26-27 First Problem Set

This is the PreCalculus H class working together on their problem set. I really value our use of problems sets in class. They are more challenging problems that require more time to process, and require working with other students. The anonymous student feedback at the end of the year continually mentions how much the students come to value these assessments.

To set the class up for success, I gave them 15 min at the end of a block to work together on the problem set. They can choose to work however they’d like. My only rule? No writing on paper. They can work together on whiteboards and then take pictures if they’d like to record the work done. This rule worked as anticipated, they naturally broke into groups and had some fantastic discussions.

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24-25 Post Feedback Quiz

Gave out some feedback quizzes in PreCalc H and when everyone was finished, I had them go over it with their groups. They didn’t have the key, nor did they know the answers, so they had to find agreement. I think this structure works well for topics where they’re already pretty good at. We took 5 minutes and went over the key and questions after their discussion.



22-23 Find the Roots

Give the class a large polynomial, I went with a quartic. Ask them to factor it. On their own, this class decided to work together and assign each student a rational root from the rational root theorem. I advised them to double up to curb mistakes being made. Despite this task being entirely superfluous with technology today, I still think that the skills that they’re learning are important. Sort of like walking to town. Yes I could drive, but walking has it’s benefits too. They’re also learning how to work efficiently. When they’ve found a couple of roots, the groups that divided and used the depressed equations then had an easy to solve quadratic left over. The other groups who never used the depressed equations had some more tough work to do. I have cut this kind of math back over the years, but I don’t see it disappearing completelyc52a79fc-e393-4e9d-ae01-d18be3e6179d2016-10-14_11h13_07

Bonus: Super interesting mistake I saw SEVERAL times by this group later on in the class period. Very interesting. Can you tell what the mistake is?


Double Bonus: Pretty picture of sunrise on my drive in. The sky was like this for less than 5 minutes.



20-21 CodeNewbie Podcast @codenewbies

Gave out this assignment in Introduction to Computer Programming today:


Great podcast, give it a listen.

Their classwork today was to take the following processing code, understand each line, and then play around and make it “cooler”.

void setup(){

void draw(){
  if (mousePressed){
    float red = 1.0*mouseX/width * 255;
    float diameter = 1.0*mouseY/height * 200;
  } else {

void keyPressed(){

18-19 Polynomial Division

How do you start polynomial division? Here’s how I started it today. This crew was already pretty good at polynomial division, and many of them even preferred it to synthetic division.



16-17 Exponential Scale

Fun thing happened when a student was graphing a log graph by hand. She (by accident) made an exponential scale and didn’t realize it. She came to me asking what was wrong because the log graph wasn’t curved. Very cool!



14-15 Manchester Mega Pixel

In programming class we volunteered to color in some pixels for the Manchester Megapixel project. Cool project from England. They sent us a whole bunch of materials and pens and we’re coloring in our section of the final image, we have 64 pixels to color. Here’s our block of pixels in the final image:

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Here’s some students coloring in pixels:

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13-14 Horizontal Asymptotes of Rational Functions

Teaching horizontal asymptotes of rational functions can be tricky without resorting to “tricks”, while still building some “function-sense”. This year I gave them a function and they plugged in larger and larger values (positive and negative) to essentially find the limit as x->infinity. Some nice previewing of a skill that we’ll address later on in 4th quarter. Then they use a bunch of examples that we gave to try and figure out the “pattern”. I break their rule a couple of times and after reforming their rules, they came up with this (student created, not teacher):


Here’s a subset of the stuff on the board that they were given in order to find their rule:


Interesting work by a student to explain the second and third cases. They added in the “0x^2” so that it fit their rule. Love it!



11-12 Rational Marbleslides and TeachNY

I was at a TeachNY event on Friday where we were giving feedback and suggestions on the future of the teacher training in NYS. Anyway, the students back at school took a quiz and then worked on Marbleslides: Rational Functions as a preview of starting Rational Functions on Monday/Tuesday. Pretty cool to get out of the meeting and see evidence of students working on the activity and putting some pretty good thought into the math. 2016-09-27_10h55_03 2016-09-27_10h55_10 2016-09-27_10h55_14


9-10 Polygraph Rational Functions – Desmos

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

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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.