Made 4 Math #10 - "Be Less Talkative"

I shared in my #myfavfriday post about teaching without lecturing or basically my new mantra 'be less talkative'. Today I'm going to post some activities that I've used so far.

In Geometry, although I haven't lectured per se I've still been leading a lot, even if that means being in the front of the room and controlling the powerpoint.

I didn't do it this way but here's what I would recommend:

Start with the Geometry Basics Graphic Organizer (modified from this post by @msrubinteach). Here is the answer key. I numbered the answer key, cut it up into squares, and then passed out one square to each student as they came in the door. When I gave students the GO (printed on bright colored cardstock), they had to copy their square down and then trade over and over again until all 30 blanks in the GO was full. (There are 30 squares and I have 29 students so I just projected the last one for everyone to copy)

Next, try the hands-on naming review. This requires some prep work but it can be used again and again. I used envelopes that the school gave me and then I cut pipe cleaners in half for segments, used fuzzy pom poms for points, cut up pipe cleaners into sixths and folded them into arrows, and wrote and cut out letters on construction paper for labeling. Each student has construction paper on their desk representing a plane and their desk represents a second plane (to practice coplanar). I display the directions and walk around as the class arranges. Then I click to show the answer. I ask questions throughout that are more like reminders, "How do we label a plane?", "What goes on the ends of a line?", "What do arrows represent?" etc. The students can use their graphic organizer as a guide.

Next I would use this Foundations of Geometry handout (doc, ppt) to reinforce labeling and properties of basic geometric figures. The last portion of this worksheet has students draw or label different figures, similar to the hands on naming review. I recommend this one last because it involves writing. Students take more risks with the pipe cleaners and pom poms (similar to dry erase boards) because mistakes are easier to fix without others noticing. Then they are better prepared to draw and can still use the GO as a guide.

Last but not least, I used @msrubinteach's Geometry Sketch game. I drew and labeled 10 drawings with geometric figures, labeling two sets of #1-5. I tried to label from easiest to hardest so each student would have equally complex drawings. Copy on to card stock, cut apart, put two sets into a sandwich baggie. Students sat in partners facing each other with their binders open and standing up as a divider. Each student has five cards. One student described the figure while the other drew the picture then traded roles. If their picture was close, they gave themselves a point on their worksheet. This is where I left off on Friday. To be continued...

In Algebra II, we started with matrices. Matrices in the Common Core don't appear until the fourth course, which would be trig/precalc here, but it does show up on the ACT, and most of my Alg II classes are juniors. (I just used a LOT of commas!)

I introduced matrices using an Algebra I station activity from the book Algebra I Station Activities for Common Core State Standards, which you can get if you request the free sample. I totally changed the fourth station and made a handout to go along with it so it is a little bit of my own creation. Before we got started, I wrote a matrix on the board with a scalar and labeled both. I asked them what they knew about the matrix and they mentioned the numbers in the movie on their own so I built on that and just said yes, the matrix is a way of organizing numbers.

Here's the setup:

I cut index cards in half to save paper.  Station 4  I changed to be word problems using matrices and I got too tired to think of how to use index cards so there are none for station four. Here is the handout. Students rotated through stations (although they hated actually getting out of their seats) in different orders. I found that students who did station four first needed more help because they just wanted to add all numbers together and get 535 rather than add the two matrices since they hadn't seen that station yet. This went pretty smoothly but did bleed over into the next day.

We finished that up and as a summary, I asked students how a matrix is like a jewelry box. Then I wanted to reinforce the skills we had already learned so they worked on a handout connecting matrix operations to geometric transformations. (You need to label the vertices of each shape before copying. It takes too long to do on Word.) I started them out on #1 by asking them the ordered pairs for each vertex and writing them into the matrix as a model and emphasized that all four problems started out this way so DON'T ASK ME HOW TO START. My students kind of sit in groups of 2, 3, and 4 so they casually worked in groups but basically just talked to the people around them. This went pretty good unless students forgot to graph the new ordered pairs. In part b. I asked them what happened to each figure and I was looking for a description like "it moved right, up, down," etc but students were more technical and used the words I was alluding to like translate, rotate, reflect, but dilate was the one they couldn't remember. Some students even went so far as to tell me which quadrant it started in and moved to. That's promising. At the end we debriefed as a class and filled in (or corrected) the words in part c with math words.

From there, it's on to multiplying, inverses, and determinants. I don't go very far into this, basically just teaching them how to do it on the calculator. Most of the time ACT asks them to do scalar multiplication on two matrices and then add them together so I don't feel a need to go in depth. Last year I did and taught Cramer's rule and all that and I just think I can use my time better this year. So this handout leads them step-by-step through the process on a TI-84 Plus calculator. Students worked on their own on this one. I found my second section did better when I started the class by asking them to put on their big girl panties and big boy boxers. I told them it would be heavy on reading and light on math, that the steps will work, and that I spent a lot of time at home punching calculator buttons and typing steps.

By far the students were the most crybaby on this activity. They would tell me they did it five times and it wouldn't work. They would indignantly say "Watch, I'll do it again" and read the steps out loud to me, punching buttons as they went. It worked, I smiled, they were outraged. Quite amusing.

Once one student got the hang of it, it started to catch on, and they naturally began to help each other. In one class, three boys basically refused to read and just stared at the paper saying "I don't know what to do. If this is on the test then I will just guess." I had to stand behind them and repeatedly tell them that they had to read the steps. They were reluctant but that's the kind of laziness and unwillingness to read/try that I want to zap in the big boy boxers as soon as possible.

All in all I'm pretty satisfied with how it's went so far. I plan to start tomorrow with them working on algebraic matrices since we've only done numerical so far. We connected scalar multiplication to the distributive property so hopefully it will be easy to connect algebraic matrix operations to combining like terms. Then I plan to try out my new ZAP! review game on Wednesday and test on Thursday, but we'll see how it goes.

Sorry this post is so long but I am trying to blog as many of my creations as possible to keep me motivated and remind myself next year of little things that happened during the lesson that will be forgotten in the next 12 months.

Hope there was something that inspired you to make for math!