Origin Story

It all started when I was hanging my Captain America picture display.

I decided I wanted the five pictures centered on the wall and centered vertically on each other. I thought the math involved in making that happen was interesting, so I came up with a slightly simpler version (DOC) (PDF) for my students.

The Setup

When I introduced the problem, I brought one of the pictures from home to show them what I was working with. I realized that my back blackboard was 12′ long, the same width as my wall, so I decided to make full-size “pictures” for them to arrange once they had their measurements.

What I Learned

I have two Pre-AP Geometry classes on alternate days. The first day, I introduced the problem and just told them to get started. This led to quite a bit of confusion, and I had to spend some time answering the same questions over and over. I thought it was fascinating that two approaches emerged — some groups were making their calculations using the information I gave them, which was pretty much the way I intended them to go. Another group, however, decided they were frustrated with the numeric approach and went directly to the full-size shapes to arrange first. They finally got everything arranged, but the whole “display” was too far to the left, so they had to shift everything over. Once they had, they went back and measured where everything was “supposed” to go. Their numbers weren’t exactly the same as mine, but I was pleased by how close they were.

On the second day (especially since my principal and evaluator were coming), I decided to give them a little more direction before turning them loose. We went through the process of finding the center of the display and how to line that up with the center of the room. I also explained how to align the pictures vertically with each other so that the tallest was 14″ from the ceiling. Overall, it went much more smoothly, and I had fewer students get frustrated and just quit.

Both my principal and evaluator complimented me on the lesson design, and on the “real-world” aspect of the problem. Admittedly, I’m not sure too many people would be as anal as I am about getting pictures aligned in this fashion, but I think the principles can be applied to a lot of practical situations.

]]>Enter a square root you want to simplify (ex. ), and it will give you the simplified radical (ex. ). Here it is: Simplifying Radicals

]]>School

- Pre-AP Geometry
- Push them harder! Too often, I find myself watering down the lessons I am teaching or providing too much scaffolding. If I want them to be prepared for Pre-AP and AP level work, I need to stop babying them. This change will mainly affect my lesson delivery and practice. I am still committed to flexible deadlines, quiz retakes, and everything else that tells a student, “I don’t care WHEN you learn something as long as you learn it!”
- Incorporate more quadratics into the problems (see previous point).
- Incorporate more Geogebra
- Create a running thread of connecting the logic of programming with the logic of Geometry by teaching them the basics of coding (see CO + DE = MATH).
- Change the seating each week based on which students are on pace and which are behind. Place the students who are behind closer to my desk.
- Astronomy
- I kept the class at too slow a pace last year. There’s definitely a balance between giving students enough time in class to complete their projects and their having so much time that they can just goof off half the time.
- Part of the reason for the slower pace was that I realized part-way through that I didn’t have enough material to fill out the rest of the year. That’s not a problem I’ve ever had before, and it kind of caught me flat-footed. I will definitely address that this year by bringing in more lessons that I had skipped over in previous years.
- I’d really like to find some sort of way to have the students perform some sort of observations. I’m also toying around with having some sort of star party attendance requirement. I’m really nervous about trying to have any kind of official class activity at night, especially off school grounds, but I don’t know what to do.
- One of the pieces I appreciated about the rubric that Matt Baker and Kat Glass shared about their student presentations was that they also graded them on how they spent their time doing prep work. I think if my students knew they were going to receive a grade on how they used their class time, they might take it a little more seriously.
- UIL (I’m UIL Coordinator for our school)
- I wasn’t crazy about it at the time, but after the fact I liked the table I set up during our “VikingFest”, a kind of school fair that is held the first Wednesday of the school year. It let students know what UIL was and all of the different events that were offered. This year, I want to have some flyers printed that list the events, the coaches, and the rooms where they practice.
- I made a whole presentation to a local Rotary Club about how I want to expand student participation, so now it’s time to put those ideas into action. I need to get with the other coaches and set up a rotation of people to speak to the AVID classes to let them know about UIL. I also want to try to talk to some of the upper-level math classes about Calculator, since that’s my baby.
- Advisory
- We’ve had these types of periods before, and they have usually not worked out well, but I’m hopeful that the changes we have made will give this a better shot at working.
- We want students to spend the entire time productively, which means that I need to come up with some “evergreen” activities for students to do if they say they don’t have anything.
- Geometry: Factoring quadratics (X-Puzzles), lightning math, WODB, Estimation180, PSAT practice, coding (trinket.io), student-created videos for lessons
- Astronomy: SAT/ACT practice, ???

Personal

- Plan and prep meals on Saturday. (Sunday never seems to work out.)
- Plan to leave school by 3:30 except on Tuesdays and Wednesdays.
- Make time to practice my flute and play with Flutissimo.
- Go to the gym at least three times each week, but ideally Monday-Friday.
- Get back to study of Romans
- I worked all summer finally getting my house clean and tidy, so let’s keep it that way!
- Continue learning Python
- Get back into cross-stitching or quilting.

I want to do all the things! Arrgh!

This year, especially after all of the inspiration at TMC, I’m having trouble narrowing down what I want to do on the first day of school for my two Pre-AP Geometry classes. The last few years, I have tried to get away from reading through the syllabus/procedures and have kids actually doing math. That has come back to bite me a few times because I think I didn’t spend enough time setting norms while we were doing the math. The 1-100 activity by Sara Van Der Werf has been really popular with the MTBoS this year, and I think this setting of norms combined with doing math has a great deal to do with it.

Here’s what I *have* to get done on the first day:

- I have a flipped classroom, which means that I really need to explain the flow of homework, classwork, and quizzes to my students. The biggest mistake students make in a flipped/mastery learning classroom is getting behind, and I really need to pound that into their heads!
- For the first time, we gave all of the Pre-AP Algebra I students a summer assignment. It wasn’t a huge amount (two pages of problems), but if I’m going to honor those who did the work and take this seriously, I need to do some sort of assessment on that first day. Our plan is to give them a quiz on the first day, and anyone who made less than 80% would then re-take the quiz (different version) on the second day.
- Gather student information. For the last few years, I have used a Google form to collect information such as preferred name, whether they have internet access, favorite subject, how confident are then math, etc. I always have some students who are shocked when I call them by their preferred name almost immediately, and I have to remind them they told me what they wanted to be called!

I’m figuring that will take about half of the class (about 35-40 minutes). With the remaining time, I can’t decide whether to do the 1-100 activity or have them read an excerpt from *Have Spacesuit, Will Travel*. I’m currently leaning toward doing the 1-100 activity, and then after my 8th graders leave (they have to leave about 20 minutes early every day to catch a bus back to the junior high), use the remaining time to have my 9th graders read the excerpt. Or we might just use the 20 minutes attempting to explain the wacky schedule we’re going to have this year — we’re going to have a 23-minute rotating advisory period every day.

For my three Astronomy classes, I like the plan I’ve used for the last couple of years:

- Let them sit where they like (these are mostly seniors, with a few juniors mixed in), although let them know I reserve the right to change them up if they can’t behave. I usually use a paper form to gather names to make my seating chart, but I’m thinking of integrating it into my Student Info form.
- Collect student information. I have a form similiar to my Geometry form that I collect similart types of data.
- Create a “Pocket Solar System”. I give each student a 3-foot long piece of adding machine paper. We label one end as “Sun” and the other end as “Pluto” (or “Kuiper Belt”), and I ask them to lay out the planets according to how they think they are spaced out. When they are finished, I have them flip the paper over, label the ends the same way, and I show them how the planets are really spaced out. We can then talk about how little mankind has really explored. To give them even more perspective, we will work through calculating how far away the nearest star is.
- I then go over the basic format of the class, how the grading is set up, and what my expectations are. This year, I think I’m going to try using Consensus Rounds to have them come up with respect agreements for Teacher-Student and Student-Student interactions.
- If I have time left, I’m contemplating using the 1-100 activity to get them thinking about group work because they will be starting their first group project the next week.

My final “class” is a class babysitting students as they attempt to make up Algebra I, Geometry, or Algebra II credits using ixl.com. Aside from getting them registered on the site and explaining how the process works, I’m not sure if I’ll do anything else with them.

]]>I want to organize ALL THE THINGS!I am slowly moving docs I will use this yr to google so I can link in my planner,but it's taking too long.

— Jessica (@algebrainiac1) August 7, 2017

Constructions was MUCH better this year!

Exploring Length with Geoboards and Desmos

First Day Name Tents

Five Questions to Ask Your Students

Check out my new Out of Office sign! Let me know what you think! #FlipgridFever pic.twitter.com/cixVLBtA94

— Shelly Meyers (@drshelly268) August 5, 2017

Most-Referenced Classroom Decorations

21 Ideas for the First Weeks of School

Geometry PBL Curricula

— MATH (@fayzshafloot5) August 5, 2017

It is like the standard base, but instead of the place value being for 1, 10, 100 etc they are for Fibonacci numbers+

— Edmund Harriss (@Gelada) August 4, 2017

Bonjour !

by @sansu_seijinhttps://t.co/hfsoYoGlAx pic.twitter.com/mlvPATKErl— Vincent PANTALONI (@panlepan) August 4, 2017

Designing some tasks centered around the concept of area. My favorite so far: Write your name using 100 units^2 #MTBoS #iteachmath #mathchat pic.twitter.com/X1UCqPTQ8J

— Ilona Vashchyshyn (@vaslona) August 3, 2017

All finished and I'm so happy with how it looks! #MTBoS #geomchat #SwDMathChat pic.twitter.com/RFcufnJsYh

— Anya Ostapczuk (@anyaostapczuk) August 3, 2017

A #FlapperGeo vocab/ construction mini book work in progress. Yes. I made flapper tabs into a hashtag. #GeomChat pic.twitter.com/M5NI3PnTaF

— Jennifer (@JennSWhite) August 2, 2017

Eclipse Activity Ideas

Growth Midset Posters

Scripture Journaling

My Favorites (TMC13) Thursday Afternoon (Student Engagement Wheel)

The Desmos conference was *very* interesting. I ended up in a two-person session on Polygraphs with Chris Danielson, and we actually ended up playing the polygraph I created for my Astronomy class — which was great, because it made me realize that I needed to edit the pictures to make the names more readible. We ended up working on a possible polygraph idea for parallel lines and transversals, which I’m definitely going to work on this year.

The other session that I found interesting was First Steps with the Computation Layer. This has kind of been my summer for programming, and I thought it would be interesting to drill down into what makes Desmos tick. It was fun, in a frustrating kind of way, but I’m not sure the additional flexibility is really worth my time investment right now.

Again, trying to be more outgoing, I spent the evening playing games with a table of guys — thanks Chris (@Plspeak), Jonathan (@rawrdimus), Bill (@roughlynormal), and Josh for making me welcome!

Thursday, the actual TMC17 conference began. Here are my recaps and takeaways:

**Morning Session: Playing with Exeter Math**

I already wrote up how much of a blast I had in this session. Part of the reason I chose this session is because my summer conference load has been pretty heavy and I wanted some time just to play with math. The other reason I chose this was to give me an opportunity to experience math from a student’s perspective — expecially the frustrations that happen when you can’t quite get things to work the way you want. I was *very* glad I picked this session!

**Session #1: “An Object to Think With”: The whole body as a tool for mathematical sense making by Malke Rosenfield and Max Ray-Riek**

This didn’t really turn out to be what I thought it was. We ended up making 3-D structures out of rolled-up newspaper sticks and tape. What I found interesting was the way Malke and Max facilitate the session: they started us up *very* open-ended and added structure as we went along. It was also fascinating how different the three groups’ structures were (my group’s was *very* free-form). I’m not sure what takeaways I have for my classes, but it was a lot of fun.

**Session #2: Expos: Student Presentations in Math Class by Matt Baker and Kat Glass**

I really found this session to be interesting because they use student presentations to (a) review before tests and (b) practice giving presentations. I especially liked the rubric that they shared with us. I already do presentations in Astronomy, and I think I’m going to add giving students grades on how they work in their groups on the presentation. Part of me really wants to have my Geometry students do presentations for review and part of me is a little nervous about the time commitments by both the students and me.

**Session #3: A Trig Exploration: Exact Values and the Golden Triangle by Rachel Kernodle, Jamie Collins, and Molly Tanner**

This was a *whole* lot of fun! After refreshing our memories of 45-45-90 and 30-60-90 triangles (and the corresponding trig values), we were then given a 36-72-72 triangle and asked if there was any way we could use this to find more exact trig values. Very cool!

**Session #4: ****CO + DE = MATH by Stephanie Reilly and Tamar McPherson**

This might be one of the most useful sessions I attended at TMC. One of the reasons I’ve been getting back into programming is because I think there’s got to be some way to correlate the logical thinking from programming with the logical thinking in Geometry. This session may have given me a really good tool by introducing me to Trinket.io. Until my laptop’s battery died, I was able to take their templates and build a tool for finding the third side of a right triangle, as well as one for calculating the distance between two points. I’m definitely going to be playing with this as school gets started!

**Session #5: An Hour of Codebreaking by Bob Lochel**

This was a fun session to play with different types of code makers and code breakers. The simulation of the Enigma machine especially boggled my mind. I’m not sure how much (if any) I can use in Geometry, but it was a good session.

**Session #6: Clothesline Math by Chris Shore**

I was *so* happy they added this session on because this I wasn’t able to attend his earlier presentation. I’m not sure I can adequately convey how much my mind was blown by the simple arrangement of some paper markers on a piece of string. For the initial stages, it was interesting to discuss what was the absolute minimum amount of information needed to fully represent , , and on a number line; and I also enjoyed the discussion generated by placing , , and on a number line containing 0, 1, and . It wasn’t until we were looking at solving an equation, that things exploded. On the number line, we placed and clothespinned together. Chris then had us place and , and that’s when we realized that had to be 9 units away from the equality on the left and was 6 units away on the right. The gap between was 15, which was . Wild! From a teacher standpoint, Chris also gave us some good words of advice, such as making sure the students not at the board have whiteboards or the equivalent, so they have something to do.

This post has gone on too long, but I don’t want to forget about my favorite My Favorites:

What Else Can Google Slides Do? by Jennifer Fairbanks

Dynamic Web Sketches by David Petro

Maybe next year, I’ll be able to break my pattern and go to TMC18, even though it’s an even-numbered year!

]]>This is my recap of what I learned at CAMT this year:

**Session: Making Sense of Geometry by Andrew Stadel (@mr_stadel)**

Even though this session was listed for 6-8, I decided to attend because I have followed Andrew for years on Twitter. It was definitely worth it. One of the things I will definitely use this year is having students guesstimate how a bottle’s circumference compares to its height as a reminder about circumference.

**Session: Plick Me! Flipping Geometry by Sarah Ashley**

While I have been saying I wanted to use Plickers for a couple of years now, I always seem to find some reason why it’s never the right time. What I appreciated about this session was that she actually had us using the Plickers and showed us how she set things up. She also provided some links to some useful sites, most of which either required iPhones or I already knew about such as Desmos or Geogebra, but she did mention a few I hadd not heard of such as Splashtop.

**Session: The Importance of Getting It Wrong by Michele Adams**

I’m not sure this session really answered their question of how to get students to persist, but it did have some interesting activities that reminded me why I shouldn’t forget about the Shell Centre for Mathematical Education resources. The activity that I especially want to remember when we hit volume was comparing bottles and graphs of their volume vs. height.

**Session: Engage and Motivate All Students by Aaron Daffern**

This was one of those sessions where you make a pre-judgement based on your initial impression of the presenter that turns out to be completely wrong. Aaron is an interesting guy. He’s currently a curriculum direcctor for a charter school which he had previously served as principal. One thing he said that really stuck with me was that as principal, he should be able to “walk into any classroom and teach any subject.” I know my current principal also has that philosophy, which (although it can sometimes come across as arrogant) is *such* a change from having principals stand up and publicly state that they aren’t that good at math (laugh, laugh). Aaron had us model a strategy that I’m probably going to use for my first day classes: consensus rounds. He initially had us come up with three to five characteristics of a good math lesson. At the beginning of the session he had given everyone slips of paper that had three different groupings on it. He then had us find our first group (which got rather chaotic in a room of ~100 people) and come to a consensus of three characteristics. He insisted that each member of the group needed to “own” the list. It was also important that we each write the list down because after two minutes, we regrouped and did it again. After two minutes, we regrouped one last time. By this point, most groups had talked through different ideas, but the main consensus of the whole room for the main characteristic of a good math lesson was “student engagement”. Of course, how we achieve engagement is the tricky part.

**Session: Revamping a Classic: Interactive Notebooks Gone Digital by Amanda Packard and Rita Gongora**

Although this was billed as a commercial product demonstration, Tiffany and I decided to attend because we thought it might give us some good ideas, which it did. We saw some good uses for OneNote for Classroom, as well as using Google Slides to make a template that students would then use to fill in for their notes.

**Session: Breaking Down Barriers – Geometry Redesigned by Julie Kidder and Caroline Robb**

This was a very interesting session. These two teachers are fortunate enough to teach at a private school that let them completely redesign their Geometry curriculum. One of the most fascinating decisions they made was to eliminate Pre-AP (Honors) Geometry as a separate course and put all different skill levels in the same classes. How they then handled the Pre-AP part was to designate parts of their assignments as “Honors”, and students had to accumulate a certain number of points to have their course credited as honors. Students were given a choice of ways to accumulate those points, which also included things such as competing in UIL events. While I certainly can’t implement that sort of thing in my classes, I really did like their lesson design.

I have been sitting next to James Cleveland, and he has a knack for asking interesting questions, which really make me think. For example, on problem 33, we have to show that a triangle is isosceles by setting the two distance formulas equal to each other. James realized that once you square both sides, you have two circle equations, and connected that to how we construct perpendicular bisectors by drawing two circles and marking their intersections. It became even more clear when I graphed the equality on Desmos, and Desmos produced it as a straight vertical line. Cool!

We also looked at problem 21, which asked us to divide the shape into two congruent shapes. We conjectured that any shape with a 180° rotational symmetry would have an infinite number of ways that it could be divided. In order to satisfy the conjecture to my satisfaction, I set it up in Sketchpad:

Yesterday, we looked at problem 45, in which the corner of a paper is folded down to the bottom of the paper. The original problem asks us to find the area of the triangle created. It then asks us to find the value of *x* that would maximize the area of the triangle. Working it out algebraically, we found that for a side length of 10, *x* would be . This led James to conjecture that it would always be of the length of the side. After a *lot* of hairpulling, I got the following set up in Desmos that shows this to my satisfaction (I used a slider for , and the equations were and along with a parabola to fit the maxima as varied.):

Today, which was our last day, I had thought to finish up problem 45 (I added the vertical line at .) Once again, James was working on a problem, but this time, he got almost the entire group intrigued by it. Problem 133 sounds simple: Dissect a 1-by-3 rectangle into three pieces that can be reassembled into a square.

We quickly realized that since the area of the rectangle was 3, that the length of each side of the square would need to be . We immediately went to 30-60-90 right triangles, but we couldn’t figure out a way to make the cuts. Finally, about 20 minutes before we were supposed to leave, Annie Perkins figured it out using Sketchpad. This is my re-interpretation of her solution:

I’ll probably write up a full reflection on my experience at TMC, but I wanted to get my morning session experiences written down before I forgot about them.

]]>- The Notes
- The Classwork
- The Quiz
- The Test

As I mentioned in my last post, I have students take their notes from a slideshow that I have created and posted on slideshare.net. Because we are a national AVID demonstration school, I require them to take their notes in Cornell notes fashion. One of the big tenets of C-notes is the idea of going back over your notes after 24 hours to highlight important text, add questions and a summary. In order to enforce this, I only give them a 50 for taking notes over my slideshow (the right-hand side of the page). The next class, I check to see if they have highlighted text, added questions, and written a summary. Questions and highlighting earns them an additional 25 points, and the summary adds the final 25 points. I have done this the last two years, and I really like the way the idea of the flipped class works with C-notes.

At the beginning of each chapter (what our district, for some mysterious reason, calls “bundles”), I give them a packet containing every worksheet for that chapter. This has two major benefits: Since I try to post notes for the whole chapter when we start, students can work ahead if they want to; also, if a student is absent, he automatically knows what he missed, and he already has the work. The worksheets vary between Kuta worksheets, worksheets I’ve found or created over the years, and exploration/extention problems. For each worksheet, I post solutions to the odd-numbered problems, and since this is practice, I grade the worksheets on completion. This is the real strength of the flipped classroom, because they have most of the 80-minute class period to work problems. I have them seated in groups, so that they can ask for help from their fellow students or me. I check the work from the previous worksheet when I go around checking notes.

When my district switched from Moodle to Canvas, I started setting up all of my quizzes there.

This is the really magic part of my class. Because I also do SBG, I allow students to retake quizzes to improve their grades. Canvas allows me to set up “question banks” for each quiz, so each time a student takes a quiz, it will be different. I calculated once that one quiz had more than 1,000,000 different possible versions. There are two ways that this works. The first is the multiple choices for each topic:

These can be either multiple-choice or free-response. The next type of question is my favorite: the formula question. I can set up a range of values, along with a formula for the answer, and let Canvas select the numbers:

As long as I can get a numeric answer, these work out great! There’s other cool stuff about Canvas — if you’re interested, let me know.

The test is the summative assessment over the bundle. It’s made up of a common assessment part that all of the Geometry teachers at my school give (we use GradeCam to handle creating the scantrons and managing the data), and a Canvas part that is generally questions pulled from the quizzes.

This is the format that I have used the last couple of years, and I really like how it has shaken out. If you have any questions or comments, let me know!

]]>