First I had compasses and protractors and had them make 3 different circles in their notebooks. Then they measured the radius of each and recorded it. Then they "carefully" used a ruler (my compasses are the orange cool ones with a ruler on them) to "wrap around the circle" one radius length. Then they measured the angles.
We talked about how we're human, and it will be off, but we noticed the numbers were similar. Here's the page of my notes.
The next thing that worked was a table. I made them create a table with 3 columns, angle in standard position, degree measure, radian measure. One row at a time, I would give them one of the values, and they had to figure out the other two, and then we'd discuss it and their strategies. The highlighted portion is what was given to them.
I liked this because it's all ordered in one table, and they can absorb it and see connections and such as opposed to my last year's notes where I sloppily just did a few around the page and put all the information on the graph.
Sweet! The table looks awesome! :D Very handy reference for the students as well.
ReplyDeleteAt our school we have gotten out of the habit of using compasses and protractors. I love bringing it back. I also love the organization of the chart!
ReplyDeleteThanks! Hopefully, thinks will stick in their brains faster this year.
ReplyDeleteI like the organization you have with the chart and how students are able to see connections. When I was in school this was thrown at us to memorize, so in the end I wasn't really learning anything. I am currently a student studying to be a teacher with a concentraton in math. I like how at the end you mentioned allowing the kids to discuss strategies, and I believe that to be super important in kids learning. Thanks for sharing your strategy on radians.
ReplyDeleteI really love how you made the idea of radians a concrete idea. Normally it is just a teacher saying "this is what radians are, memorize it." The example you provided actually forced them to LEARN the concept, not just have them memorize it.
ReplyDeleteWhen working with radians, my students always seem to struggle with estimating an angle's size/position on the unit circle. I use to just tell the students to convert the angle to degrees, but that was avoiding the issue.
ReplyDeleteI have found that if the students could move/act out the angles, they will remember their size. So, I take the students down to the gym to the wrestling mats=pre-made circles and plenty of space. Using masking/painter's tape, I make a line from the center of the circles to an edge to mark the positive x-axis. Using a bunch of cards, the students take turns walking around the circle "graphing" the angles in standard position. Teammates check the work--I made a graphing calculator program to draw the angle on the screen--and the cards are left on the floor. After typical pi radians are graphed, I give decimals, whole numbers, etc. After a while, I ask the small groups of students about any patterns they see: themes in denominators, positive/negatives, etc.
PS. I did this once with dry-erase markers on tiled floor...doesn't really erase!