Sunday, September 29, 2013

Discovering Matrices

I wasn't sure if my Accelerated Algebra 2 kids would be able to "discover matrices", but I wanted to try.

I have taught matrices before - the boring direct teaching, here is the vocab, here are the operations, let's try it, you try it.

Then, I switched to a 3 day project on the computers.  Two days doing a webquest and one day of students presenting to the class.  This went well, but each year, I would feel like there were kids who were still confused.

So, I brought in the idea of "what you notice"?  Matrix Discovery Lab

When I was first designing it, I thought I had to do add, subtract, multiply, and determinants in one day.  Then, I remembered I had planned to do multiplication the second day.  So, I told the kids to do the first and third sheet.  All I told them was that we were starting matrices.  None of them had done or seen them before.

I showed them matrices of different dimensions with the dimensions written and asked, what do you notice?  Some noticed the brackets.  Some figured out the rows and columns, but without those vocab words.  They talked about the height and width.

Then, I gave them 2 addition problems that worked with the answers and one that was not possible.  They figured out why it did and didn't work and they figured out how to add the matrices.  They didn't have the vocab, so they said things like "add the upper left number plus the upper left number and put it in the upper left spot."

Awesome.  They were struggling a little bit to describe it without having the vocab, so they were seeing a need to know the vocab. 

Next up was scalar.  They saw that this looked like a distributive property.

Turn the page and next up is determinant of a 2x2. I gave them two examples, each with the answers.  I told them they could use their calculator.  They worked hard trying to figure something out.  I would say about 3 people in each class figured it out.  Finally, they were onto the 3x3 with answer.  Nope, they didn't figure it out. 

Then, we shared.  What did they figure out about the first few problems?  And, I gave them the vocabulary.  We worked our way through the worksheet, adding the vocabulary and important tips, like how and when.

When I got to the 3x3, they thought I was making it up.  I did the diagonals method.  I color coded it on the board and they got it. 

The usual questions came up, when are we going to use matrices, what is a real world problem with this, what is a determinant used for.  I hinted that they would soon love them.  We have already done 3 equations with 3 unknowns and I suggested that matrices might help us with that type of problem. 

It was a fun class. 

I am going to see what they can do with multiplication.  I am secretly hoping somebody may have already googled it.  I will see if they were curious enough to find out before I teach it.  I think if I was a student I would have done a sneak peek.

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