Tuesday, October 31, 2023

Which One Doesn't Belong? Never Gets Old!

The right answer should not be all we care about in math class. As teachers, when we only focus on being right vs being wrong, we send the message to students that being right is all that matters. The process, the thinking, the struggle, the journey to get there... all of that is majorly important in addition to finding the right answer. So we have to pause and reflect. Do our activities align with this idea? If students are going through an activity to practice or reinforce a skill, are we only having students find the answer and then move on? Where could we grow from here?

This is why the idea of Which One Doesn't Belong, and the thinking and justification skills that go along with it, is one of my favorite ways to get students looking at their work and their answers and talking about more than just the answer being right or not. I have posted about this before, so check this out first. 

In working with a team of Integrated High School Math II teachers this month, I designed an activity about factoring quadratic trinomials using the WWDB framework. 

Check out this first station: 

At first glance, you could start by saying that A doesn't belong because it's the only quadratic trinomial with a positive b value. That's true! And if a student said that to start, I would be thrilled that they are able to identify the different coefficients in a quadratic trinomial and recognize that the sign belongs to the b value and matters. Let's keep diving in....here are the factored forms... 

Next, you could say that C doesn't belong because the two factors are not identical like in A and B. If a student was using their new vocabulary from this unit, they might say that C is not a perfect square trinomial, which would just about make my heart burst with joy. 

You could also say that A doesn't belong because it doesn't have a factor of (x-3) like B and C do or that B doesn't belong because it doesn't have a factor of (x+1) like A and C do. 

Here's the thing, you can say any of them don't belong for any reason that mathematically makes sense.

I want students talking. I want them making a claim and backing it up with mathematical evidence while using academic vocabulary. This activity not only allows students to practice factoring, but explore and engage with quadratic trinomials in addition to finding a right answer. 

Here is a link to the entire slideshow. The trinomials get more interesting with more complex differences. Make a copy and edit as your heart desires! 

Monday, February 27, 2023

I Have Who Has: Let's Talk!

I am always looking for ways to intentionally engage with vocabulary. One of my favorite strategies to get students speaking and thinking is an activity called I Have Who Has. Each student gets a card (see the example below). The teacher starts with the start card and reads it aloud. The student who has the answer to that question responds by reading their card and asking the next question. The game continues in this way until the end card. 

Things I love: 

1. Every single student speaks out loud. How often does every student get a chance to speak whole group in your room?
2. Students have to really focus and listen to the definitions as they are being read. Speaking and listening are two language domains that can easily be overshadowed by reading and writing but are equally as important in language development! 
3. Students are somewhat forced to engage because if they check out or stop listening they become the weakest link in the chain.

It is important to acknowledge that ELL students may be super overwhelmed to read out loud whole group but that doesn't mean they shouldn't get the opportunity. A little pre-teaching or scaffolding may be needed. Set them up for success!

As part of my work as a high school learning coach (instructional coach) I was fortunate enough to work with an AP Human Geography teacher who was looking for more ways to purposefully plan and engage with vocabulary. We created a deck of I Have Who Has cards for all of her 7 units for the year and placed visual cues or hints on the back of each one.

In addition to doing the whole group read through of the cards, we also had students work in small groups to race to make a chain of cards (like dominos). The discussions, arguments, and excitement as students worked together to define the words and find the matches was loud and super engaging. 

Another goal of the teacher I worked with was to implement ways for students to think about the connections between the vocabulary words within a unit and between units. To do this, we handed small groups a mixed up set of cards from multiple units. We told students not to worry about the I Have Who Has part, and instead just focus on the I Have term. Students were instructed to write a complete, content related sentence using as many of the cards as possible, with at least 2 terms for different units. 

The time and effort required to make the cards may seem laborious, but once the cards are made there are so many ways to use them in your classroom to purposefully engage with vocabulary!

Tuesday, February 14, 2023

Two Truths and A Lie

1. I lived on Kodiak Island in Alaska for a few years.

2. I am one of 6 children.

3. I am not a huge fan of horses.

Two of the statements above are true and one is a lie... can you guess which one?

I think we have all been somewhere and used this strategy as an ice breaker or get to know you game. When talking about myself I actually dread this activity because I never know what to say. My lies are usually way too outlandish, and I don't have many deceptive truths about myself. If you guessed #2, you are correct. I am one of 4 children. Horses are not my jam. And my father was stationed on Kodiak Island for a few years when he was a pilot in the Coast Guard.

As much as I don't love this game outside of the classroom, I LOVE it in the classroom with students. It's a fantastic protocol for so many different content areas. Here's two ideas!

Language Arts Example:

Have students read a piece of text. From the text, have students write two true statements and one false statement. Share whole group or switch papers between small groups and have students figure out which statement is the lie. I love this as a way for students to engage with the same piece of text multiple times. Each new set of three statements creates a new purpose for reading. Students continually have to reference the text to check or dispute a statement.

Here’s an example of my three statements from this text:

Math Example:

Give each group 3 problems to solve and tell them to solve 2 correctly and 1 incorrectly on purpose. They definitely need to show all their work during this activity! Share whole group or switch papers between small groups and identify which one is solved incorrectly. I love this as a way to reinforce the process of showing work and creating conversations around common misconceptions and errors!

As an exit ticket, you could give an example set you create and have students independently identify which one is solved incorrectly and why and justify their reasoning. This is a great way to hit on the math practice standard “critique the reasoning of others”. Here is an example of how this could look.

Which one is solved incorrectly?

Friday, September 16, 2022

A Little Competition to Increase Participation

 There's a very blurred line between student engagement, participation, and compliance. You start down that rabbit hole and you quickly find that true student engagement is a tough thing to achieve. But somedays, and I hope I am not alone in this, you'd just be happy with whole class participation! Not every day is a student engagement masterpiece lesson, and that's okay! When I start to notice that students are a little down, a little tired, and a little too interested in their cell phones than normal, I like to throw in some fun ways to get kids motivated to participate through a little healthy competition! 

Now, before we talk about two of my favorite easy strategies, I have to first say that I am not a huge fan of games in the classroom that only reward the "smartest" kids who are the fastest at answering. Being a strong mathematician is about more than being fast, especially when content is newer. When the fastest and smartest are the only ones rewarded, I actually find that games can make more students check out then check in. Why participate if Sally is just going to win every time? We all have a Sally. We know who she is. And bless her, as teachers we do love Sally. I was Sally. 


I first saw this game at a CPM conference in San Francisco back a few years ago and was wildly confused until I finally tried it in my classroom and saw the simplistic beauty of it. Take a collection of problems you want students to practice solving. You know those days where you just need them to practice a skill and really hammer it home before you can dive into some of the deeper contextual connections that will truly promote student engagement? Yes, those days. 

Have students sit with a partner. They are going to be competing against this partner. 

Each student needs to fill out a MATHLOVE board. Here is my very not fancy version made in a table in Google Docs: 

Direct students to put four 3's, four 2's, four 1's, and four 0's anywhere on their board. When its finished it should look something like this: 

Okay now here is the fun part! Put a problem up on the board or direct students to complete a problem on a worksheet. Everyone works independently on the problem. When students have the answer they circle it on their paper. The circled answer is their final answer. Reveal the answer and have partners check each other to see if they got it correct. 

If they got it wrong, they get 0 points. If they got it correct, they have the opportunity to earn points. How many points? Here is how points are awarded after each problem. 

Create two cups and cut up the letters M-A-T-H in one cup and L-O-V-E in another cup. 

Draw a letter from each cup. Loudly, with lots of gusto and zest, announce the letters chosen. Students, once they know what's going on, will be holding their breath in anticipation. 

"M and V" you announce. The crowd explodes with noise. Chaos breaks out. I love it. Students check their board, and whatever number is at the intersection of the two letters is the number of points they earn for that problem. Students keep track of their points and the "winner" is whatever partner has the most points. 

Things to mention:
1. Some students will get the right answer and still get zero points, leveling the playing field a little for Sally who gets every single one right. Calm down, Sally. She will be very upset about this but that's the game. Her partner, on the other hand, will feel like he still has a chance.

2. Everyone is working on the same problem right now, together, and there is a time limit to get going. There is a sense of urgency to tune in, get started, and start working to get it done in time. 

3. If you throw each problem up one at a time students can't work ahead. I actually love this. Sally would do all of them in 5 minutes. This way as you go over the answer or address whole class misconceptions, everyone is hopefully more tuned in. 

4. It could not possibly be more low prep. Get some problems. Copy a very not fancy table. One you make the cups you can reuse them. It's great on days you need something but don't have time to create, laminate, cut, etc. 

5. Heads up... the first time you try this students will treat the board like a Bingo board and try to cross the numbers off. You could draw A & V multiple times over the course of a game so every single square stays in play the entire time. It's a one time issue and they figure it out pretty quick. 


Want to win the lottery?! Okay not really… And if lotteries or gambling is going to get you a parent email on this one maybe just change the name.

I 100% snagged this idea from a coworker. A win for one of us is a win for all, am I right? Students work in pairs and have a set number of problems to complete (I usually do about 10). Each right answer earns them a lottery number. You'll have to make sure you have enough lottery numbers for every group to claim however many they need. 

After they get a problem or two finished, they check their answers with me for approval and then go up and claim their lottery numbers by writing their initials on the whiteboard. I just ran around the room like a mad woman checking answers and addressing misconceptions with students. I love days where I get to connect one on one or two on one with everyone in the room.

At the end of the period I pulled up a random number generator and selected 10 numbers. Winners for each number got candy and everyone got great practice in for the day. Engagement? Debatable. Depends on the student and the content. But whole class participation and valuable practice time? You bet. 

Friday, June 3, 2022

When Math Gets Artsy.... Update!

In 2020, Covid-19 shut down our schools before I could take on another chance at one of my favorite projects. Check out my original blog post here

Then, in 2021, I had taken a job with an online school and didn't teach content that was applicable for this project. So again, I mourned the loss of another shot at this. 

Bring on 2022! The excitement and anticipation I had for this project was borderline insanity. I counted down the days until we could start all spring. I just knew that my group of students was going to absolutely crush it. A few changes to note from 2019 to 2022:

1. A more detailed attempt at a rubric. I wanted this project to be purposefully open ended with very little restrictions. Check out the 2022 rubric here: Desmos Art Project Rubric. Rubric writing is something I am still working hard to get better at. Students seemed to really understand the success criteria and I had very little confusion or questions arise about the rubric. 

2. We started the week long project with a full period of exploration in Desmos. I wanted to put out as many fires as possible before they started so they could really focus on the mathematics and the creativity could flow with out roadblocks. We covered all kinds of logistical tools and components in Desmos and I just let them explore and ask questions. This helped tremendously and I believe led to an increase in the quality of the projects turned in.

3. A Padlet for posting projects so that students could view each other's finished projects. They absolutely loved being able to see each other's projects and I do think that the fact that they were responsible for posting their project for others to see led to an increase in quality as well. The Padlet helped me stay organized and made for quick and easy sharing with colleagues and parents. 

So here it is, my 2022 Desmos Art Projects:

 2022 Desmos Art Projects Padlet

I could not possibly be more proud of my students. The work they put in and the amount of effort and grit they showed along the way to make the best possible version of the picture or image they could was beyond inspiring. 

4. After the project was over I asked them to complete a survey about the project and their experience. Here is the survey: 2022 Desmos Art Project Reflection. The results were almost as heartwarming and exciting as the projects for me. Here are a few direct student quotes from the survey: 

"I liked that creativity was important in this project which isn't the “usual” in math class, so that one thing i enjoyed."

"I liked the freedom and creativity and that there weren't really any rules that came with the project. It was easy but hard at the same time depending on what grade you wanted to get."

"I liked how challenging it was, some parts were harder to understand; especially the shading. I will say, I restarted like five times before I just stuck to a basic picture I knew I could create."

"I had a lot of fun figuring out how to move each line to match up with other lines. I was thinking about doing more for fun on my own."

"I enjoyed the process of moving around the different functions to perfect certain parts of my project."

"It was a fun way to review and get more practice on this units material."