A new school year has just begun and I’m on both sides of it as a teacher and as a student. My graduate class this semester started with a discussion of different types of problems that exist; well-structured, complex, and unsolvable problems. To simplfy describe them well-structured problems have one best solution, complex problems have many things to use in order to solve it in many possible ways, and unsolvable problems are self-explanatory – they can’t be solved. These unsolvable problems are also mentioned as wicked problems and often the “solution” is just the best that you can come up with at the time with the information possible. These wicked problems can exist for may years, with new “solutions” replacing the past “solutions” when more time and knowledge is available.

This week I thought of well-structured and complex problems present in the area/perimeter unit of Geometry. I will work with a couple Geometry students in my virtual Title 1 classroom and I want to use a mix of well-structured and complex problems to help them learn the material. The complex problem that I adapted came from an activity I did my first year of teaching in West Virginia. I was in a more traditional brick-and-mortar school teaching mainly Geometry to 10th grad students. I handed students a piece of graph paper, instructions, and told them to design a dream house using all polygons that we had learned. They then “bought” material from me in the form of scrapbook paper and determined how much it would cost to cover the floor in their dream house. Students enjoyed this project and I heard a lot of good conversation around the room about how to solve for the area of each room and then the cost of each room. However, I am a virtual teacher now and I can’t complete this activity in the same way.

My park created using Floorplanner.com

I am happy to say that I found a free program that will help me complete this complex project online! Floorplanner is a free tool where you can search for items and then create a layout on a grid from a top facing view. Using this tool students start with a blank grid on the screen. They can then search for items to place on their grid to show their park layout. I searched and found a circle pool, a hexagonal gazebo, a rectangular park bench, and more! I would also allow students to design something other than a park if they desire as long as they place different polygons into the area. With Floorpanner I am able to complete this project in a virtual environment and students can share their work online with each other. With the program being a free download all students in my class can have access. Students can get immediate feedback from me and their peers on their project rather than having to mail in a physical model and wait for me to receive it and critique it. Floorplanner also will allow students to quickly change their design plans by just clicking and moving their object instead of having to literally cut and paste or redraw their object.

Complex Problem: Use Floorplanner to design a park with 10 structures located in it. You must have a structure with a following shapes: regular polygon with 5 or more sides, rectangle, circle, and square. Use your floorplan to design your dream park and then determine how much sod you will require to cover all open space with new grass.

(That video was created using Screencast-O-Matic – which is a wonderful free site that I love! I have my students create these and send them to me throughout the school year because they are so easy to create and share.)

I’m excited to see how their project will work out this year! Students always find many ways to solve this complex problem and they learn a lot from discussing their ideas with their peers. I’ve had students determine the area of the whole park and then subtract each object’s area. I’ve had students “cut” up the grass area into easier shapes and figure out the area of each before adding them together. I’ve had students approximate with the boxes on the grid paper and then defend why approximation will work well for purchasing sod. The fact that there is not one correct, or even best, way to complete this project is another reason why this classifies as a complex problem.

I could see this work in brick-and-mortar classrooms as well with 1:1 technology, partners, small groups, computer labs, or done as my original paper idea. If you try this out with Floorplanner or have done something similar before in your classroom I’d love to hear about it below!

One thought on “Complex Problem in a Virtual Geometry Classroom”

Hi Stacey,

I just wanted to begin by saying that I admire your ambition and courage to teach a virtual math class! I’m interested to hear how that goes throughout the semester as I’ve always wondered what it would be like to teach a Spanish class online.

After reading your blog post and watching your screencast, it sounds like you will be able to address both well-structured and ill-structured problems very well with the help of technology. I’ve never heard of the site floorplanner.com but it reminded me of a tool that we used in CEP811 last spring, SketchUp 3D. From the looks of it, the one that you chose to use looks as if it might be a little more intuitive for students to use which will be very beneficial. Also, I love that it gives students autonomy with their choice of what to design and as you said, there is no right or wrong way to go about creating their park or figuring out how to measure the different areas, there are just multiple ways to do this. They have a lot of options as to what they create, how they use the site to accomplish this, and how they go about measuring the area of each shape they use. I could see how this could create a lot of discussion between peers and create excitement for students when they are able to figure things out and produce their end product.

Given that I am a language teacher and consider myself a novice when it comes to math, this seems like a very fun, interactive way for students to explore the topic at hand. As you mentioned in your post, I also like that this allows for students to change their projects easily as well–without having to deconstruct an entire physical model to make adjustments. This is a great tool for students to see the results of their project quickly while also easily sharing their work with both the teacher and their peers to receive feedback. I would love to see some of the outcomes of this project now that you’ve adapted it to use floorplanner.com and see all of the differences and similarities that will be displayed in the student’s work.

When you described the complex problem back from when you taught in a physical classroom, I could easily see how students can measure the area of their designs using multiple tools or ways. Besides having the students look at the graph paper that floorplanner.com provides, what are some other ways that students could go about measuring the area of the different structures? Again, given that I am not a math person I would just be interested to hear all of the different solutions that students come up with because I know how creative they can be.

Good luck with this project and I hope you have fun teaching your virtual class!

Hi Stacey,

I just wanted to begin by saying that I admire your ambition and courage to teach a virtual math class! I’m interested to hear how that goes throughout the semester as I’ve always wondered what it would be like to teach a Spanish class online.

After reading your blog post and watching your screencast, it sounds like you will be able to address both well-structured and ill-structured problems very well with the help of technology. I’ve never heard of the site floorplanner.com but it reminded me of a tool that we used in CEP811 last spring, SketchUp 3D. From the looks of it, the one that you chose to use looks as if it might be a little more intuitive for students to use which will be very beneficial. Also, I love that it gives students autonomy with their choice of what to design and as you said, there is no right or wrong way to go about creating their park or figuring out how to measure the different areas, there are just multiple ways to do this. They have a lot of options as to what they create, how they use the site to accomplish this, and how they go about measuring the area of each shape they use. I could see how this could create a lot of discussion between peers and create excitement for students when they are able to figure things out and produce their end product.

Given that I am a language teacher and consider myself a novice when it comes to math, this seems like a very fun, interactive way for students to explore the topic at hand. As you mentioned in your post, I also like that this allows for students to change their projects easily as well–without having to deconstruct an entire physical model to make adjustments. This is a great tool for students to see the results of their project quickly while also easily sharing their work with both the teacher and their peers to receive feedback. I would love to see some of the outcomes of this project now that you’ve adapted it to use floorplanner.com and see all of the differences and similarities that will be displayed in the student’s work.

When you described the complex problem back from when you taught in a physical classroom, I could easily see how students can measure the area of their designs using multiple tools or ways. Besides having the students look at the graph paper that floorplanner.com provides, what are some other ways that students could go about measuring the area of the different structures? Again, given that I am not a math person I would just be interested to hear all of the different solutions that students come up with because I know how creative they can be.

Good luck with this project and I hope you have fun teaching your virtual class!

Lindsay