|Somehow, I forgot to take a picture of my whiteboard...|
I HAD A VISITOR TODAY!!!! My good friend, Jami, came to observe my classes!
In geometry, we continued our work of angles of depression and elevation. I gave them a critical thinking problem that will be the lead-in to the astronomy project I want to do next week.
Kwan-Yong measures the angle of elevation from the ground to the top of Ayers Rock to be 15.85 degrees. He walks 500 meters closer and measures the angle again, finding it to be 25.6 degrees. How tall is the mountain?
I LOVE this problem because of the extensions we will use with it next week. It was also a MUCH more difficult problem than we've done in that class. It requires some lateral thinking and playing around with the numbers and trig functions. Students need to be ok working with multiple equations at once and not getting an answer immediately.
I love this problem.
The pre-algebra classes started by going over the homework word problems (which no one did). I sat in the back while I had students put the work and answers on the board. I battered them with questions about why they set up the problems in the manner that they did and what each number represented in the problem. When they finally got the end, my standard statement is "Great! Tell me what that answer means in the context of this problem."
S: "So X is equal to 7.1"
Me: "Great! Tell me what that means in the context of the problem. In a complete sentence, please."
S: "On a bill of $35.50, a 20% tip would be $7.10."
After we finished up the word problems, we started talking about percent error and percent change.
I put up an #Estimation180 problem from earlier in the year and asked the students to estimate the number of cheese balls in 6 containers. I wrote my estimate of 4200 on board. Then we looked at the answer, which was 4416.
Me: "Aw man! How far off was I?"
S: "216 off."
Me: "Would you say that's pretty close, or no?"
S: "Yeah, that's pretty close."
Then we looked at the one from today and made the estimate that the roll of quarters contained $226. It actually had $10.
Me: "Aw man! How far off was I?"
S: "216 off."
Me: "Would you say that was pretty or no?"
S: "NO! That's SUPER far off!"
Me: "But wait! You just told me that being 216 off wasn't that far off? Why was is close for the cheese balls but not for the quarters?"
When they didn't quite get where I wanted, I brought out my giant bag of jelly beans.
Me: "I've given 2 jelly beans to Anton and 10 to AJ. I don't think that's fair, so I'll take some back."
**I ate one jelly bean from each kid**
Me: "So, I've taken 1 jelly bean from each of them. That's fair, right?"
S: "No! You didn't take the same amount!"
Me: "But I did! I took one from each of them. Isn't 1 jelly bean the same as 1 jelly bean? Why isn't that fair?"
We continued along this conversation until I got the response I wanted.
S: "1 jelly bean to Anton is worth more because you took half his jelly beans! It was a bigger percentage."
I was incredibly pleased with how this example worked to get them to understand the idea. We continued it with the idea of grades.
Me: "In the first marking period, Niya got a 50% and Malik got a 70%. In the second marking period, they both worked harder. Niya brought her grade up to a 70% and Malik earned a 90%. Who had the bigger improvement?"
There was an excellent discussion about how they both went up 20% and how that means they should have equal improvement. So I asked about the jelly beans again. This lead into a talk about percent of change.
The additional example that I used in period 8/9 was that if you were to give $1 to a homeless man and $1 to Bill Gates, who would appreciate it more. I think more than the others, this extreme example helped to solidify the point I was trying to convey.
Period 4/5 was ON THE BALL today! They rocked every aspect of today's class and the participation was excellent. Right before period 8/9, however, there was a huge fight right outside my room. A situation that had been bubbling all day finally spilled over and I ended up dragging some girls apart. It was very difficult to keep that last class where I needed them to be after that, but overall, they did very well, especially when I brought out the jelly beans.
My lesson from today: Teach Like You're At Seaworld! Bribery will get you everywhere.
Knowing that there was the possibility of jelly beans, my students were much more likely to participate and do what I asked of them. I was temped to dangle some jelly beans and see if they would balance a ball on their noses.
After we completed the 8 word problems, I asked a simple question:
Me: "What did I not see in any of these problems? What tactic was not used?"
Me: "Did anyone even think to use it?"
YES!!! One trick nixed! Tina would be so proud of me and I had Jami as a witness!
It was a great day with lessons that went well and interactions that I enjoyed. It's a shame that it had to end with a fight...
Regardless, I'm so happy that Jami was able to join me and I look forward to hearing her reactions and thoughts.
Seriously, if you can get someone to spend a day in your class, watching what you do and being a part of your environment, do it. Do it ASAP!
And, by the way, cute puppies do NOT take the place of pictures created on your whiteboard.ReplyDelete
I know... I'm sorry... I'll take it tomorrow and edit the post...Delete
I'M SUCH A DISAPPOINTMENT AS A SON!!!!
Isn't perspective part of the math world?Delete
Not sure what happened to my first comment (thus the "And" that started the previous comment) but here it was although it's not as brilliantly worded as the first time I wrote it:ReplyDelete
I think it's great that you welcome observers and then actually want to know what they think. I imagine it's difficult to put so much of yourself into a day of lessons and then be willing to hear other peoples' take on it without defending everything you said and did. Good work.
My Favorite Line: When they finally got the end, my standard statement is "Great! Tell me what that answer means in the context of this problem."ReplyDelete
I so need to steal this and make this a habit in my classroom. Today, I gave my kiddos a post-test in Algebra 1 that asked them to explain what f(0)=65 meant in the context of the story problem. Almost every single kid left it blank. This is not going to happen next year. My kids are going to love me when I make them explain their answer in context every single time!
Thanks, as always, for the inspiring post!
What's great is that I've done it enough now that all I really have to do is say "what am I going to ask you?" and they reply with "to give you a complete sentence in the context of the problem."Delete
This comment has been removed by the author.ReplyDelete
It was abundantly clear to me as an observer that the kids were accustomed to Justin's probing questions and knew they weren't going to get away with just rote sorta responses. This was true with his expectation that they put their final answer in a sentence in terms of the context, but also in his questioning throughout the process. And I loved how he avoided the whole Clever Hans phenomenon. He turned every question back on to them and they knew they had to justify or figure out what they were doing. I was very impressed with them...the work Justin has done with them was very evident to me, even if he doesn't see it in the day to day struggle of it all. Just sayin'. =)ReplyDelete