Each year, my colleague Jarrod and I tweak our geometry curriculum with the intent to improve and build on the previous year. Some years we make major changes, such as an overhauled grading system. Other years we integrate new technology. (This year, another colleague [Adam] is teaching geometry as well.)
One of the goals of our high school is to improve student engagement. We (the geometry teachers) are trying to implement more problem-based activities into our classrooms. We've had great success each spring semester with a Floor Plan project. We wanted to create a project for the fall semester that met these checkpoints: low floor / high ceiling, open ended, (semi) real-world application, and connected a number of learning targets together. Additionally, we knew that we wanted to build something that we could expand on in future years, specifically to be able to connect community experts / partners with our students.
In our HS geometry curriculum, we focus on writing the equation of a circle and finding areas of sectors. In years past, we would not cover those topics until the spring semester. However, last year we moved the target of writing the equation of a circle into the first semester. In our first unit, we revisit the Pythagorean Theorem, derive the distance formula, and then write the equation of circles on a coordinate plane. This year, we decided to also move the concepts of arc length and area of sector into the first unit. (We treat circumference and area of a circle as prerequisite skills that students have learned in middle school.)
We were intrigued by a Desmos activity called "Water the Lawn". In the activity, students are asked to place sprinklers at locations of their choice in order to cover a rectangular region that represents a lawn. (Take a peek.) The Desmos activity primarily focuses on finding the areas of circles. We needed to make the activity more challenging and aligned to our HS learning targets. Let's dive in...
Task:
Install a sprinkler system in the yard of the given diagram. (Link to diagram)
1. You must water the entire yard.
2. You must stay within the boundary of the yard.
3. Overlapping areas are necessary. The amount of overlapping area must be less than 3000 sq ft.
Requirements:
1. Neatly sketch (using a compass, ruler, & protractor) your plan on the blueprint.
2. For each sprinkler head, you must find the following information.
On the Lowe's website, we found three different types of sprinkler heads. (Note: the two bigger sprinkler heads had minimum degree restrictions. Also, none of the heads have a radius between 16 and 18 feet. This created a bit of a challenge for students.)
We showed students an example (albeit, a bad example because of too much overlapping area) to help get them started.
And that is it! We gave students 1 full block day (90 minutes) to work on this project in class. It was then due one week later.
Results:
I was very pleased with the overall results of the project. Here are some examples of what students created.
Student Reflection:
At the conclusion of the project, we asked students to reflect on their experience. In an email to their parents / guardians & their geometry teacher, students had to answer the following questions.
1. What are two things that you learned by completing the project?
2. What was the most challenging part of the project for you?
3. What piece of advice about completing the project would you give to future geometry students?
4. What do you think the geometry teachers could do to improve the project for future classes?
Here are a few quotes from the student emails:
- "If I were to give advice to future geometry students about this project, I would tell them not to overthink the goal and try ideas first. When I started this project, I found myself thinking too hard and not trying the ideas I had come up with because I feared the area of overlap would be too great. After finishing the project, I was under the maximum requirement of overlap. I should have carried through with my other ideas instead of trying to make it perfect."
- "Two things I learned from this were that building sprinkler systems are hard, and even when you think you can’t solve the problem, you can."
- "This project allowed me to learn quite a lot, and I enjoyed it. It made learning more exciting."
- "It is also fun to be creative with this project. I found that it was useful to use other angles besides 90, 180, 170, and 360-degree angles."
The students gave us some great ideas on how to improve the project for next year. One common suggestion is to have a budget on the cost of the sprinklers.
Future Years
We think it would be great if we could have a professional landscape specialist from the community be a part of this project in the future. The community expert could potentially help launch the project by providing greater details about how sprinkler systems are installed and bring some of the sprinkler heads for students to see (and maybe learn about how they restrict the degree of spray). Or, we could have students present their plans to the landscape specialist and they could provide feedback.
Final Thoughts
Overall, I'm happy with the first year of the project. Students applied areas of sectors and wrote equations of circles, which met our learning targets. They also improved their skills with a compass. I look forward to improving this project in years to come.
I do understand the project has its limitations. I mean, come on...who needs to design a sprinkler system that doesn't extend a little outside of the boundary of your yard? What if the wind is blowing hard one day? Isn't the water going to leave the yard a bit anyway?
If you're interested in any of the files we used, enjoy!
