can only go up to ten rows or columns.
After our initial work with matrices, I give students this worksheet as a homework assignment. They can begin it in class and can work with their table groups on any issues that they have. In the homework assignment students will be introduced to matrix subtraction. Like today’s tasks, the overall emphasis will be on interpreting matrices since the calculation are fairly simple.
In the video below I talk about a problem on the assignment that introduces a relation matrix to students.