SWBAT to make meaningful comparisons with large distances

We can use the concept of distance, rate and time to add context to large numbers.

10 minutes

This project gives students a creative option to play with large numbers and distances in scientific notation.

I share the first paragraph of this article on Long_Distance_Relationships to start the conversation. The rest of the article is distracting, but *mostly* appropriate for middle school. If you want to have them review the entire article with your students, make sure you do a bit of censoring.

The premise of this project is simple: "How long would it take to reach your partner if they lived in a distant part of space?"

I ask students to work in partnerships and pick a location and method of of travel.

I give students these three links to pick their destination:

They can choose any reasonable method of travel. For example, they can fly a rocket, drive a space car, ride at warp drive in a space ships or even ride a bike. The basic rule we will follow is that the method of travel has to be linear and can not involve worm holes, dimensional shifts, etc.

Even though our travel times will be based on a made up premise of traveling in space with any vehicle we want at an average speed based on vehicle performance, we don't want to allow a method of travel that reduces the actual distance. Instead, we only allow methods of travel that go really fast or slow through the distances required.

During this project, students choose a location to travel and then tell us how far it is, how long it will take to get there and their thoughts on how much the trip will cost.

**Article Source**:

25 minutes

This is a project that students begin in class and finish at home. They use computers during this work time to search for a distant location and find a few methods of travel to get there. I place some useful links on my website for galaxy locations, but they can use any acceptable website to find their method of travel. However, I ask that they cite their sources. For citation guidelines, I always ask the humanities teacher for updates. I use the same format and expectations for this project that they would have in a research project in humanities. The goal is to be consistent.

For students, the goal during this 25 minutes is to find the information they need and begin saving critical links. I let students work on the main goals of the project without yet giving any detail (unless they request it). I usually give the hand out at the end of class, since they need some time to work with this project before they recognize questions.

I used to always give all the information upfront, but I find that this overwhelms many students. Instead, I give the information out to those who request it and then give it to everyone at the end of the session.

My goal during this time is to circulate and to listen. I want to hear the students' ideas for modeling the cost, time and distance of an interstellar trip. I record great ideas on the board and quote the students as they work. This helps me lead a meaningful conversation at the end.

20 minutes

Projects are a great opportunity for students to engage in mathematical practices. In this project, they need to be precise in their work, to model an abstract problem, and to argue about the validity of their algorithms. I use today's summary time to highlight mathematical practices as we review some of the ideas students have already generated about the project.

I start by reviewing basic expectations of the project and give out this hand out: Long Distance Guidelines. I explain each step and give examples of what it means to "show your work." I make sure to model this process, because every teacher has different expectations around explanations. My expectations are very high and want students to understand what I am looking for.

The toughest step for many is modeling cost. Many students are looking for the "right" answer, when in reality they are only modeling a range of possibilities. We don't know what this trip would cost. Even if it were a real trip in a real space vehicle, there are many unknowns. In this project, students get a chance to deal with the unknown.

I give students about a week to finish this project, but ask them to work individually and at home. Students can stay in for lunch or after school if they want help. As always, they can email me at any time if they are stuck with some part of their project. Partners can help each other (since they chose the same destinations and methods of travel), but each student submits his/her own work at the conclusion of the project.

I finish today's class by giving out the rubric and explaining how I will use it in the grading process: Long Distance Relationships Rubric.