Why did they do so BAD?

I just gave my first unit test in my Pre-Algebra classes. Now, historically, this test (not the unit itself, that is great!) does not go well. So, I made some more adjustments this year to help prepare them. Formative assessments, more practice, a different homework approach. But the test were horrible AGAIN. There is some disconnect between what happens in class and what they do on the test. I’m feeling frustrated, and I know my students do too. I could tell during the test that they did not think they were doing well.

Here’s what I’m going to do about it this year. Reflection. Getting the students to tell me what happened. But I’m struggling with how to do this. So, I’ve created a reflection table for them to use. I need some feedback. Or maybe you have a better one that you’ve used and has been helpful. My goal is for the students to take ownership for their learning, reflect upon why they did not do well, and what they’re going to do about it next time. I’m also toying with the idea of giving them some extra points if they can produce evidence of their engagement in class (relevant notes, practice problems, homework, etc.) I’m not sold on that idea. I also debated about whether or not to tell them what each question was about. I decided to put it in myself, basically to save time during class so they could focus on what type of mistakes they were making and rummaging through their stuff to find their notes.

So, here’s the document. It’s not so many pages in my original Word doc. I would really appreciate any feedback. Good, bad, ugly, whatever! Thanks everyone!



Triangle Congruence with Bendy Straws

New to me this year, is teaching the Triangle Congruency Postulates (Theorems? Which is it?). You know the ones. SSS, SAS, AAS, ASA, HL? So, my first attempt didn’t go over so well, trying to use spaghetti. Fun, but it really only worked for SSS. Without angles, it ended there. (We did make some cool similar triangles, so that was a bonus!) So I needed a new plan. I’m pretty good at coming up with big ideas, but pretty poor at finalizing the details. I reached out to my Twitter world, and got some suggestion, but didn’t have time to look into them. Here’s what I ended up with. I made it a partner challenge.

Triangle Challenge: Can you Make A Different Triangle than Your Partner?

I gave each student a set of triangle parts. I made sure that no two students sitting next to each other had the same color straw. The box I bought had red, yellow, blue and green. I included some “angles” and some “sides.” I just cut the bendy part out of the straw leaving about a cm on each side.


Triangle pieces.

The first direction was: Using 3 sides and 3 angles, make any triangle you want. You may cut the sides to make them shorter if you like. They could probably also fit straight pieces together to make longer sides too, but I didn’t try that. (It is really important that they use 3 separate angles and 3 separate sides.) Then trace your triangle on the worksheet. (I haven’t typed this up yet, so will post that soon.)


A completed triangle.

Next, take 3 parts of your triangle off and label them on your drawing. (This picture shows 2 angles and a side: ASA) Then give them to someone who has a different color straw.



Once you have received pieces from another person, the challenge is to NOT make the same triangle as they did. Here are the rules. You must keep the angles and sides they gave you the same and in the same places! Use their drawing to help you remember what they gave you and where the piece were. Use your extra pieces to make the rest of the triangle. Could you make a different one?

The goal of the activity is this: Depending on what combination of parts you were given you will or will not be able to make a different triangle. For example, if someone gave you all 3 sides, you could NOT make a different triangle. Therefore, 3 sides (SSS) guarantees congruence. If you were given 2 angles and 1 side in the ASA order or the AAS order, you could NOT make a different triangle, proving that ASA and AAS guarantees congruence. The students already understood the HL postulate, and no one made a right triangle, so I didn’t worry about it in this activity. 

Now, of course, the sassier students will argue that they can make triangles that aren’t exactly the same. And that’s probably true because they’re just straws! It’s not a perfect material. However, for 8th grade, it was convincing enough. The other problem was that students only gave each other the ASA or SAS combination, so they rest came from me. The other problem is that the partner can move the angles if they are being sneaky, but even bendy straws stay pretty well in place.

So, overall, I think it was a success! The students definitely now have an activity to refer back to and it made the postulates (or are they theorems?) concrete and understandable. I’m putting together the worksheet soon, but plan on using this again next year! I would recommend cutting the straws apart ahead of time. I planned on doing this, but due to a late night (cough-2 year old not sleeping-cough), I did not get to do this. My first class however, was helpful, but the cutting out the angle was way harder for them than I thought. They got way too caught up in how far away from the bendy part to cut.

So, please comment, share your thoughts, ask questions. See any glaring inaccuracies or misconceptions, please let me know. This is the first activity like this that I’ve done that actually worked the way I wanted to! It’s about time! Or, if you’ve done this before and I totally stole it from you I apologize. I promise it was not on purpose and really just came from my brain. But great minds think alike, right?

Another Grade Follow-Up AND Equations Around the World!

So, after the quiz grades, here’s what I did. I gave them a worksheet that basically asked “What went wrong?” They individually analyzed their own work, and tried to put into words why they lost points for each question. It was good for a few reasons. One: it was individual. Two: it made them get over the initial shock of a bad grade. So, the student who immediately threw his on the floor, declaring he was stupid was forced to take a closer look. And you know what he found? Careless errors. Things in the questions he just didn’t pick up on. So, he felt silly for making those mistakes but didn’t feel stupid at math. Score!

Then after looking at the responses, the majority of responses were “I didn’t understand the question.”  Or “I thought the question meant…” The next day we spent time analyzing questions. READING math. We talked about looking for anything to start with. Does it say make a table? Great! Start there. Even if you don’t know the variables to put in the table, you can at least set it up. Draw the lines at least. Now, you’ve started, and when I look at it I can tell you put some thought into it. You did something! The test is tomorrow. We’ll see how that goes.

Equations Around the World

Many times, I’ve thought that I don’t have many exciting lessons to share, but there is an activity I use to review skills that I thought would be fun to share. I call it Equations Around the World, but you can insert any skill you need. It works best with skills that have clear answers. So you could use it with simplifying, adding, any sort of computation, or anything with a beginning and end. Even vocab could work.

Here’s how it works. There are several cards around the room that look like this:Image

The students can pick any card to start with. They open it up and see this:


They solve that equation and the answer is on the front of another card. Once you find the answer, go to that card, open it up and solve that equation. Continue this until you end up with the card you started with. Can’t find your answer? Then you made a mistake. Go back, check your work and do it again.  The students like it because it gets them up and moving. They get practice without having to look at a board or at a book, and I get to just follow them around, see how they’re doing and answer any questions. I usually get more questions than usual during this activity. I think students are more likely to ask questions when the atmosphere seems more casual.  One word of warning to teachers who are making one of these: It doesn’t work if you have the same answer more than once. So make sure each problem has a unique answer. Happy solving!

Another day, another grade.

I just finished grading a quiz from my Pre-Algebra students. I was hopeful when they were taking it that they were doing well. I let them use their notes for this (I did not tell them this ahead of time). And, to my surprise, those that had taken notes, were using them very effectively! They were asking good, clarifying questions, and I could point to examples, etc in their notes to help them. Students were working hard, and very few gave up. Woo hoo!

So the result is about half of them got B’s and A’s and the other half, F’s. No middle ground. There could be a million reasons for this. Maybe I graded it strangely. Many some questions were worth too many points, and others not enough. Maybe some students take terrible notes, or none at all and have not learned as much as I thought they did. Maybe it wasn’t the math, but the reading on the test that gave them trouble. Maybe this, maybe that. Maybe I don’t have as good a read on them as I thought. I could go on forever.

But I need to focus on what to do. What do I do with this information? I always allow corrections to be made, because I want the students to learn. But I get the feeling that half of them can’t make corrections because they don’t know what went wrong. So, maybe we’ll do them together, and then take a retake.

I’d also like to do some sort of student reflection and hear from them. I’ve tried to do this in the past and it never really gives my the info I want. I need some help with what questions to ask them.

This definitely changes how I approach the next unit. I need to be more in tune with my students, without giving quiz after quiz after quiz. I need to give them more opportunities to show me what they know. To show me how they’re doing. This isn’t a very inspirational post, or very helpful to anyone but me. Just doing a little reflecting on my own to get my thoughts in order. Thanks for listening, internet world.

I’m trying to notice!

This week, I tried out my first Problem of the Week from The Math Forum thanks to their free trial. I have been reading about these from other people and their awesome experiences with them so I wanted to get in on the game. 

I started with “You think you’re teacher is tough?” I like the idea of “I notice, I wonder” and figured it was just what my students need. My students, as I’m sure many others, just look for the question, look for some numbers and just start doing math. They don’t re-read, they don’t analyze, they don’t think about the situation, they just want to find an answer and be done. I took the suggestion of how to start out, and took out the question and just posted the situation. I then asked the students to write down something they noticed. I was faced with a ton of blank stares, so I tried to explain what that meant. This was way more difficult than I thought because I didn’t want to give a ton of examples. I wanted them to think for themselves. I think I ended up saying something like “Anything that comes to your mind when you think about this situation.” That seemed to work a little better. After a few minutes, we shared and got some really interesting “notices.” Obvious ones, funny ones, deeper thinking ones, etc. Good. This was good.

We then moved on to “I wonder.” This was easier, and also provided many good questions and discussion. We were really discussing the situation, taking it apart, having fun, making sure we understood, questioning each other. It was pretty great.

Then I finally gave them the question. Cue the Darth Vader music. It was like I had asked them to take every book in the library, move them outside and then back in again. All of the inquiry, engagement, interest went right out the window. Very few students were willing to try anything, write anything down or discuss with their peers. It was a little devastating. Throughout the week, I did this with each group with the same result. With much prodding, I did get them to find the answer.

I can’t figure it out. Everyone said these PoW are so engaging and students love to get to work on them, and their interesting and fun. Not for my students. Ask them to actually do any work, forget it. Was it the problem I picked? Was it my delivery? Was it the fact that their 8th graders? Was it the fact that they are not used to teachers encouraging them to solve problems with any means possible? Were they uncomfortable with the openness of it? Was it the fact that this was not actual math class, but workshop block? (Workshop is designed to give teachers a chance to do something enriching, out of our normal curriculum. Most students think of it as “free time” no matter what we tell them or ask them to do.)

I’m going to try another one. I still have faith that these problems, and “I notice, I wonder” will help them. I think.

Why am I doing this?

I was always good at math. But never really liked it. All of my math teachers starting in middle school would encourage me to join the math team, or become a math teacher, but that is not what I wanted to do. I wanted to be a hair dresser, then a concert pianist, then a teacher. A teacher of little kids. Elementary kids. So that’s what I went to college for. However, unlike most of my elementary ed counterparts, I didn’t take the recommended math courses. I took the math major math courses. I like to be challenged, and Calculus II was definitely a challenge!

I decided I wanted to try out middle school for my student teaching. Who voluntarily teaches middle school? Me. So, I ended up teaching 6th grade math. And I discovered a wonderful world. I LOVED middle schoolers. Middle schoolers are really the best. They are fun to joke with, keep me informed of the latest trends, and are a perfect mix of “I’m too cool for this” and “I love stickers!” I LOVED teaching math. I love the challenge of explaining something in a way that relates to their life. Who knew? I then went on to get my master’s degree in math education. I guess all my teachers were right.

My first teaching job landed me in 5th grade, mostly teaching reading. Then 4th grade for 4 years, teaching everything until we finally departmentalized and I taught math, science and social studies. It was a step in the right direction, but I wanted to be in middle school. Don’t get me wrong. I enjoyed my days in elementary school too. Some of the best accidentally inappropriate spelling errors come from elementary school. Here’s what I learned teaching 4th grade. Classroom management. Record keeping. All of that stuff you can’t learn in college.

My husband and I moved back to our hometown, and the first job I got was as a part-time math tutor at my husband’s former middle school. So close! Next year, a long-term sub job in 8th grade, then they hired me for real for the 8th grade position, and here I am today.

So, why do I love it? Why do I do it? Because I really believe that everyone can do math. EVERYONE. A student told me today “The only reason I like math this year is because of you, Mrs. Freitas.” WIN! So, there’s hope. If I can make math tolerable for students who have previously hated it, then that makes me happy. It should not be acceptable to say “I’ve never been good at math.” My response to that: You just had the wrong teachers. I’m not going to be that teacher.