Daily Archives: May 9, 2014
This was me:
We are doing a unit on statistics in Integrated Math 1. So far, I’m loving it (way more than I thought I would).
When I thought of basic statistics appropriate for High/Middle school, my mind wandered toward mean, median and mode. I could work with these concepts decently enough. I even understood how they were similar yet different. Only now that statistics is a larger part of the CCSS curriculum am I taking it more seriously (better late than never). We (myself and other integrating math 1 teachers in my district) are doing a unit that includes the basic descriptive statistics. Now we’re working our way through linear regression and my appreciation for the content is increasing, in a concave up sort of way. I’m see the big picture, or at least starting to.
First, we had covered the basics of descriptive statistics at the beginning of the school year. We included some fun activities getting data from various things the students were involved with. Recently we reviewed the content courtesy of some awesome practice via Khan Academy. Yesterday and today the topic was correlation. We focused on developing intuition and applying such insight toward predictions. We used a great activity from @yummymath to try and make a prediction for how much the lifetime gross of Amazing Spiderman 2 will be. We were able to also incorporate @desmos into the work to get some more pretty graphs. Early next week our content team plans to continue with this topic going further and using some data from the students in the classroom.
The awesomeness today came from multiple students having the conversation about the strength of the correlation in a data set was only so-so because there were a few outliers that weren’t close to our guess for a line of best fit. One student even used language like, “it’s not that strong cause it varies too much off the line.” I didn’t prompt them to do it. Nobody did. They came up with half or more of the academic language without me defining it for them. The students covered nearly all, if not all, of the CCSS SMPs with very little explicit direction on my part.
I feel slightly ashamed to not have had this appreciation for statistics before. #facepalm If you’re not including statistics and probability as a large part of your math curriculum, please ask yourself, “Why not?” I consider myself a math geek and now I’m gaining a better overall understanding of how Stats ties in. The support and opportunity it provides with math modeling and critiquing the arguments of others is invaluable. I used to think that statistics was too “fuzzy” for me. Not anymore.
It’s Thursday. Yesterday we talked about circles, chords, and kites. Today we asked a very similar question:
Here’s the applet in action: (click the animation to open the applet)
This was similar to Wednesday. We asked the same type of questions. We saw similar relationships. But it stood out enough for a unique post because a student enlightened me with an observation I didn’t articulate. When I repeated yesterday’s question, “What shapes do you see inside the triangle?” one student almost immediately replied, “Is that a kite?” I had to look at it myself. “Yeah, wow, that makes this conversation easy.” My original plan was:
- Focus on the Right angles/right triangles
- Question if certain segments were congruent
- Look at the reflection or congruence theorem that helps confirm the congruence
- then finish off with some color coding.
Instead this students recognizes the 3 kites, then refers to her knowledge of the symmetry in kites. Congruence, simplified.
To help students in transcribing the diagram onto paper to start doing some hand calculations we took a tip from a student in the first class:
- Lay Chromebook on its back
- Increase brightness of screen, turn off some/all light in class
This was another good introduction and discussion with segments in circles. We of course spent the last 1/3 or so of class practicing and becoming fluent with the skill with problems like:
At the end of the week we took a short quiz. 2 questions, same as these. Today/tomorrow I’m going to try something new with how I grade them (thanks to some inspiration from Michael Fenton, Michael Pershan, and Ashli Black). More on that later this weekend.
In the meantime, let’s keep rounding out this circle thing and see what other shenanigans we can come up with.
In geometry we had some fun with kite like shapes for the last couple of days. On Wednesday we asked:
See it in Action (click image to open)
I asked the students to play with the applet. I prompted them to ask for more information. Some noticed the sample questions below the applet and asked those to start the discussion. The key question had to do with decomposing the shape into other shapes that we had more familiar tools to work with. The students were quick to see the right triangles. Once we were able to identify that, the next question was, “How does that help me?” Getting students to connect and then apply relationships they know into a seemingly new context is a constant challenge, but they are getting better. I reminded them to recognize what are we trying to find. Once they narrowed in on the task of finding a length, and the length was a part of a right triangle, some started to see it, “Pythag Thyrem.” (this seems to be a tongue twister for the general high school math population). “Okay, how do you mean?” was my reply. Some didn’t see the given values for the hypotenuse that was also a radius.
Circles seem to be a pain for many geometry teachers, and I feel that it’s because so many people approach circles as a never ending list of formulas. We need to find ways to simplify the overall question and give students an opportunity to fill in the structure(s) needed to respond to the question. I know there are some awesome activities out there dealing with volume and area with round objects. Here I’m trying to put together a series of interactive questions the see the overlaps and relationships with circles, segments and angles.