I'm trying a reboot of my blog. My goal is to keep posts short, update what is going on with what I'm doing as a teacher and to make up for the years of blog posts that I spewed disgusting technology and data focused ideas...
This year I've made it a goal to get students out of the classroom on a weekly basis to see the math that we are learning appearing in the world around us.
We walked the perimeter of the school grounds which I learned (after being here for 14 school years) is actually about a mile. Our shoes got wet but we now have a good memory to connect with perimeter!
We went into the cafeteria to find the area and that looked like counting floor tiles and subtracting areas of the room that had closets or protruding sections of wall.
We went outside to look for right triangles and determine if objects being measured represented right angles.
I'm finding the students are enjoying getting out to be active and the more often we do this I'm able to see the students' creativity in finding ideas present I wouldn't have thought of.
I'm early on in developing this activity for my class and who knows--I may even be thinking about it incorrectly but what I do know is this game is both addicting and very relevant to my students right now. What I'm considering posing to them as a question in our exponent unit is:
"What is the best and worst case scenario of the amount of time I would need to 'beat' the game and get to the 2048 tile if I take 5 seconds with each move?"
If you don't know the game you can check out this video but I'll warn you--while you are playing this game life happens around you without you being aware of anything going on (very addicting).
During the game you continue to get new 2 and 4 tiles that you must push together to try and build up to a tile of value 2048 (211). In a worst case scenario you would continue to get all 2's as new tiles or best case scenario all 4 tiles (neither happens but it sets up a range of what could).
Here are some scenarios that could give you a range of values for acquiring the 8 tile and the 16 tile:
What I like about the idea of this problem is there is real motivation in wanting to get to an equation but the student will need to be sure that the range of moves can all be generated. I haven't presented it to students yet so more may be following on how that goes.
I will leave the 4 tile graphic out to allow students the opportunity to consider it on their own and maybe I won't even present them with these scenarios early on in the problem either. Comments or suggestions welcome as always in the comments below. If there is a better example of this somewhere else too please let me know!
In starting a new unit today I wanted to give context to students for writing inequalities. In our algebra class students have not yet learned the triangle inequality theorem which states that:
The sum of any two sides in a triangle must be greater than the third side.
Seems like a great opportunity for some 'ruler math'. I kept the rulers on my desk until after the bell because spring break starts after today and I know how middle schoolers can we with unstructured time and these tools...
In anticipating the pacing to be different for each student I made the activity as a Google presentation and provided students the link, instructing them to do their work on paper and answer completely any questions asked of them in the activity--noting that I would be breaking in periodically to the whole class and facilitating some discussion.
My favorite part was #4 of the first drawing where many of them grew frustrated with not being able to construct a 1 cm, 2 cm, 5 cm triangle--thinking it was something they were doing wrong. Kind of a fun way to watch them squirm and I know I'm not the first math teacher to have ever done this.
I had some awesome conversations with students while they were working. One student changed what he said mid-sentence. He went from saying
"The two lengths need to be at least the length of the third...The two lengths need to be more than the third length..."
I asked him why he changed his wording and he explained the difference between the two correctly. Pretty cool--I made sure to highlight that to the class in our whole group time. This kind of mathematics is so much more fun to teach than the traditional "do this, copy me, don't think" style. I overheard the same student above before leaving say to his neighbor
"Math is my hardest class because you can't just memorize stuff and copy it down. You actually have to understand the concepts to do well."
I told him I will take that as a compliment.
I am not expecting all students to go here but I am hoping that some make some connections to they pythagorean theorem and how it relates to acute and obtuse triangles in the last slide.
I've already made some revisions to the activity since teaching it one period and I wouldn't be surprised if it changed a little more as the day goes on. As always I'm open to other ideas or revisions to make it a better experience for my students.
Today in class students were choosing different practice activities for review for our test tomorrow. One pair of students was working on a worksheet that involved dividing an integer by a fraction. This is a topic we have not reviewed yet but that students have learned in past years. As I looked at his work I knew that I wanted him to explain his process to me. As I listened I knew this was something that I wanted to share. While some of his explanation is now based on procedures I really get the feeling that he has a deeper understanding than a student that is just taught to 'flip and multiply'.
In preparation for looking at it in a future lesson I tried to look at what is happening with the mathematics behind his explanation and what to do when a problem addressed is a little messier.
Comments, suggestions and additional strategies are welcome!
Here is the student's work from when he showed the class:
This is my take on what is happening as the student is moving forward with his procedure:
If I thought yesterday was boring--what did the kids think?!
Yesterday I reflected on how tragic it was that we talked all day about dice, coins and cards and never had them in student hands. I thought about what aspects of this new class I thought were important and what things could be discontinued (or as Google would put it 'deprecated').
What I want to continue:
Student self-reflection based on learning target rubrics on a semi-daily basis
Activities and labs centered on the learning targets (ideally incorporating multiple targets)
Short, meaningful yet challenging applications of the learning
Computerized practice and resources for kids that need it
As I was playing with my 'What's in the bag?' app I found myself thinking about my accuracy each round, trying to minimize the number of draws before I could see the solution and wishing there was a way to measure all those things. So instead of mowing my lawn, playing some guitar or other fun things I decided to figure it out. What I think I have is a finished game that could be used in my class at various points in the year and at different levels. (Click here for a link to the game)
1. Scoring points: In the scoring structure I tried to reward behaviors each round like minimal number of draws and maintaining a high accuracy level. I also didn't want a kid to be able to just keep doing poorly but getting more points just for persistence. (This feels like a metaphor for classroom grading policies...). As part of my class activities surrounding this game I will ask students to create a function that rewards these game behaviors using something like desmos.com to set up some sliders and view possible point values. Maybe some will actually figure out the function I have in the game itself.
2. Probability: I want students to be thinking about sample size, potential combinations, experimental vs theoretical. There is a high reward value for guessing the correct combinations without drawing be we all know how that will end. I anticipate many conversations when they get one wrong that shows 8 greens and 3 red and the actual composition in the bag that round is 2 green and 2 red.
3. Ending the game: I didn't want to have to program an end to the game and I wanted students to decide when that stopping point occurs. As the number of games played increases, the points possible for each round will reduce...and actually approach zero : ) I like that it is hidden in the game play and they will discover it as they get further along. #evilteacher.
4. Programming: I want to template the code a bit to give students a structure for creating their own javascript games later in the year. This may be naive wishful thinking in that I've never tried to teach javascript to algebra students and I have know idea how many will even go for it.
Anyway, I know what I'll be doing while I watch TV tonight. I'd love to hear your thought on this in the comments and would highly encourage you to start learning some programming. There are so many applications for it in my classroom.
For each lesson that I've been preparing this year I have been trying to have practice, review and extension options for each learning target. This unit I actually have the extensions ready to go ahead of time (probably having to do with us just having 10 days off).
Our progression
We started the lesson a few days back with a large group investigation, following the golden ratio idea. Yesterday we did some more formal practice. Students that were rating themselves at an understanding or mastery level began to work individually on their practice material instead of staying with the large group. I used a couple clicker questions to help students identify how well they were understanding the material.
Student choice
We started in a similar fashion today and added a tier of activity for students that completed the practice yesterday in class--beginning work on extension activities for this learning target from a menu of choices (example).
Throughout class I had students moving about the room, helping each other, asking me questions and digging deeper into the concepts. I love my job.
I'm experimenting with some new tools I've acquired this summer. Camtasia 8 for video production, Tracker for analyzing motion in a video and also contemplating embedding shortened url's at the end of the video pointing to data for student investigation.
I'm not all that defined at this point in the lesson but I'm hoping to tie in quadratic equations, reflections and some introductory physics ideas. I'm hoping students will think the return path of the ball is the same as the path leading up to it and the progressive analysis in the video will challenge them to investigate what happened to cause the ball to follow a different path after the bounce. Some possible follow up experiments for the students their own video analysis and varying the experiment a bit--what happens when the ball is on its way up or down at the bounce? What if it hits the ceiling and then the wall? What if the ball is more bouncy?
My plan is to use this lesson with Algebra, Geometry and Algebra 2 students. I'd love comments or suggestions as to where to go with this.
