Made 4 Math: Distance Formula Project

Earlier in the year I talked about teaching slope with the method somebody later tagged "stack and subtract". This worked so well for me that I decided to use the method in my geometry class for the distance formula. We did a lot of practice and I decided I wanted to a do a little project instead of a standard test to assess this concept.

We did a mock version of finding the perimeter of a figure on a coordinate plane by using a simple version of @pamjwilson's idea mentioned on her blog here.

I even created an Excel file to check their work- just plug in the ordered pairs and it will calculate the distance of each segment and the perimeter of the polygon. (To know what I'm talking about you really should go read Pam's post!)

I created my scoring guide first.

But I decided to walk my students through the requirements one at a time before giving them the guide.

We started by creating a design with no more than 4 horizontal and no more than 4 vertical lines and at least 10 slanted lines. Make sure you have plenty of extra graph paper on hand.

I checked each student's design individually before giving them the next step, which was to label each endpoint with a capital letter and find the ordered pairs. Some students wrote the ordered pairs on their designs, some wrote on a separate sheet, and some wrote in the margins. I also checked these individually- it will save you a lot of time in the long run!

Next I told students they had to find the distance of each segment and then the perimeter of their entire figure. I offered copy paper or notebook paper but they had to decide how to organize their work.

Once finished with that I asked them to completely color their design and gave them the scoring guide so they could make sure they had completed all of the steps.

Here are some samples:


I again used my Excel spreadsheet to help me check the work but I'm not gonna lie, it took me some hours to grade 23 of these.

Two common mistakes: one was just not finding the distance for every segment. Sometimes this happened because they labeled incorrectly, didn't label at all, or just completely left things out.

Second was that some students listed their ordered pairs in alphabetical order and then found the distance AB, BC, CD, etc....except when you looked at their design, some of those endpoints didn't even make segments- they weren't even connected. This was probably due to the fact that it worked out that way in our 'mock' project we did the previous day, which meant that students took it for granted that it would always be that way.

That tells me that I still missed the mark. I thought I was doing something more valuable by asking them to apply their knowledge of distance but there was still a disconnect. Students still just understand how to apply a formula to numbers without making the connection that this is the distance of an actual thing.

I avoided asking them to memorize a formula, gave them an alternative assessment, and created a project where they had to apply their knowledge...and I didn't accomplish anything more than I would have with a standard worksheet and test.

I did more work for equally or even less effective results.

Working harder but still not working smarter.


  1. I've been teaching 20 years...its been refreshing to read your blog and be inspired by your enthusiasm for teaching. It's obvious you love it and your students. I hate to see you say "you missed the mark." Despite the rhetoric,we are not magicians. We study, prepare, and try to improve. At some point our students must do, at least, some of the same. Take care of your beautiful self. You have a lot to offer.

    1. Thanks for the encouraging words. I'm feeling pretty bored right now with my teaching but I am definitely not a magician.

  2. I like this project. Could you have maybe asked the students to "critique" or evaluate the project after it was all done? Maybe by getting their feedback on what they felt was on point or missing, it will help you to improve the project for next time. This can even be an anonymous survey just to get feedback.

    1. I usually do that on projects but I forgot about it this time. I have realized that I had the highest amount of students who were willing to make corrections to this project for more points as compared to other tests. And I noticed when we did the Pythagorean Theorem on a bell ringer that I had a ton more participation and accuracy so I guess I did get some good byproducts.