2017-09-04 Numberless Word Problems

There are two things that I learned about toward the end of last school year that got me so excited I couldn’t wait to try them, Numberless Word Problems was one of them. One of my #eduheroes, Brian Bushart (@bstockus on Twitter), created this idea some time ago, and I was just learning about them. So, I wanted to get a couple reps in ASAP, and I was able to get a couple of reps in before the end of the year, and it confirmed my initial excitement.

With this school underway, I want to jump in early and often to get everyone on board with this idea, exposing all students to this opportunity and making it an ever growing area of powerful learning. On this journey last year, I was able to modify this into a sequence of learning events, where we start with a #NoticeWonder activity that builds the Numberless Word Problem the students create. Since students create the word problem, whether or not there are numbers is there choice, and it is so interesting what they come up with. The students smash their questions together to make a new question, and then they answer their question (or switch with another group and answer theirs) four ways.

Once the students have shared their answers and we’re all on board with the questions and answers, we compare our information to the state standards example(s). Students are always surprised that their questions are much harder than the state examples and think the state question is easy. Compared to previous times when given the state question, they typically shut down because it’s “too hard,” I’d say this is an amazing outcome.

Anyway, it’s still a work in progress and I’m super excited about it. Thanks Brian for sharing and making us all a little better.

2017-05-16 – Day 6 – Clothesline Math

Over the weekend I created my first tent series for Clothesline Math. In my Integrated Math 3, I want students to explore the input/output of trig functions and their values from the unit circle. Ideally, students would be interacting to make sense of the relationship between the input/output of trig functions and the connections to the various values of the unit circle.

(Dramatic music cue) The answer seemed obvious once I understood how I foresaw students working with the content: Clothesline Math.

I built my first series of tents for the clothesline math, I went to the store and bought eight $1 jump ropes for my groups to use as a clothesline, and created the tents. On Monday, we tried it…


Dreaming of all the ways to utilize this idea, we had so much fun. The HS students were a little hesitant at first, but once they got into it, they were enjoying it. Our next step is to take their individual groups and make it whole class, this is where the learning will make the most impact, I am anticipating. I also am waiting for the moment when students realize there are two sets of infinite answers (periodic functions) for each of the cards, with a few exceptions like the cosine and sine obtain their max and min values at only one set of infinite answers.

All in all, I am so in love with clothesline math and will be utilizing it in a much more poignant way next year. If interested in using this same structure, or if you want to talk about ideas, I have a series of resources from many of my math heroes like Matt Vaudrey and Andrew Stadel.

2017-03-28 On The Spot Ahhhaaaa

Although I have many blog posts on the tarmac ready for lift off, this entry takes special priority as I had a powerful Ahhhha moment that lasted two full periods.

Quick background, I have been teaching about trig functions in IM3 and coordinate geometry in 8th-grade math.

My IM3 students look similar to Fry from Futurama….(see below)….when I begin discussing trigonometric functions and their relationship to a right triangle and the unit circle.


Yesterday, I thought I would slow the progress down and focus on right triangle trig relationships, then move back up to unit circle and beyond. Before I even began today, the students’ lips were moistening with anticipation of the drool onset….So I changed directions, had handed out a sheet of paper to every student, and we began folding.

I didn’t know where I was going with this, but I was on an inspirational kick and was going for it. After students folded their papers, I checked each stage, I’d ask a question and have them label their own triangle, the students would confirm with their partner, and stand up when they agreed.


The 3 step process was extremely helpful in uncovering areas of stuckedness and bringing their understanding to light. My next step was to have them write each of the trig functions according to their triangle they had created.


Time quickly ran out for the students when were at this point, so tomorrow, they’ll finish the trig functions relationships. Students literally gasped when the bell ring, they were so into the lesson they couldn’t believe the period was over.

Then my 8th-grade party began, immediately after IM3, and I’m working on giving the students plenty of repetitions on problem varieties to allow them to be successful. Yesterday, the progressions began with a problem having them plot three ordered pairs, which form the vertices of a right triangle.

The students would plot the three points, then find the distance between each of the ordered pairs. Students should find that the two of the lengths are easy, just counting the distance between points, the third combination would require the use of the Pythagorean theorem. The third stage in this progression asked students to determine the slope between points forming the hypotenuse, with the hint that if stage 2 was done well, there shouldn’t be any additional requirements for calculations. The final stage asked for an explanation of how students know that the triangle formed in stage 1 was a right triangle.

Well students shared they were having a hard time with the concept of slope, so fresh of the triangle fame of IM3, I gave the same concept a try in 8th-grade.


Since this was near the end of the period, I performed a think aloud to indicate my learning. Tomorrow I’m expecting that this will be part of their work, creating the ordered pairs on a triangle, perhaps on centimeter grid paper, and do it exactly. Anyway, I felt the explanation landed with the students, several heads were nodding with that smug look of understanding….


Which showed I was on to something that may uncover more of their thinking as we explore and shed light on that which was previously in the dark.

My excitement for this simple idea and the reason for posting this moment is tied to my developing understanding of students learning and being back in the classroom for a couple of periods. Addressing students understanding in visual ways, with a manipulative and a slow pace were all pieces that helped gain students attention to make it truly impactful.

I always love these inspirational teaching moments that shed light on understanding for students, and the fact it worked in 8th through 12th yields potential for my favorite kind of tools that go K12.

What were some experience you’ve had that are similar or different? What about those experiences made them turn out the way they did?

Mission Accomplished

As I publish this reflection, I fear that this moment may turn into something along the lines of another famous moment….


I am very honored to have met #IRL (in real life) the person that inspired this learning goal for me this school year: Having students produce a weekly learnings podcast for public consumption. Joe Young is an incredible TOSA for math and education and he shared this idea a long time ago, and when I had the pleasure of teaching two courses this year, I wanted to challenge myself and use this as one way students would show what they know.

Finally, this week, I found the magic recipe to making this happen, I assigned two students, one in each class to get the job done. Friday marked the turning point for me in doing some of the things I wanted to get done and continue to build on. Friday was also our first Mystery Skype with another group of students. While the connections prevented less opportunities for conversation, it was an entertaining and fun sort of thing.

While doing the Mystery Skype, we also produced our weekly podcasts for both classes. I loved the idea of having students interact with other students around mathematics and this public display showed a proof of concept.

All in all, I was very excited to have been able to edit, publish, upload, host, and publish to iTunes. I am currently waiting on a review of my two podcasts to be approved, and if that works they’ll be in iTunes. The Mystery Skype provided the opportunities for students to strategize their thinking and be able to try to problem solve.

The podcasts are linked:  Math 8    &/or     IM3

Well looking forward to another great week. Hope your week is as magical and moving you forward to meet your new goals.