9-10 Polygraph Rational Functions – Desmos

Did the wonderful polygraph of rational functions by Desmos as a warmup to rational functions.

fullsizerender-1 fullsizerender-2

And I “caught” a student googling a math term:


Was only making sure she spelled it correctly. Good call, don’t guess on this word.


7-8 Feedback Quizzes and Desmos Activity

First feedback quizzes of the year in PreCalculus H. Here the students are giving themselves feedback with pens after looking at the key. They’ll turn it in and I’ll check them over and make some comments.


After the quiz they were tasked with the following on paper:

And then they worked in pairs on this Desmos Activity where they were exploring how the graph of f(x) is affected when you look at |f(x)| and f(|x|). The second one is particularly tricky.



5-6 Forced Interaction Time

Many students (especially students who sign up for computer programming) like to work by themselves and not interact with other humans. So we work on interacting and communicating with the other humans in the room. Here is some forced interaction time, where they introduced themselves and helped each other out with their programs. 2016-09-15_13h31_56


3-4 Domain and Range

Fantastic Desmos Activity on Domain and Range (from Suzanne von Oy) in PreCalculus H. Needed an extension for the students who finished early. Threw out this question:


When a group had a new graph, I had them come up to my computer and put in their function. One group even got REALLY close with an arcsin graph. Amazing, and fun.



1-2 First Day(s) of School

Note: I’ll be (hopefully) running a photo90 this year, every two days I’ll make a new post.

I’ve changed how I start the year a little. Instead of doing the old first day puzzlers, the students worked on the classic car talk puzzler, Gone Fishing. Had a lot of fun with this activity!


2016-09-09_11h33_25 2016-09-09_11h33_58 2016-09-09_11h34_16

Love the groups that try algebra first (they normally struggle with this particular problem though):



157 – Calculus End of the Year Feedback 4

Here are interesting bips and bops from the feedback.

2016-06-08_13h06_39 2016-06-08_13h07_10 2016-06-08_13h07_28 2016-06-08_13h08_17 2016-06-08_13h08_28 2016-06-08_13h09_01 2016-06-08_13h09_12 2016-06-08_13h11_56 2016-06-08_13h13_10 2016-06-08_13h13_20 2016-06-08_13h13_53 2016-06-08_13h14_15 2016-06-08_13h15_59 2016-06-08_13h16_06 2016-06-08_13h16_28 2016-06-08_13h16_42 2016-06-08_13h16_52 2016-06-08_13h17_01 2016-06-08_13h17_33

And … WOW.



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.


155 – Paula Krieg Visit!

Paula Krieg visited the calc class! She talked about derivatives and integrals with the students, and then we made really cool foldables. This will happen again.

2016-06-07_09h02_06 2016-06-07_09h02_09 2016-06-07_09h02_13 2016-06-07_09h02_17


154 – Calculus End of Year Feedback part 2

Here are some selected answers to the prompt: What is working well in class? What would you like to see more of?

  • Working together is extremely helpful, more examples in notes would be helpful
  • Working on whiteboards in small groups
  • Practice questions
  • I found the take home tests to be helpful in learning a topic and more might be helpful, maybe even during preparation for the IB test.
  • Whiteboards and Take Home’s.
  • notes and trying it with teacher assistance
  • Practicing questions works very well but we don’t spend very much time going over the actual work. Sometimes it might be more effective to go over the work even when nobody asks because sometimes people are afraid to speak up despite not understanding how a solution was reached.
  • Whiteboards and group work are both engaging and educational. If possible, integrating more technology could be worth trying.
  • More worked examples in notes
  • The take-homes are great for review purposes. Maybe more group work outside of school?
  • Using whiteboards and working in groups

My takeaways?

  1. Keep whiteboarding.
  2. Build in more take home exams (this was requested in other spots of the feedback as well). We went from 20 take homes to 7 with the shift to the IB curriculum (less class time than we had in BC too).
  3. Make sure that struggling students are more “squeaky” so that they can get grease. Any suggestions for how to encourage this further?



153 – Calculus End of Year Feedback part 1

The IB Math HL year 2 group filled out an end of the year feedback form. Here’s a copy of the form if you’re interested. Please try this. The students write amazing things. Some productive, some funny, some incredibly humbling, and some that seem like you wrote it yourself. Mostly humbling though. Thank you seniors, I’ll miss you!

These are all the responses to this question:  What is working well in class? What would you like to see more of?