Complex Problems

Complex Problem in a Virtual Geometry Classroom

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.

Complex Problems

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.
Floorplanner Dream Park

My park created using

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!
1. Celestine Chua. (2013). Problems. Retrieved August 31, 2014 from Flickr:
Musical Room Lesson Plan Word Map

Musical Room Open to All Students

This week I learned a lot more about the principals of UDL (Universal Design for Learning). UDL is all about adapting your classroom for all learners to ensure every student gets a fair opportunity to learn. Fortunately, all the changes that you make to your classroom to help some students ends up helping all students. Schools that have easy access to text-to-speech applications helps dyslexic students, ADD students, auditory student, hard-of-hearing students, and more!

To really immerse myself in these ideas I was asked by my CEP 811 course to look back over a lesson plan I created a few weeks ago and make changes that help all students. If you’ve been following my blog you may remember the lesson that I created where students worked together using a MakeyMakey to create an interactive room for guests to walk through and interact with. If you want to remind yourself of that post please click here.


I’m a list person, I make lists upon lists upon lists to stay organized. I make them on my computer, phone, sticky notes, … anything I can find. Therefore I was so thankful that my professors gave me an editable list to go through and take notes on to see how my current lesson addressed all the key UDL principals. If you want to look at my notes just click here. The writing in black is the notes I took on my original lesson plan, while the purple font reflects some of the changes I made this week. I think this could be a helpful tool to use during every unit I teach and to keep in the front of my mind for daily lessons.

Throughout the last six weeks this is actually the third official draft of my lesson plan for a musical room. In the same vein as the list, the black is from the previous draft and the purple font is what I altered with the UDL ideas in mind. I’m really pleased with how much more inclusive and in-depth the lesson became after these changes. Originally I thought that an open-ended exploratory framework for each day would be great. While I didn’t add many specific tasks to any day I did help chunk my lessons into more manageable pieces that students could follow along with on their summary sheets. I created a worksheet of sorts for each day where students were asked to answer a few questions that would review the previous day, have them think about their plan for the current day, and self-reflect on how they spent their day. Those are all skills that are addressed in the UDL ideals and helpful for all students. Below is a word cloud that I created using Wordle by copy and pasting my five days of planning to see what words I used the most. I was overjoyed to see that my most used word was “student” – UDL helps make the students the focus of the lesson more than anything else. I also used the words MakeyMakey, summary, explain, sheet, room frequently. Wordle is such a fun way to visually see the focus of a set of words! I had heard of Wordle before, but I never tried created one myself. I wish I understood how easy and helpful these can be! I can see myself working these into my lessons more frequently after finally trying one myself.

Wordle: Interactive Musical Room Lesson Plan

In my updated lesson plan I also took more advantage of the 1:1 technology of my school. Since I teach online at a public charter school all students are provided with a computer and headset. In my original lesson plan I had the students look up MakeyMakey examples online if they wanted to, but that was about it. During this revision of my lesson plan I provided the summary sheets in their email so that students could use their computer. This can help with students who need text-to-speech, speech-to-text, are better with typing than writing, prefer computers, need spell check, etc. I also adapted an earlier instructional blog post to create a how-to sheet for making a piano using water in drinking glasses. I even used to create a brainstoring map to show the flow of my 4 day lesson. This tool is going to be great to use with my students in a virtual classroom to create an online mind map that they can share. I’ve tried using Microsoft Word in a similar way before, but it’s more difficult and time-consuming than this site.

Created using

Created using


I also added a portion of a summary sheet with a graphic organizer to fill in at the beginning of the lesson unit. I had originally planned to discuss conductivity related to using a MakeyMakey, but now there is a physical representation that students can fill out. This list will help reinforce the information that we verbally discuss as well as provide a spot for students to look back at later in the unit.

Overall I am much happier with my revised lesson plan. I honestly thought that it was a good lesson before this week, but after taking each UDL principal into account while revamping it it’s gotten so much better!


Rogers, Carissa. (2008). kid to do list, list, Be happy and go home. Retrieved August 10, 2014 from Flickr

Research Based Musical Room

Last week I was asked to create a lesson plan using my Maker Kit (MakeyMakey) that would engage students in creative learning. I chose to have my students work together to create an interactive musical room as a version of an ice-breaker / team-building task. I did not place many guidelines on the assignment, because I wanted students to be free to create whatever they wanted. You can click on my lesson plan to view it (with changes from last week in purple) here –> Weinlander MakeyMakey Sample Lesson Plan.

This week I watched a TED talk about the digital divide between educators who use new technology to replace old techniques and educators who use new technology to do things that couldn’t be done before. Richard Culatta spoke about three main challenges schools are faced with currently – treating all learners the same, holding the schedule constant, and performance data being shared too late to be helpful. These challenges resonated with me greatly. It’s actually one of the main reasons why I love working at my current job as an online Title 1 teacher at Michigan Connections Academy. Students are assigned a certain number of lessons each day to evenly distribute their course throughout the semester. However there are no hard deadlines other than the end of the semester. Students therefore can spend 15 minutes or 4 hours on a single lesson, however long it takes them to understand. They can work on school 5 days a week for 6.5 hours, or split their time another way. At the end of each lesson 3-7 multiple choice questions are asked to see if students understand the material. These do not affect their grade, and instead are to be used to direct future learning and gaps in knowledge. never teachI was pretty convinced already at this point, but I did more research to see if personalized learning, collaborative problem-solving, and immediate feedback were the direction education should be taking (Cullatta, 2014). As I searched, I had my original lesson plan in mind. Yes, I had allowed students to work at their own pace, collaborate, and problem-solve, but I knew I could do better. I wanted to add an option of solving a problem I had given them, not just problems that they encountered along the way. Problem-based learning is a popular method of teaching in which students are given challenging and relevant problems to solve in a small group. “This approach is often used to increase learner interactions by working together collaboratively. Teams determine the needs, and work through the steps to solve the problem.” (Holland and Holland; 2014) Frequently that is how problems outside of the classroom will arrive – without direction. I hope to teach my students how to handle that in any way that I can.

I’ve updated my lesson plan to include some problems for students to think about, knowing that I could be interacting with students from Kindergarten to High School. A lot of these are open-ended questions to get the group thinking and discussing together. I’m planning on writing these on cards and having them placed in a common location for students to grab when they need. This way if the group feels that they are “stuck” or need a challenge before I recognize it then they can help themselves. Holland and Holland also talk about the benefits of active hands-on learning since students “need to hear it, touch it, see it, talk it over, grapple with it, confront it, question it, laugh about it, experience it, and reflect on it in a structured format if learning is to have any meaning and permanence” (Holland and Holland; 2014) I believe that with my added task after our four days together and the “problem cards” I have extended the learning experience for my students. Practice doesnt make perfectWhile thinking through this lesson I was concerned about classroom management. I work online, students and teachers are not used to interacting in person as a whole group. Using a MakeyMakey after state testing will be a different experience than many are used to. Plus, this is a lesson where students are supposed to get noisy, move around, work together, talk, rip things, build things, move things, laugh, etc. However the focus still needs to be on the task of building a musical room. While I was reading an article about motivation with games I checked myself against the three requirements of motivation from the self-determination theory: “autonomy, competence, and relatedness” (Eseryel, Law, Ifenthaler, Xun, & Miller; 2014). Students were given a lot of autonomy in this lesson; they decided what they made with whatever materials they could. Students would be gaining competence each hour and each day because of the ease of use of the MakeyMakey. This technology is weird to use at first, but it gets easier. Students will gain ability relatively quickly while working in their group and the MakeyMakey. Lastly students will have relatedness because they are all working together for a common goal using something that most of them (if not all) have never seen before. There is a straight forward goal of making a room come alive by just touching it, but they get to decide all the details to get there. With these three main things ‘checked off’ I think that classroom management will be stress-free since students will be motivated and engaged. The main concern I have is students waiting for the MakeyMakey. I think I can get at least one more kit before I put this plan into action however. 🙂

  1. Culatta, R. (2014, July 14). Reimagining Learning: Richard Culatta at TEDxBeaconStreet. [Video File]TEDxTalks. Retrieved from July 17 2014


  1. Eseryel, D., Law, V., Ifenthaler, D., Xun, G. & Miller, R. (2014). An Investigation of the Interrelationships between Movidation, Engagement, and Complex Problem Solving in Game-based Learning. Journal of Educational Technology & Society, 17(1), 42 – 53. Retrieved from July 17 2014 (14364522)


  1. Holland, J. & Holland, J. (2014). Implications of Shifting Technology in Education. Techtrends: Linking Research & Practice to Improve Learning 58(3), 16-25. Retrieved from July 17 2014 (87563894)


  1. Kathyschrock (2009). Teaching. Retrieved July 17, 2014 from Flickr:


  1. Shannon (2012). Practice Makes Progress. Retrieved July 17, 2014 from