Math

I am a math teacher.

When I first started college, I entered as a math major, with a minor in English. I loved math. I loved the fluidity of how numbers worked. I loved how numbers could make sense of things. However, when I took Calc III the first semester of my freshman year, I quickly stopped loving math so much. It moved to theoretical, and if I'm honest, it was just hard. I soon changed my focus to English, keeping only a minor in math. 

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I entered the teaching field, then, focusing on English. I've always loved literature, and I love the plethora of ways I can creatively teach it.

However, since I went to college in Michigan, I was able to receive credentials in both my major and my minor subjects. Therefore, when staffing changed at my school a few years ago, I was asked to begin teaching a math class as well. 

At the time, I knew nothing about teaching math. However, I did know two really cool math teachers who both loved math, and more importantly, loved kids: John Stevens and Matt Vaudrey. At Back to School Night last night, I've realized just how much they've really impacted my math education philosophy. Here's what I've learned from watching their practice: 

Math should be fun. Math gets a bad wrap for being drill and kill and a bland lecture format. Although my math class still has moments of lecture, you'll often hear sound effects or hand movements or crazy wording to help us remember things.

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Math is more than a worksheet. I love teaching pre-algebra because so much of it is "real world" math. I've learned to look for how students might use our mathematical concepts in their world with their ideas. We do big projects and little projects and get our hands dirty as much as possible. 

Mathematical excellence can occur with little to no homework. The more I talk with families, especially here in the Bay, I'm struck by the soul-killing and family-killing nature of math homework. We can practice skills in class a lot and have little to no homework every night. Turns out this creates a way more math-loving culture, too. 

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Math can be a team sport. When I think back to my math classes, it's amazing how much of math class was listen to the teacher, do a worksheet by yourself. There's so much beauty to me in students working together to solve a problem. I love the mathematical conversations I hear in my room every day. 

The more time I spend processing the last several weeks of the beginning of the year, the more I realize that I am truly a math teacher. I'm not just a language arts teacher who teaches math anymore. I love watching my math students learn and create and work together and have fun. I love making crazy lessons for them that put our mathematical concepts to good use. I am a math teacher.

Turn Off the Faucet!: Exploring with Linear Models

Sometimes I still have to tell myself that I'm a math teacher, not just a language arts teacher. But last week it felt for realsies when I wrote my own math lesson plan: a hand washing experiment

Every unit I try to do a hands-on project to reinforce the importance of the math we're learning and to help the students see how much they know. We had just finished a unit on linear models and all of the different things you can predict. A few years ago, we used this to explore the leaky faucets on our campus and to get the school district to replace one. But now we didn't have any leaky faucets, so we needed something new to explore. 

I started exploring all of the different ways we waste energy on a regular basis. Did you know that PG&E has a whole analysis of your bill with energy-saving tips? We looked at YummyMath's lightbulb and toilet activities, but I really wanted something that my seventh graders had power over. And they needed to be able to do it with a sub since I'd be away at a conference. 

Enter hand-washing. Seemed perfect for the amount of sniffles I hear in my class on a daily basis. Did you know that the CDC now recommends that you sing the Happy Birthday Song TWICE through while you scrub your hands? That's a ton of water waste while you scrub your hands! 

My students did a great job exploring this task together and asking each other for help if there was a step that they didn't understand. I'm happy to report that they completed the experiment and the math without me there to guide them. Afterwards, we were able to debrief, and they helped me clarify a few of the different points. As I looked at them, for example, I realized their final measures were in mL, which have very little meaning to them. We decided it would be better to convert it into L or 2L since that's something they can picture a little better. We added a screencast of my favorite way to change between measures in the metric system so we could better understand the data. In addition, they helped me clarify the directions in different places. I can't wait to try it with next year's class! 

Take a look and let me know if you have any advice. And if you decide to use it with your class, let me know what you think! 

Are You a Good Steward? Bridge Building with Spaghetti

Last year, we made the switch the CMP3 math curriculum, which focuses way more on high-level thinking and applications of math concepts to real world problems. Our first unit of the 7th grade year focuses on two-dimensional geometry. We build, we measure, we analyze.

We really realize how much of our world is dependent on polygons. They're everywhere. We like them aesthetically, and they can be used really effectively. Consider for example, the tesselating hexagon shape that honeybees use in their hives.

I think it's so cool that God created them like that. They're such great stewards of their resources thanks to hexagons. This, along with hexagonal thinking, has really made me fall in love with hexagons over the past couple of years. It's by far my favorite shape. 

In the course of our study, we also learned about how strong triangles are in the building process. When you look at bridges, you see them everywhere. We learned more from Chris Woodcock, a bridge architect: 

We discussed all of the factors that a bridge building team needs to consider. Materials. Design. Weight load. Length of the bridge. Budget. Weather. 

Then we talked about stewardship: How might we responsibly plan to use resources to build a strongest bridge while responsibly using (or not using) the resources we have? 

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I handed out this packet and had students form groups of three to four, and they got busy planning their bridge building. The bridge with the best weight of bridge to weight of load would win. They knew their resources would be spaghetti and hot glue, but they had to remember a few things: 

  • Hot glue weighs a lot more than spaghetti.
  • Any scraps created would count towards the weight of their bridge. I gave them a cup to collect them in as they built. Some students weight the extras separate. Some used them to reinforce their bridges. 
  • Use the power of triangles.

I loved watching them build and listening to their conversations about polygons and stewardship.  (Not to mention they started cheering when they realized that we had an 80-minute block of math instead of the standard 40-minute period.)

Then we began the weighing process. I took a red solo cup, punched some holes in it, looped a string from the cup to their bridge, and we started adding weights. However... we didn't have enough weights to break them. Oops. My students bridges were too strong. 

We ended up having to reconvene at a lunch period to try again, this time with ice cream buckets which we filled with water. Even then, our system wasn't great. I need to get a bigger bucket for next year so that we don't need to add a second bucket. 

We were all a bit surprised by how strong triangles of spaghetti and hot glue really were. The lighter bridges were actually stronger in our class. 

We had a lot of fun and truly realized the power of polygons! Here are a few of the things my students wrote in the reflection process: 

  • "We used mostly triangles because they are the strongest polygons in building architectural designs."
  • "I learned that it takes a lot more work to build something, even something this small. I can’t imagine how much work it would take to build an actual bridge!"
  • "We chose that our bridge was a little longer than others because if it bent it would have a higher chance of falling."
  • "We chose to do the smallest sizes we could that would fit the requirements to save resources and minimize waste."
  • "Sometimes things fail and you have to try again."
  • "I would use more glue on the bottom of the bridge instead of focusing on the sides, and I would have accounted for where the weights were hung from."

So many wins there. I look forward to doing the 2.0 version of this project next year. I think next year I'm also going to give them a budget and make them buy their materials. I'll make hot glue cost a bit more so they have to use it more sparingly. 

Doughnut Math

My 7th grade math students are currently studying surface area and volume. Over the course of the unit, I've learned these skills are something I take for granted. I started out assuming they knew way more about this than they did. However, we slowed it down a bit, and now they're doing wonderfully. 

Yesterday I had some doughnuts left over from my 8th graders, and it dawned on me that it was a great way to review the surface area and volume of cylinders we'd been studying for the past week or so. 

I cut the doughnuts in half and told the students they needed to calculate the surface area and volume of doughnut (in organized lines of equations) before I would let them eat the doughnut. Talk about motivation. 

Wonderful mathematical things about using a half a doughnut: 

1. There's a hole in a doughnut! They not only had to calculate the surface area and volume for the whole span of the doughnut, but they had to do it for the missing hole as well. This gave them some extra practice and had them thinking of the deeper level problems that we've been solving. 

2. It's a half! Even though they started out calculating the volume and surface area of a whole doughnut, they really needed to remember to halve their calculations. Again, it added a greater depth to the problem. 

3. You get to eat a doughnut! Who doesn't love sugary goodness? Okay, that's not mathematical, but it's true. 

It was a great way for me to check their understanding and progress in our unit. Another one of my happy accidents in teaching. :) 

Probability Cardboard Arcade

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Most of you have probably seen Caine's Arcade (and if you haven't, stop and watch it).  I loved the innovation the first time I saw it, and we've even done a school-wide arcade here at San Jose Christian a couple of times. 

Last week my seventh grade math students finished up their unit on probability, and the final project in the curriculum was to design and build a cardboard arcade game using the principles of probability. And since I was going to be out a week on a class trip, it seemed like the perfect sub plan. I'm so glad that I did it! 

My students started off by writing a proposal of their game. They had to sketch it, calculate the theoretical probability, and ultimately sell me on their idea (and if applicable, their team). They made themselves a schedule for the week and thought about what they needed to create it. They had to think through how much money they'd charge, what the prize would be, and ensure that they wouldn't lose money. I wanted them to reuse and recycle as much as possible, so I sent an email home to parents asking them not to buy their students anything for this project. Most of them complied. 

I was awed when I came back from our trip at both their creativity and their execution. The games looked great. 

When we were finishing up the activity, one of my students really wanted to play for money, specifically for quarters. At first I didn't get it, but he then explained that he wanted to win quarters for our school's quarter drive for Feed My Starving Chidren's MannaPacks. Love it. The grades are competing to raise the most money, so I thought we might be able to work with that level of competition as well. 

So today we had a carnival in our middle school during lunch. Students paid a quarter to play the game. If the game won, the quarter went toward the seventh grades collection of quarters for the drive. But if the student won, the seventh grade creators of the game, took TWO quarters from the seventh grade collection and gave it to the winning student's grade. We ended up raising about $42 in quarters in 30 minutes and had a ton of fun in the process.