## Carl's Teaching Blog

#### Category: Math Resources (Page 1 of 2)

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.

### Voyage of the Creole (google drive version)

Map of Americas from eduplace.com

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 still feel kind of weird saying this but, I just gave a keynote at Twitter Math Camp! Actually I gave it a day ago, but I had to process the whole thing, travel home, and help @BwalkerQ get his blog up and running. So anyways, here is the stuff from the presentation for anyone that is interested, and a little explanation of my process after that.

#### Presentation info

Video:

Slides:

Periscope:

Forgot to put this up easier. Thanks to Sadie Estella for recording this!

Desmos Activity:

The people at Desmos gave this one some extra juice, so I can’t share the activity builder yet, but if you want, you can go through and participate it in here.

MTBoS Roll Call

This website links the pictures of people with their first time posting on #MTBoS. This is a temporary thing, as the data is going to get stale, which you can see in the missing profile pictures, so check it out while you can!

Pre MTBoS Interviewees

I was super lucky to be able to interview Andrew Stadel, Christopher Danielson, Michael Pershan, Sam Shah, Dan Meyer, Fawn Nguyen, and Sadie Estrella. whose quotes are included in the presentation in that order. They were super generous with their thoughts and their time. I didn’t mention them on the slides because I wanted people to focus on the words, and not where they came from, but I am very, very grateful.

MTBoS Data

For this talk I used a chrome extension to scrape information from twitter’s website. Twitter doesn’t have a way to get your old tweets, unless you just want to download your own tweets. The scraper led to some errors, and my data isn’t all that great, but if you’re interested in playing around with it, I have a database that I can query with other questions.

#### Summary

Sharing your teaching online in a community like the #MTBoS has lots of research-supported benefits. Potential new educators are often hamstrung by lots of barriers, the biggest of which seems to be feeling like they are not ‘Whatever’ enough (Witty, photogenic, cool, smart, etc.). Data on #MTBoS hashtag shows that these problems haven’t stopped the #MTBoS from growing much larger especially in recent years. A set of interviews with teachers who shared years ago described a community of support, comfort, bravery, and a commitment to reflection, feedback and learning. Lastly, my own journey to sharing online illustrates how important connecting with people are, and asked the audience to think of new ways to make connections for other members of our continually growing community.

#### Takeaways

My whole plan was to make a big twitter chat, and it worked! Except that the twitter bots came on strong at the end and after the #pushsend hashtag started trending. It got more popular than anyone imagined, way too quickly, and now we have to figure out ways to make sure people’s voices didn’t get lost. Seemed fitting.

I got Sketchnoted!

This whole process left me feeling very vulnerable, and also very supported. Thanks to Lisa, Tina, Kate, Ben, All the people I mentioned earlier, and everyone else who helped me with this. I learned a tremendous amount from the process of making this talk and I’m forever grateful.

I like the idea of a sneaky project, that creeps up on kids. For example, I’ve started a unit project by asking my unsuspecting students the following question on the board:

What would you do with a million dollars?

The project, linked here, leads students to learn about budgeting for an economics class I taught. Students reply to this with the typical fantasies.

I’ll buy a new car, and some new Jordans, and a new house!

But by adding a few caveats, we’re able to grab all of these kids wildest dreams and smash them against the rocks of reality. The main caveat is that students have to survive for 20 years off the million dollars, and they have to pay taxes. They first have to choose whether to receive the money all at once, or over 20 years. Kids immediately go to calculating the tax bracket and realizing that receiving all the money at once means you pay much more in tax compared to having the money split up over 20 years. At this point I tell students to opt for regular payments (although I imagine an interesting side story might be to take the money upfront and try to invest it in a stock market simulator to see if they can earn back the original amount).

From this point in, students have to figure out how to live on 50,000 a year. This is pretty close to the US national Median income, so it should line up with what they’ll make as soon at they enter the work force.

So then I ask them to think through what they would do with that 50,000 yearly amount, and make them budget how much they would spend on all of the following things:

• Clothing
• Household Products
• Furniture
• Utilities (heat, electircity…)
• Inside Entertainment (Cable/netflix/music/videogames)
• Phone
• Gas
• Health insurance
• Life Insurance
• Outside Entertainment
• Anything else…

Once they come up with these numbers, I have them put it all in a spreadsheet that gives them little suggestions of websites to use to estimate all of these amounts. The final thing I have them do is write a little paper describing what they did with the money.

If I had more time I would have them actually learn the mortgage formula ahead of looking for houses on Trulia, and use the mortgage formula to estimate a range of houses they want to look for. My kids used the estimators on Trulia and Zillow, which assume a down payment, and also don’t let the kids use their brains, so I would like to not depend on those.

This year there was a pretty spectacular conference in the hills of Berkeley California that brought a number of people who are involved in Developmental Math including Deborah Ball, Bill McCallum, Hyman Bass, but mixed among them were some lesser known names including Gregory Larnell, and a scene stealing group of high school math teachers from NYC.

The Mathematical Sciences Research Institute (MSRI) is a magical place in the hills above the University of Berkeley near the Lawrence Hall of Science.  It’s home to a group of academic researchers who work on their research from the inside of a beautiful complex, largely funded by MFA creator Jim Simons, which plays hosts to a number of national conferences with various focus on a yearly basis.  The annual Critical Issues in Math Education meeting was held in March and had the focus of “developmental mathematics at two- and four-year colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels.”

In my last class I focused a lot on proportional reasoning, and at the end of March I wanted to give the kids a project that would be rich with a lot of different examples of the topic.  My original idea was to do a theme based on turning a beat into a song, but it seemed contrived.  Frustrated, I headed down the street to the only empty grocery store, and thought about how all the prices there were really high.  Suddenly a flash of insight hit.

The students can take down their expensive local grocery store!

Kids can imagine a product that they like to sell, and then look up how much cheaper it would be at a warehouse store, and compare the difference in prices.  Then students can use evidence from their local store to estimate how much money they would make from a day of selling the products, and then scale what the products would make over a month.  I went back home and scribbled a bunch of notes about the idea with a Doc-Brown-Esque level of enthusiasm, but I didn’t really put together a polished task until last week.

Here is what I gave kids, although I really wish I could have made it better.

• It is a pretty straightforward task whose end goal makes enough students that all students can really understand what their end product should mean.
• Students need to use proportional reasoning in so many different places that there are countless numbers of places to discuss it.
• Since all students can do different products at different stores, the entire class can come up with different project results so there is no copying fear.