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.


153-154 Course Feedback – PreCalc H

Here’s a breakdown of some of the Course Feedback from my PreCalc H students

-1. If you had a friend taking this class next year, what advice would you give them?

  • Challenge yourself with problems you don’t know the answer to yet. Try to figure things out on your own before you learn the real formulas and methods.
  • Make sure you study the feedback keys and know the technique/skill instead of just memorizing the questions on the feedback quizzes.
  • Don’t be afraid of this course. Mr. Anderson has an amazing teaching style that makes this course a lot less intimidating so don’t be scared. Also, take advantage of reassessments and don’t leave them till the last couple weeks of the quarter.
  • I would tell them that throughout the year, Danderson is going to teach you things that are just way above your head. He is going to use these complex examples that make no sense to you… at first. Soon enough, he’ll explain how he is getting all of these crazy formulas and all the shortcuts to get the answer. So, the biggest thing is that you can’t give up during class. You have to stay focused and try to understand even if you have no idea what is going on, because later on, you’ll be able to look back and understand everything that he did and learning the material is much more easier.


0. What could we do differently in class (and out) so that you could learn better?

  • Have more time practicing, or go over a few things before quizes.
  • I would try your best in class, even if you thi k you are messing up. You learn from your mistakes. Come afterschool if you need help on anything.
  • I think maybe before we take b quizzes we could do some practice problems the class before so we are able to ask questions on the material if we have any.
  • If we do homework, I would like it if we went over the material a bit more.
  • Assign questions for homework that would be checked.
  • … Out of class, assigning mandatory homework would be great as it allows you to try problems totally by yourself. Then, we should make it a point to go over it the next day in class.
  • I would like to have a recap at the end of each class, maybe 2 minutes to review what we did.

5. In this class, we learn to correct our mistakes.

  • If you make a mistake, most of the time Danderson won’t tell you what the mistake is exactly, he will tell you where you made a mistake, but it is up to you to find out how to fix your mistake. I like this because it helps me to not make the same mistake again.
  • Whiteboards are great because we can erase and fix our mistakes.
  • Even when Mr. Anderson makes a mistake he encourages us to correct him, this sets a good example for the rest of us
  • Definitely. We always are learning from our mistakes.
  • It is hard when you don’ t always answer questions (gave a 2 out of 4 on this question)

6. Any last comments?

  • This was by far my favorite year of math yet!!
  • For a person who doesn’t particularly excel at math, I really enjoyed this class. It made math more likable and doable for me, especially with the standards based grading.
  • This was the most enjoyable math class I have ever taken and I am looking forward to another year of it.
  • Hopefully next year will be just as fun and i will gain more knowledge of the subject that i enjoy most which is math
  • Thank you for the year. This class was the most fun I’ve ever had in a classroom. The way you run your classroom makes it engaging and fun to learn the material, and it taught me the hard work that I will need to carry on into my senior year, college, and everything that comes after.

0B. What is working well in class? What would you like to see more of?

Grid Responses:


151-152 Curve Sketching

Curve Sketching requires so much time and space. I’m lucky to have the space! This problem took 20 minutes!


149-150 Computer Programming Project Preview

Super exciting computer programming final projects in progress. Here’s one student who’s making a dynamic dragon fractal and working out the math in Desmos before he implements it in processing.

Another student has made a couple of different graphing programs in processing, one that reads in a string, like “y=2x+x^4” and graphs it, and another implicit grapher. Very exciting! More info to come.


147-148 Not fully ready for a Feedback assessment

It’s May. The students might not be fully prepared for each feedback quiz, especially since they’re not graded. These students were taking a feedback quiz on derivatives of transcendental functions (exponential and log functions). The instructions at the front:


145-146 Proof of a Derivative Rule from @3brown1blue

Here’s a nifty trick that I’ve never seen before. Thanks 3Brown1Blue (Grant Sanderson). Can you tell what derivative formula this student just derived from the exponential rule and implicit differentiation?


143-144 Long Calculus Problems – Give them some room to breathe

Not much to say here except I love this space for giving students some space to do some long calculus problems.


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?”


139-140 Implicit Differentiation and Difficulty of Math Problems

Megan asked a great question on twitter:

To speak to my response, here’s a problem that we started off today with in PreCalculus H (started calculus early because they have extra time throughout the year).

Tough problem (unless you solve for y first!). Pretty tricky calculus with a product rule inside of a quotient rule, and some tricky algebra too. Here’s some sample work:

Every student made at least one mistake in this problem. BUT, they had a high level of support, they worked next to their peers throughout, and every couple of minutes I’d show my work. This is a small example of a difficult problem that I’d not put on homework or a test because the hurdles are high and numerous without the support.


137-138 Derivatives of Trig Functions

To find the derivative of sin(x), they drew tangent lines to sin(x) (printed out on paper), measured their slopes and then graphed the derivative point by point. Here’s a desmos version.

From that derivative fact and noticing that the derivative of cos(x) is -sin(x), they have enough to find the derivatives of tan(x), csc(x), sec(x), and cot(x). Let them at it.