Graphing quadratic functions foldable

Nothing too fancy or mind-shattering here, but perhaps someone may find this useful. Just a quick, little graphic organizer for the steps I want students to follow to make a nice graph of a quadratic function.

Graphing quadratic function foldable (updated) by Anna

You need to print both pages and copy from one-sided to two-sided so that you can fold over the top and make it look like this:

Students should cut each numbered flap and then fill in each step with an example problem. Here is what the final copy will look like:

Outside:

Inside:

Group success!!

Today had one of those class periods. You know the ones. Where everyone is working and discussing and arguing and engaged and I'm? I'm just there. Totally and completely unnecessary to the workings of my class. Amaze.

Today was the first day of learning to solve systems by substitution. We went through an example together using @cheesemonkeysf's patented "substitution by stars" method. Then, I passed out some problems for them to work through, telling them to work with their group members and only go to the next problem when everyone in the group was totally good with the previous one. There were some where students had to apply the distributive property and some where they had to isolate a variable first. We had not talked about these. I did not stop class to discuss and fix and give hints, just circulated the room and looked on. Not one kid asked me for help for the 20 minutes that they worked - they puzzled through and argued and made mistakes and erased them and made some more and eventually figured it out all on their own. Holy wow. You guys get it. We all want group work to go exactly like this, but it so rarely does.

But finally!! All of the working on norms and redirecting questions with, "Have you asked your group yet?" or "Is this a group question?" and biting my lip to avoid butting in have paid off and there was just this amazing energy and focus and I was so, so proud. Cause there aren't that many glorious classroom moments like this, and it's so easy to focus on all the ways that we aren't perfect and they aren't either. So I want to stop and acknowledge that today was exactly right and keep it in my memory bank for when I'm feeling frustrated and disgruntled. Hooray!!!!

Article on "Math People"

Soo.... I wrote an article for Quartz magazine on why so many people identify themselves as "math people" or "non math people" and what we can do about it.  It's the first time I've ever been officially published and I'm both terrified and excited.  The magazine editors came up with the article title and the subheadings but the rest is mostly my work.  Here it is.

I don't know how many people will read it, but so far it's been well worth the two weeks I stressed over it because of some of the wonderful responses I've gotten from former students.  I have to share them.  If the article was terrible, it was worth writing just to get these wonderful words of encouragement from my students.

Student 1: Congratulations on having your article published! I miss having you as my teacher so much! You were the best teacher I have ever had <3

Student 2: You are so brilliant! I am so lucky I had you as my teacher. Not only were you a good teacher, but a super-cool one. I miss you!

Student 3 (this is the one that made me cry): I want to thank you for writing that article. I have been so scared to take another math class because of the last one I took. It was Math 110; basic college Algebra. I failed the class. I went to the math lab regularly, I participated in study groups, office hours, the works. I tried hard, but the teacher just could not explain things in a way that I could understand well and remember. After that class, I decided that I could not ever have a career in the math/science field despite my love for them because I just was not a "math person." A few weeks ago I was reading a Biology/Science textbook and realized that those were the only textbooks I had ever read for fun. I always have. But right then I nearly started crying thinking about how I just did not have the math skills to ever pursue it. Your article has given me hope... I now have the courage to try again. Thank you so much. I am so grateful for the time I had as your student. I know that all of your former students feel the same way. We love you. You are the best. Don't believe anyone who tells you otherwise

Axis of symmetry for a quadratic function

My two-year Algebra course is just starting our study of quadratics. So far, we've looked at graphs and tables for quadratic functions and compared them to linear functions and talked about the symmetry of the shape and finding the axis of symmetry from the x-intercepts and finding the reflections of points across the axis of symmetry. I would like students to derive the formula for the axis of symmetry: for the quadratic function . The Exeter Math 1 curriculum does this by having students graph functions in the form , then generalizing the idea that one of the x-intercepts is zero and the other one is . I created a worksheet that extends on this idea using desmos to graph and having students also derive the formula for the axis of symmetry by averaging the two x-intercepts to get . Then, just like in the Exeter packet, I will have students compare graphs of  to graphs of  to realize that the axis of symmetry is not changed by adding a c value to the equation. I'm hoping that the logical progression of the graphs will make sense and that the questions are open enough for this to be genuinely based on student thinking and discovery, but with enough structure that students who are not necessarily used to deriving formulas will have something concrete to think about and answer. Any and all feedback welcome!!

Axis of symmetry by Anna