Matrices!

I’ve been doing Interactive Notebooks for the first time ever this year in my Algebra 2 classes. The students LOVE this form of notetaking – it helps them to know what the most important concepts are, helps them summarize them, it’s pretty, and their notes are always organized.

The notebooks have been a combo of me borrowing already created pages from others and editing them slightly, and occasionally making my own.

We’ve hit our unit on matrices, and I have not been able to find ANY resources online really for INB pages or even notetaking guides on the skills we need for this unit. This is the first unit I’ve created all the pages entirely on my own, and I thought I’d share the pages if there are other teachers also failing to find resources for this content!

Keep in mind that I am an INB beginner, so most of these pages are similar layouts because they’re the ones I’m comfortable with creating. 🙂

 

The skills we cover in the unit are adding/subtracting matrices, scalar multiplication, matrix multiplication, finding 2×2 inverses by hand, and using matrices to solve systems of equations with inverses.

 

The first page we included covers the basics of matrix terminology on the front, with examples for students to practice adding, subtracting, and scalar multiplication as a whole class on the left inside. The right side of the inside I used as their individual practice for the section. We had to discuss that “matrices” is NOT pronounced as “mattresses”…

Next, we covered matrix multiplication. I don’t know how much I love the way this foldable is laid out after using it, but it worked well enough. The front breaks down one multiplication problem into each pair of row and column that you need to multiply to get each element of the solution matrix.  The inside has example problems that we did as a class. I think my students may have benefited from having some sort of written out instructions as well as the illustration on the front, so that’s probably what I will add for next year. (start by pairing the first row of matrix 1 with the first column of matrix 2, etc.)

The inverses foldable has 3 sections: how to check if two matrices are inverses of each other, how to find the determinant of a 2×2 matrix, and how to calculate the inverse matrix using the determinant. I should have had one example that were inverses and one that were not inverses. I should have had matrices with determinants other than 1 or -1 for the examples of finding inverses. Otherwise, this page worked well for the students – we just had to talk about what to do when 1/det(A) was a decimal while they were practicing individually!

I also might have them add words next time I do this to the Inverse Matrix section saying “switch the a and d values, change the signs of the b and c values” because in practice, they kept switching BOTH pairs and getting confused, so having it in words as well as symbolically may help with that.

For systems I just did a basic flowchart of steps with one example, along with information on how to input matrices into a graphing calculator and use it to find inverses. Our standards only require them to find 2×2 inverses by hand, so I’m just doing 3×3 and larger using graphing calculators. We did many more examples as a class that just didn’t go in their notebooks.

 

After we did inverses, I created a problem set where they decoded a message by using inverses and matrix multiplication. I think this was great because they got to practice two skills at once! Also, it was nice to get a positive message out to my students sneakily hidden in their math work. I could have organized the boxes where they wrote their decoded message better so the words weren’t on separate lines (one of my students got confused because it looks like it says ‘edible’ at the end, oops), but I was trying to finish this up pretty last minute so that…didn’t happen.

All the files are included here, PDF and Publisher versions, including the decoding problem set. The actual matrices are mostly screenshots from Word, so if you wanted to change those you would have to go into Word and take your own screenshots.