Race Training and Slope – 8080

Jen Perego, Deep Run High School

Summary

To begin the lesson, students view several images of hills and rank in order which of the hills they would want to run/walk. The student justifications lead into a short discussion on “steepness.” After this short discussion, the teacher asks the students to rank the hills in order of “steepness” and justify their responses. In pairs, the students use ActivInspire tools and an online manipulative (which allows the students to adjust the slope of a linear equation) in order to create a formula or process to calculate steepness. Students share these processes with the class and the teacher provides direct instruction on calculating slope.

After students sufficiently understand the idea of slope, they use Google Earth to locate hills in their neighborhood that a runner could use to “hill train” in order to prepare for a race. Students locate three “hills” and use various GoogleEarth tools, including elevation profile, and their knowledge of slope in order to mathematically justify which of the three hills would provide the best opportunity for hill training. Students share these hills and their processes with the class. For homework, the students are asked to think of a problem in their life that involves slope. The students explain that problem and describe how an understanding of slope could help them solve that problem.

The following resources provided a helpful foundation for this lesson:

• Staircases and Steepness – Blog Post by Fawn Nguyen
• Desmos Investigation – Blog Post by Mrs. Hester

Lesson Reflection

Teacher:

“I’ve always wanted to do stuff like Dan Meyer, and I feel like this task was a step in that direction, but could have been more abstracted. I think the videos of running the hills would be a better hook for the students and abstract the task more before giving them the pictures of the hills on the worksheet.

I thought the ActivInspire Flipchart really added to the lesson and I thought the students came up with extremely clever ways of solving the problem that I would never have thought of.

Several students made some great visual observations on steepness and I think it helped the class to talk about the various methods to solve a problem.

When we completed the Day 1 worksheet, 1 group approached the hill problem as if they had to run the hills all in once race. They ranked the hills in the order in which they would want to run them during the race, and used steepness to justify their explanation. When I do this lesson again, I think I will talk more about how you train for a race and how it is a progression and weave that context into the lesson.

I didn’t anticipate the negative slope when students made their paths downhill instead of uphill. I liked how it lead to a discussion, but had I been more prepared for that to happen, I would have been able to ask better questions to the students. We changed this lesson initially to mainly focus on positive slope, as it was designed to be an introduction to the concept, but maybe I could change this lesson for the future so that it incorporates a more thorough and overall understanding of the concept.

While completing the Google Earth Activity, some students made their first hill short (Google calculated the total distance in feet) and their second hill really long (so Google calculated distance in miles) and comparing ft/ft and ft/mi for “steepness” does not work! Next time I complete this lesson, I will make sure to have students create short paths. With a more advanced class, I could take the time to show these different examples and discuss how you would need to convert to like terms in order to make a proper comparison, but I don’t think it would be appropriate for struggling students.

Overall, I think the lesson went well and I’m looking forward to referring back to the activity when we learn about the slope equation. I think that this activity helped students see the subtle “look fors” when determining slope of a line and truly make sense of slope.”

ITRT:

“Originally, the teacher and I wanted the hook for this lesson to be video based. Instead of beginning the lesson with several pictures of hills of varying steepness, we wanted to have several videos of an individual running on streets of varying elevation. We wanted to use the videos to have the students discuss which of the segments they would rather run and justify their answers. I taped myself running several hills using a GoPro, but due to an unstable mount we were unable to diagnose the steepness of the hills based on the video.  I think these videos would really do a much better job at hooking the students into the lesson, and provide them with a better vision of why slope really matters. That said, I think the way we began the lesson still worked very well, but it could have been better.

The teacher and I decided to complete two separate “discovery activities” within this lesson rather than just one. The ActivInspire flipchart with the pictures of the hills and the Desmos manipulative serve very similar purposes – both are integrated into the lesson so that students can develop their own methods of “investigating” steepness and visualizing slope. We could have developed a scenario in Geogebra that combined the aspects of both the aforementioned tools, but I think separating it into two sections was the correct thing to do in this scenario. The ActivInspire chart on Day 1 really abstracted the task, while Day 2 focused more on what slope looks like in a mathematical context. This lesson was originally completed with remedial students, and separating the two activities seemed to help with understanding.”