## October 31, 2017

### Matrices WODB

I've managed to avoid teaching Algebra 2 for all but one year of my career (prior to this one). Between Algebra 1 and Precalculus I am familiar with most of the topics in the course, but matrices don't appear in either of those courses in our sequence. I forgot how much familiarity with content makes a difference when prepping! Pulling from our textbook and David's lovely post on matrix multiplication I made a packet to introduce matrices and their basic operations while I'm out. I wanted to start the next class with a Which One Doesn't Belong? but I couldn't find one. So I thought I'd make one. I started out thinking about dimensions- the top right is the only one without a dimension of 3, the bottom left is the only one without a dimension of 2. Then I thought we could play with the numbers to get something interesting.

But when I was chatting with my colleague we were struggling to come up with what other reasons we could set up. I know that when Christopher first started making these he asked people for four characteristics and then made each shape using just 3 of the four (so each one wouldn't belong due to the characteristic it was missing). We tried to think what other characteristics we could include and decided to use the scalar multiplication and equation solving from the packet to build other aspects. I also made the sum of the digits equal 10 for three of the four just for fun.

But when I tweeted this set I still wasn't getting the kind of responses I was hoping for. And I am confident this is because I'm not familiar with matrices. I'm going to have to spend some time familiarizing myself with inverses before I can teach them. By the end of the unit I'll have an entirely different idea about what important characteristics of matrices are. So until I get there, help me out? Describe a matrix using four characteristics and let's see if we can build a good WODB together!

#### 1 comment:

1. This is an interesting question.

When I think about WODBs, I like for them to highlight aspects of mathematical importance. For example, if they are all quadrilaterals but with varying amounts of congruent sides, parallel sides, types of angles, etc. to focus on the key features of quadrilaterals.

I would not consider dimension or sums of elements to be mathematically important features of matrices. Technically important, yes, but not really at the heart of the mathematics.

On the other hand, the things that are mathematically important are much harder to get at and depend on context. What are you doing with your matrices? Are you using them to transform points in the coordinate plane? For example, have matrices that rotate, reflect, and scale points? Or are you using them in the context of systems of equations where they could have infinitely many, one, or no solutions? Just some thoughts. But then I'm wondering of WODB is really the right structure for those types of things.