Day 50: Lying to my students

[update 3/27/16: I described how I use AngLegs to introduce this lesson here]

I lied to my students today. Really, I fantasized, because I wish my lie was true.

I told them that I was going to choose some of their work and send it to Ohio for another math class to critique. Then I told them that I also got work from a class in Ohio (I  have no idea why I picked Ohio, but they were into it!) . In reality I was using the materials that the Math Assessment Project includes in the triangle congruence lesson. They constructed their “proofs” first, convincing me that 2 triangles with 2 sides congruent in each triangle & 1 angle do not have to result in congruent triangles. They used mostly diagrams, very few had much of an explanation. They did put more effort into it, thinking that someone else, in Ohio, would be looking at it.



Then I gave them samples of student work.

I teach at an alternative school. These students identify themselves as being “behind” the rest of the world. 

They all looked discouraged when I passed them “Jorge’s” work. It looks so nice – sentences, labels, proper notation. Then we read it. They realized that he had some false assumptions. One boy got so excited he asked if he could come to the board and he presented a beautiful argument comparing SAS to ASS and how one would result in congruent triangles but not the other. I immediately realized that I need to keep a charged battery in my camera at all times, just in case. Many of my students were so happy they could logically argue and prove an idea that someone in Ohio cannot!

Then we looked at “Kieran’s” work. Immediately a quiet student in the back yelled out “That’s how I did it!”. His body language changed, he sat up straight. he decided he was just as competent, maybe more, than students in Ohio!

Wouldn’t it be awesome if I didn’t have to lie…If we sometimes exchanged work with students in another state, maybe even share video clips of other students discussing one of my students real work. I don’t know how to start, but I have to find a way to make this happen.

Day 49: Intro to triangle proofs – better then expected!

I debated for a long time on the best way to teach triangle congruence proofs. I decided to start with the Math Assessment Project’s lesson Analyzing Congruency Proofs.

I broke it into a multi day lesson since we have 50 minutes classes, and I do not want to rush this! Some students got frustrated with pencil & paper constructions, since they are time consuming. I handed a few students who were struggling a set of AngLegs & a protractor. Boom! they understood what the task was.  Next year, I plan to modify this lesson to use the AngLegs instead of pencil & paper to increase student engagement. Once they draw conclusions, then write it down & explain. They even got frustrated and excited and debated about weather or not they could construct 2 different triangles meeting the specified requirements. The most hotly contested one was weather or not they could make 2 unique triangles with 2 sides the same & 1 angle. I thought about videotaping the debate, but I was scared that me pulling out a camera would disrupt the awesomeness. This was all individual work, but tomorrow they will work in small groups and compare their conclusions.

Day 47: Tying up loose ends

Since I had quite a few students struggling with their origami angles project as well as many other assignments, we broke into groups by needs (project, update INB, extra challenge, study for quiz). Yay differentiation! Students all seemed relived to have support to work on what they needed. Big quiz tomorrow will tell me if this was effective!


Sonny claimed he was done with all of his work and he was playing with post-its & sitting next to this whiteboard. I challenged him to convince me of precisely how many post its it would take to cover the board. He jumped to the task:



Day 46: Triangles & angles & I am feeling like a crappy teacher

Today is Mole day (6.02 x 10^23), and I said happy mole day to the staff this morning. Nobody, not even the chemistry teacher, could explain what a mole is. Geez!

I decided to go with workstations because I know they needed more practice with all of the angle stuff. I’m not feeling very creative this week. Really, I’m just being trying to be quiet and they need to just think.



I did have a group of students come up with this, all by themselves, no help (Alternative high school & all!)




Day 44: Triangle Side-Angle Relationship


We analyzed the relationship between sides and angles within triangles using my fun AngLegs and developed conclusions as a class. I noticed this student has some errors in her notes & practice. We will be reviewing these conclusions and correcting any misconceptions tomorrow at the start of class.

Unplanned but awesome: some students noticed that some lengths did not create a triangle, which led to great discussions and an awesome lead into tomorrow. They are wondering when you get a triangle & when you don’t and why!


What is “Problems around the room?”

Awesome, that’s what!

Instead of having students sit and complete a boring worksheet or text book work independently, I can spend about 15 minutes and make a self paced, differentiated, student directed, self checking, collaborative activity.

I take or generate about 8 problems (with unique answers) that I want students to practice, then I make them big and put 1 per page. I write the answer to each problem on the top of the next page as below:

Then I make a sheet for students to write their work & answers (printed 2 in 1, double sided):

I print the problems on brightly colored cardstock & place them inside of sheet protectors, and tape them all over the room in no particular order, preferably with a whiteboard nearby.  (like I did here)

Students are directed to start at the problems closest to them, so that there are only a few students at each problem. They can discuss, or just listen but they must show work in the 1st box, once they decide what they are doing. Once they find a solution, they find it on the top of their next problem. If they cannot find their solution, then they should go back to the last problem and double check their work.

This gets everyone up and moving at their own pace. I listen and support students who need help. usually there ends up being discussions on the whiteboards where students debate their strategies. They are done when they get back to where they started. Sometimes we run out of time, sometimes I tell students they must do at least x number of problems based on the students, or time, or both. If I notice a large group gathering & getting stuck at one problem, I can quickly learn where they need clarification and support their understanding.