It’s the second day of my class, and it’s going…OK. It’s a new class, and it made sense to do some review activities so I rolled out the OUR curriculum and tried one of their lessons. Specifically lesson three of their 8th grade linear unit. We had a number talk, which I updated a little bit to this:

The number talk went ok. Good actually, I considering it was my second one ever. There were definitely some kids who rolled their eyes at the beginning, who were engrossed by the end. There were also kids engrossed from the beginning, that felt defeated by the end. I think I need to do better work at making strategies visible and accessible, but that’s another post.

After that we started the task. Immediately it felt like there was no time left. We were either going to finish the second part of the task, and have to end the class their since our school had shorter periods to make room for our thanksgiving potluck. The kids energy and affect seemed low, so I thought more problems would make kids loathe today and want to cut my end-of-the-day class tomorrow. So, I asked the class, “Hey, would you guys rather do the back of the worksheet, or do an activity? Let’s have a vote.” To my surprise, the info gap won, 3-2.

An info gap is an activity where students are given either a data card and a problem card. The problem card person has to work with the data card person to get the task finished. This task turned into more of a pair exploration because I didn’t explain that the data card person is supposed to be a tough guy, but that was ok. The info gap we worked on had an unfinished graph and on the problem card, and a table with a couple of values on it. The students with the graph knew they needed the data from the data card, and they asked the questions to get that information. The students with the tables though they had a task of their own, to make set of larger points out of the small set of points they were given. They were each working on making a representation of the same linear relationship, but they had different tasks. This allowed them to genuinely help each other, without merely copying. Is this what was supposed to happen? I don’t know, but I do know we are doing some more info gaps before this cycle is over.

Today was the first day of class! Again! One of the things that’s great about our school is that every 9 weeks we start again with new classes, new kids, and essentially a clean slate. This provides our students an opportunity to have a lot of “at bats” but it also provides our teachers with fresh swings as well. This is good because I could definitely use another set of swings.

Last cycle’s class came with a jarring set of disruptions. My wife had our second child, about 2 weeks earlier than expected. Adjusting to baby Isabelle was the headline reason for my difficulties last cycle. Additionally, I was teaching a curriculum that I didn’t really like (irony alert: it was my curriculum from 4 years ago). I haven’t blogged or tweeted much because I’m short on time, and a lot of the time that was left I devoted time into starting an admin blog which no one really reads. I’m not really big on trying it because it’s hard to be honest and clear when talking about admin work, but that is a whole other post. Last cycle was also difficult for a number of other non-infant related reasons, so cycle 2 represents a welcome a fresh start.

This cycle, like every new cycle, is a clean start. In most of my blogs I get pretty excited about new cycles and this is no different. This is essentially the start of the year for me. My first cycle course was a course that I didn’t modify too much because someone else would be covering it for me at some point in time. This time it’s more or less brand new from the ground up and also incoporating all of the new things I learned from TMC, TMC-NYC, the MFA Big Think, and the wonderful firehose of ideas on the #MTBoS. Planning is a lot like a game of sudoku. With only 22 days of class this cycle and a solid 6-8 days are going to be needed for work time for kids I’m trying to be more deliberate than ever to fit things in. I’m picturing 3 5-day cycles where I am going to bring up Proportional Relatinoships, Linear equations, piecewise equations, and I’ll try to hint about exponential functions along the way. Each cycle should look like the following:

Day 1 : Opening task. This would be a problem, in the PBL vein that introduces the math that needs to be studied in a rich context. The students will work together on it for most of the period, and complete some kind of exit ticket that can help me plan what’s next.

Day 2: Gather Questions. This could look like a circle, or an instructional routine, or some other activity, but it is to get the students to start to generalize away from the first day’s task. As issues of notation and vocabulary come up, I want this to be conversive, and I want introduce kids to formal vocabulary.

Day 3: Problem Set. On this day I want to have students finish a bunch of different problems. We could have an “important stuff section” that they work on and share out that day. Then students can try their other problems and share them out later.

Day 4: Share out from problem set & practice. So on this day I’ll ask the class to share out more of the interesting problems from the problem set, they can then do another instructional routine, and then do another big exit ticket.

Day 5: Project: Students will work on a portion of the project that is for the end of the class. This portion will directly involve the math we used this week. It will also provide a space for student to reflect on what they have learned so far.

Friday was the first day of the class, and it was pretty exciting. Only 5 kids showed up out of 15, but they were all pretty excited. I was actually doing a really good job until the end where I mistakenly used the wrong gender pronoun for a student and now feel like a jackass. Aside from that, it was a good start to the cycle, let’s see if I can get a post up after each class!

Rochelle Gutierrez is one of my personal academic rock stars. Since I saw her close out Shadowcon16 I’ve held her work up as what I needed to learn more about, and what I was so glad that people were doing. While I haven’t had time to read as much as I’d like, listening to that talk, and her Global Math talk was very powerful. Both challenged me to do more for the student populations that I serve, and comforted by the fact that researchers in the field are out doing work to challenge people like me.

Not everyone appreciates challenges, however. In a recent work, Gutierrez drew a number of connections between math and whiteness, which sparked the ire of a number of people. In response, critics led a tiki-torch parade across all media platforms with Fox News itself sparking the rally. Their main argument, it seems, is that whiteness should not be challenged.

While I don’t know the full detail of the argument, I want to make it clear that whatever side Rochelle Gutierrez is on, will be the side I am on. The idea that someone can pick apart a scholars work because it doesn’t match with your beliefs is an assault on all scientific disciplines. Without science, we as a people lack a firm way to connect the problems that plague us to solutions we would need to create. The clearest example I can think of, was the achievement gap, which has been the goal of our country since the at least the 90s. It has made less and less sense to me since the phrase became popular, but when I began reading the articles around this controversy, I made the connection between the gap, and this mathematical trend towards whiteness pretty early. “Why should the non-white people’s goal be do what the white people are doing? What if they should do something else?” But I thought my ideas were on the fringe. Listening to Rochelle’s work made clear that there was a connection, and there was a way to utilize the truth in that connection between Whiteness and Math to improve outcomes for students. Making these kinds of connections are important to making progress with math, or with science, or to make a more perfect union. The right for people to make connections, create knowledge, and push their field further is something that shouldn’t be threatened.

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So I originally sat down to write a post about this last week. The draft was about as long as this, actually. But it sat in my drafts folder next to posts about Charlottesville, Betsy Devos, and other things that haven’t gotten posted. When I come around to edit these kinds of posts at some point I let life’s business and distractions get in the way from my pushing the send button until it never gets pushed at all. It happened so often that I decided to give a talk about it at TMC, not as an expert, but as someone trying to figure out the answer. In this case, I am hitting send. In part because I have time, and because of this poem, and the fear that things like open expression, and anyone pushing the send button, is at stake if this kind of intimidation is allowed to go unchecked.

If you are interested in teaching a captivating historical mini-project with linear equations that can be easily adjusted to fit your unit plan. This project is centered around the historical account of a successful slave rebellion that took place onboard slave ship The Creole in 1841. Students make decisions about where to steer the commandeered ship so that 100+ slaves can find freedom. Students use different linear representations and can also find the solution of a system of two linear equations.

Let’s walk through the different parts of this project.

Introduction and Bonus Problem

The project introduces the story’s hero Madison Washington, a slave working on a plantation in Virginia, in this first part. This section is important for making sure the students understand the scenario, and there is also an interesting open-ended problem. The problem that asks students to find the number of Quarters and Dimes in a bag when given their total value, and the total number.

Having a problem at this point begs the question, “Why are you starting the project with an open-ended problem that isn’t necessary for the rest of the project?” Beginning the project with an open-ended problem is something that can help students think about some of the ideas that will come up later in the project. Having students work on the open-ended problem can give you a chance to ease students into creative thinking, using mathematical practices, and making connections. Students can work on the problem in a variety of ways, and it might be valuable for students to begin the remainder of the project feeling confident about their ability to forge their own mathematical path. This kind of problem is one that has been presented in other ways, and you can find ideas in Dan Meyer’s post, and in the comments, from when he wrote about these kind of problems. Finally, it is also something that can be omitted if there are fears the project is going long.

Part II, III, & IV

In this section of the project the main character Madison is taken as a captive on to The Creole. Within a few days he and the other captives take control of the ship and Madison must decide where to sail the ship. For the captives to avoid returning to slavery, they will need to find a place that isn’t in the United States, and then calculate the amount of time it would take to get there.

For students, this part of the project involves measuring with a ruler on the attached map and perhaps some prior knowledge of world geography. Students will want to take the ship to places all over the map and I’ve found it’s good to let them try any of them. Students who choose to travel a really long distance won’t succeed, and that’s OK. They will use and demonstrate the same mathematics as the people who pick safe locations, and add more variety. So encourage them to explore. I typically say that they can’t pick the same location as their neighbor for the sake of variety and to check against plagiarism.

Students will also have to convert the millimeters on the chart to miles. Depending on your students, this conversion may be something you want to scaffold, perhaps with a mini-lesson about changing units. If this is too much support for your students, try removing the box with the conversion ratio.

Students will then have to use a table to make an equation for the ship’s progress. This will require them to think through how to find the speed of the ship, or the slope of the equation, and also the y-intercept. The y-intercept is negative, which may be confusing for kids. The idea that the boat would cover less ground on its first day makes sense and there are a lot things kids could say (i.e. maybe the boat started off slow, maybe they took some time to load on the first day, maybe they went the wrong way first and turned around). This is a good opportunity for the students to make sense of the situation and compare the model to the situation, not merely write down the negative number because that’s what it is. Look for students to write something on the lines below.

The final question of this section asks students to recall the distance they measured, and use the equation to determine how many days it would take them to figure it out. Be on the look out for students who want to continue the table from above and keep filling it in until they get the distance.

Part V

In this section of the project, students use a linear function to see if The Creole can outrun the faster Navy ship with only a 5 day headstart. The story says that the Navy Boat travels at a rate of 42 miles per day, and they have the urge to make an equation similar to the one from Part IV. The Navy ship could be behind The Creole, by 5 days, so that means this equation needs a constant term. Students often get confused on what amount this should be, which is five days of travel. Understanding why the sign of this coefficient has to be negative is an important things for students to understand and explain as well. Once they have this equation, students can use this equation to first, see if the navy ship could beat them to their destination. If the numbers work out right, student who chose very far destinations will find that the Navy will beat them to their destination. This naturally leads to the next question should be: “where would the two ships meet?”

Part VI

In the last part of the project, students need to find where the ships would meet if they were to keep travelling according to the two equations that have been created. Sometimes students have already figured out 1 or more methods to solve a system of equations, but if that is not the case this is still a good question for kids to explore. At this point in the project the students understand the two equations, and what they represent. It would be a great time for these students to play with the idea of finding the solution of a system of equations and would set the stage for exploration in future units. If this project is meant to be an assessment of linear equations, then the students have already shown their abilities with regards to that in the previous sections. Students who lack practice with an algebraic approach can try using a table, or an organized guess and check, and in the process learn why an algebraic approach would save so much time! So this part of the project is valuable for any students who were able to complete all the work up to this point.

For all students at the end, there is the question of whether it would make sense to keep travelling towards their same destination. Yes, a Navy ship might not be prescient enough to follow the students all the way to their destination, but the idea is to make the best decision. This section helps the Madison Washington decide the best choice and offers another opportunity to see if students are making sense of the situation.

Alternate For Parts IV and V

In writing this up, it seems like it make a lot of sense to make the equations solve for the distance remaining in the journey, not the distance traveled up this point in the journey. This would be cool because then students would each have a different value for their equations and would make things more unique. I haven’t actually taught this version, so I made this a separate google doc with the slightly re-worded questions about those equations.

Conclusion

As the project ends you want to tell what actually happened to the ship. This video does a really good job of highlighting the themes.

Project Notes

This is the project that I used to do a long time ago in a school that was far, far away. I think there a lot of things that I could do differently with the project if I were to have more time, but I don’t teach this unit anymore, so I haven’t had the chance. I would love to hear any ideas you have about the project so please let me know your thoughts in the comments!

This project could lead to a interdisciplinary exploration of other topics around slavery from that era. Many topics could be tied into this project, so it may be good to think about whether your history teacher, or your english teacher, or you want to include additional information on topics like the fugitive slave act, the slave trade, the 3/5ths provision of the constitution, and more.

The information is pretty historically accurate. However, In October of 1841 when the ship left the port, there was still slavery in many parts of the world, but not entirely. I haven’t done all of the research to know whether the slaves would have been granted their freedom if the Creole theoretically landed on any country that a student might choose. Allowing students to choose ANY country that isn’t the US and expecting freedom might not reflect what actually would have happened if the Creole landed there.

This project also has A LOT of text. This may pose problems for ELL, or students with learning disabilities, or just kids who don’t like reading. The idea was that having a story could be as engaging, perhaps as engaging as a video, and hopefully that story can drive students to follow through with the project. It can be really easy to throw the story out as you modify this for your population. Definitely make the adjustments, but please keep enough of the story to help your students emphasize with Madison’s plight.

As always, if you use this, please let me know what you think in the comments!

I was super lucky to do the Reimagining High School Math morning session with Sadie Estrella. This session first came to be with a conversation on the eve of the TMC deadline. We spent the next 20 minutes polishing up a draft proposal. A few weeks later we found out we were accepted and we […]