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.


Made 4 Math: Pencil Dilemma Solved

This year I have really been working on small things. Those small things that really are trivial but that become a big deal in your mind. Things that happen over and over, get you irritated for no reason, seem completely illogical, and that no one else really gets.

For me, my biggest one throughout all four years of my teaching is the pencil dilemma. Students who will NOT bring a pencil to class.

I have been more frustrated than ever with this problem this year because I feel enraged that I provide them everything (paper, binders, calculators, and all other school supplies and even a place to store them) and they cannot bring the ONE AND ONLY thing I ask of them. They don't even have to carry a textbook, binder, or notebook to class. Just a pencil!

I know other teachers who make students buy a pencil from them, give them a personal item to trade, send them to the office, let them go without, etc. But for me, all of those solutions interrupt my teaching, their learning, and really ruin my mood for that class period. I don't want to deal.

So my solution is literally like the simplest easiest plainest idea ever....but it has worked wonders for my peace and sanity.

I start class by asking who needs to borrow a pencil (because it infuriates me when a students lets half the class go by doing nothing before asking for a pencil!) and as I hand them out, I write their name on the board under a headline that says 'Pencils'. I started this as a reminder to myself to get the pencil back from that student. But then something magical happened...seeing their name on the board made them remember to give it back to me on their own.

I have probably went through at least 7-8 dozen pencils this year but with my new 'system' I have used the same 4-5 pencils for quite a while now.

Friday, in my class of 12, I had to hand out 5 pencils. I was very close to getting angry when I stopped myself. What is my end goal here? I want teaching and learning to go uninterrupted. So I wrote their names down, handed out the pencils, and they worked hard the whole hour. And I ended up with five pencils handed back to me.

I know that I did not solve the root of the problem. I know that I probably could do something better to help teach my students accountability and responsibility.

But ultimately, I need to be the best teacher I can be and I can't do that when my blood is boiling with rage.

Simple fix = calm blooded me.


Made 4 Math: Radical Equation Stips

This year in Algebra II I taught solving radical equations for the first time. I don't really know where this idea came from but I ran with it. I have a small class of 12 students so I created 4 sets of strips and divided my students into groups of three.

I put a star * by the strip that represented the first step in the problem. Each strip represented a different step in the process of solving a radical equation. Students had to put the strips in order, check with me, and then write down what was happening in each step of the process.

Here are the strips:

I printed them on card stock and then laminated them. But I did create the file with the steps out of order in case you want to pass them out and have the students cut them out instead of you.

Last but not least, here's the worksheet I used for them to write down the process. Here's a tip, I only created four steps but that was confusing because students wanted to write 'square both sides' and then after that write 'square roots disappear' when I considered that one step in my brain. So you may want to add another step in there.

This took most of the period and the next day I gave them a worksheet of problems and wrote the answers on the board. They worked them all with very little trouble although their were two problems with fractions which I should have included in our sequencing activity.

On their assessment for radicals, this was the concept they did the best on overall.

On a side note, I thought it was cute that when I first passed out the strips they immediately started to sort them into piles. lol See, sorting pays off!!