My Favorite Problem for Launching a Systems of Equations Unit

I love launching our 8th grade Systems of Equations unit with this math problem from an 1885 math textbook:

 “A horse thief riding at 8 mph has a 32-mile head start. The sheriff in pursuit is riding at 10 mph. In how many hours will the thief be overtaken?”

From The New Arithmetic, Seymour Eaton, 1885

Why? Because it elicits so many wonderful strategies that we return to time and time again during the unit.

Launch: Slideshow here

I tell kids that we are going to start the unit by tackling a problem called “The Horse Thief” from a math textbook from 1885. I present it without numbers at first and ask someone to read it aloud. Then kids turn and talk, so they have an opportunity to process the problem with a partner. Just for fun, I also ask three kids to help act it out. I narrate as they chase each other around the room.

Next I emphasize that the answer is the least important part of their work today; the real goal is to develop as many ways as possible to solve the problem and to make their thinking visible. Lastly, I fill in the blanks, and kids get to work. I’ve had them work on handouts, newsprint paper, and white boards.

Work Time:

Some questions I ask while kids are working: 1. How do you think we might approach this? 2. Are there any strategies we’ve used this year that might help us? 3. Can you recap what’s happening here? 4. Where would they both be after 1 hour? How do you know? 5. Approximately how long do you think it will take?

Strategies my students have developed in the past:

  1. Three-column table
  2. Two tables
  3. List
  4. Graph (To encourage this, visit some stuck kids and drop off the graph paper as you ask, “Could graph paper help?”.)
  5. Equation
  6. Double number line
  7. Dividing the distance between them by the difference in their speeds

Share Out:

I pick a couple of students to explain their strategies. I typically have them present in the order: table, graph, and equation because those are the primary strategies kids will use throughout our unit.

The beauty of this is that we can continually reference these strategies throughout the unit as the kids tackle new problems. It’s a great anchor activity.

Follow up questions:

In my experience, kids don’t typically represent the story with two equations on their own, but this could be a way to introduce the idea of a system of equations by showing them the separate equations and highlighting how the graph has two lines and how we needed two tables.

If you use this, let me know how it goes!

Always happy to hear from readers!