155-156 Optimization

What’s the biggest (open topped) box that you can make from a sheet of paper by cutting out square corners?

Gotta do this one by hand first!

Green coordinates were their original points, and the blue curve was calculated after discussion.


141-142 Curve Sketching – A beginning

As an introduction to curve sketching, the Precalc h class found out where the derivative of a function was zero, positive and negative. Then I had them draw a set of axes and start their marker at the left side of the grid. Told them to start moving the marker to the right, and gave instructions for “increasing”, “decreasing”, or “0 slope”. Asked them, “what do you notice about the spots where the slope was zero?”


97-98 BEAM problems

Had a little of extra time with the precalc students so the worked on the BEAM entrance problems. Really great, love it. Do it with your students (they’re designed for 7th graders). Love how students used problem solving techniques on problem number 3: They were making the problem smaller so that it was easier to understand.


67-68 Graph of cotangent

We are working on reciprocal trig graphs in precalc, so I had them draw the original graphs and find the multiplicative inverse of the function values to find the reciprocal trig graph.

See the open circle for cotangent at pi/2? Can you guess why they put it there? These kinds of thoughts are REALLY good signs for students. Love it.


65-66 Snowflakes and Programming in Precalc

Last day before break? Make some snowflakes by using polar coordinates and processing. Only 3 of the 34 students have taking programming, so it was a great opportunity to get the rest involved. They have chrome books and they used openprocessing.org. 

Here’s the code we started with:
And here’s the code we ended up: 


49-50 Dead Mouse and Newton’s Law of Cooling

I’m an awful liar, but I somehow totally fooled most of a class for 50 minutes! I told them that there was a dead mouse in a coffee cup on the shelf that I heated up in the microwave so that we could measure the drop in temperature using Newton’s Law of Cooling. What was it really? A cup of hot water with a thermometer. I made lots of silly comments:

It doesn’t smell too bad does it?
Do you think that the ball python in Biology will still eat it after it’s been warmed up a couple of times?
I put it in water so that the fur didn’t singe.
The microwave in the Math/Science Office has seen some messes, so a mouse in a mug is no biggie.
YES the mouse was dead before I put it in the microwave, I’m not a monster.
It was hard to get the thermometer down the mouth so that it could measure the temperature of the mouse’s center mass.

I offered anyone who wanted to look the opportunity, and the one kid who looked didn’t give anything away, in fact he added to the tale by screwing up his face in disgust. Anyway, it’s a really good activity for working with this equation. Our predictions in the two classes were just ok, I’m not sure why they were off by nearly 10%. Anyway, here are some pictures and screenshots of the good stuff.


156 – Calculus End of Year Feedback part 3

Here are the Pre-Calculus and Calculus responses to the following prompt: We switched from a default group size of 3 to a group size of 2. Which did you prefer? Did we switch groups too often? Not enough? Goldilocks amount?

  • I preferred the group 3 of three, I thought that the group switch period was good.
  • I prefer working in groups of 2 because it’s easy to get lost in a group of 3 when 2/3 students understand what’s going on
  • It does not make a difference to me. I did not like switching groups so often.
  • I preferred the group size of 3. I find that we switched groups at an acceptable rate.
  • Frequently switching groups seemed beneficial, and having both groups of two and three served well.
  • two is good if they talk to each other
  • I don’t think we switched groups often enough. Sometimes groups of 3 were helpful if at least one person understood and one could observe while the third struggled through. Groups of 2 were good for working through hard problems.
  • 2 people was better. 1-1 conversations are more engaging and it’s easier to teach to/learn from 1 person at a time instead of 2.
  • I preferred 3, but the difference is not that much. Having 3 people per group just adds another brain to help with problems.
  • Groups of 2 were better, as was switching every quarter or so
  • Both work really well. 2 seems easier to manage, but to be honest the sizes of the groups don’t matter a whole lot. We just end up collaborating between groups anyway.
  • I like groups of 3 better but for certain things just working with one other person could be better. I think we changed groups a good amount of times.
  • group of three was the best because you get two more people to help you
  • I liked 2 person groups better, and liked switching every two weeks rather then every one
  • 2 works better because its not just two people doing the work and the others just sitting there not really understanding.
  • I think every 2 weeks works well. It didn’t feel very different when we switched from three to two people in a group, so in my opinion they are both good.
  • I liked switching groups every two weeks because it allowed me to work with different people. I prefer working in groups of 3 rather than 2.
  • I liked switching every 2 weeks–seemed like the perfect amount. However, I like the groups of 3 better because it allowed for more discussion and more out loud thinking.
  • I like groups of 2 because you can really see how things are working and you get more of a personal level connection with that person which makes it easier to ask questions and figure problems out. I don’t think we switch too often, I like switching every 2 weeks, Goldilocks amount.
  • I like both 3 and 2 people. Having an extra person or two is good to have when you are struggling. I liked switching groups often so then you are with someone new every two weeks.
  • Groups of 2 when there’s a group of 3 there’s always someone left out and its hard to communicate and work together with such little room.
  • I prefer only having 2 people for the group sizes. I felt whenever we had 3 people, one person would always be a little left out and not learning as much as they could be since the other two people were just working with each other.
  • every 2 weeks was perfect, either sized group was fine
  • I think 2 works better, simply due to whiteboard space. The whiteboards were kind of awkward with groups of 3 because you either needed to huddle around 1 whiteboard or have 1 person on their own and 2 others collaborating which kind of broke up the group. I think the amount we switch is fine.
  • I think switching seats every 2 weeks worked a lot better than switching seats every week. It allowed us to get more comfortable with our partner and work better with them. I think working in pairs worked much more effective, but that was because I was paired with someone I worked well with every time. I really think that next year you should set up a system to pair kids with people they work well with, because you simply don’t work well with everyone. There are entire units that I have difficulty understanding because I was paired with someone who was discriminatorial towards me or who refused to work with me. I know we need to have the skill to work with people we aren’t close with, and I’m not arguing with that, but I think there also need to be some measures in place to avoid uncomfortable situations.
  • i prefer 3… two is too small because a lot of the times neither of us know the answer and dont have a ton of input
  • Somewhat more rotations would be good, 2 is fine, then you have an easier sitting whiteboard.
  • 2 is good; group change is nice; yeah
  • 2 is the best, 3 can be too distracting. With 2 people it is one on one so you can solve things faster and help people easier.
  • i think having three people in a group is helpful to get more then one input on how to approach or actually do a problem whereas with 2 there is more likely a chance you both don’t know how to approach a problem and your stuck.
  • I preferred the groups of 3 but should switch them every two weeks.
  • Groups of 3 were better in my opinion.
  • i preferred the groups of 2 because it required more work from both people rather than relying on 2 other partners. switched too often, every other week would be better.
  • I like the groups of two better because you both do the same amount of work and I feel like you personally come around more to small groups, which makes understanding easier. No I like how we switched groups, it’s good to work with different people.
  • I like being in groups of two because it’s easier to learn if you don’t know how to do something with less people, also I like switching as often as we did.
  • I liked group size of 3 better because you had more than one reference for the topics but we could have switched groups more often to liven things up
  • I like groups of 3 better because then one of the three is more likely to understand a concept and help the other group members. I think once every two weeks is a good amount of time for switching.
  • There are pros and cons to both; small groups makes it easier to work together, but if both people don’t know how to do something its hard. With three people usually one person has a better hold on the subject if the other two are struggling, but its easy to let other people do the work on whiteboards. I think switching groups every two weeks was good
  • “sometimes too soon, sometimes too long on switching seats 3 people is definitely more productive and helpful, especially with conversation”
    3 was a good fit because if two people did not understand a concept it was likely that the third person did.
  • I preferred a group of 3 because chances are at least one person would know what is going on whereas if there is only two a ot of times the super smart people are together and then not as smart people are together and are struggling to understand the concept.
  • Groups of two and switching every two weeks was good
  • 2 its easier to work together


A lot more noise here. I’d say that a majority of those with a preference would prefer switching groups every two weeks (as opposed to every week as we did for a bit). And a slight majority prefer group size of two. Not a big win one way or another though. I think starting off in a group size of three and then changing to two after they’ve gotten to know each other might be the way to go.

Lastly, this comment is something that I need to be on top of “There are entire units that I have difficulty understanding because I was paired with someone who was discriminatorial towards me or who refused to work with me. I know we need to have the skill to work with people we aren’t close with, and I’m not arguing with that, but I think there also need to be some measures in place to avoid uncomfortable situations.”

I hadn’t seen any of this happening at all. I had no idea students were refusing to work with others, actively or not. I need to work on this to keep this place a comfortable place for learning.