Two Proofs and a Lie

I’ve caught the crud. It is either from:

  • My tiny toddler germ factory and/or her daycare
  • My teenage student germ factory

Your guess is as good as mine, but I’m home with a 100 degree fever, and so is my kid. I’m thanking my lucky stars that I selected a primary care doctor in the same building as my kiddos pediatrician. Nothing says family bonding like getting a nasal swab at the same time as your kid. Good news: we’re flu free. More good news: my kids napping so I get to blog.

Now, to the math. Last week I did an activity in Geometry and I promised @druinok that I’d blog about it. I called it Two Proofs and a Lie, its based off the Two Truths and a Lie structure that I first saw on Jon Orr’s Blog (he’s done a new posting on it recently which re-reminded me how much I love it!). What I love most about this structure is that you need not waste a time explaining what to do–its in the title, it says, “hey student, I’ve given you something that contains two true things and one lie…figure out which is which.”

We were on our second day of quadrilateral proofs. Students had figured out that most of the proof center around finding a triangle that helps prove the thing we want, prove those triangles are congruent, then CPCTC (i.e. their favorite mathematical acronym). I wanted to push them a little. But a doable amount. So I gave them the handout (here) and told them they had 5 minutes of no writing brainstorming with their peers. They were to discuss what it is they are being asked to prove, what was given, and how they think they might find that information.


Students were then told they could use whiteboard markers to collect their brainstormings into a proof rough draft. My kiddos don’t like the #VNPS for some reason (probably because chalkboards aren’t as ‘cool’ as whiteboards), but they LOVE writing on the desks with markers…so I have #HNPS (horizontal non-perminant surfaces).


This drawing is from one of my most reserved students. They never really talk in class, and always take a back seat to their peers. I was walking around and their group was 100% confident they had found the lie, and this student, my usually quiet one, goes “um. guys. I don’t think your right. I found the triangles like Mrs. White said. This ones true.”

The thing I like about making them brainstorm twice is they actually have to say what they are thinking out loud. I do believe that there is an added benefit to verbalizing what you’re thinking when it comes to math, but in particular with proofs. The biggest hurdle I’ve noticed with my students is forgetting a step in a proof because “they know its true.” Well yeah, its true, you know it. I know it. But you’ve gotta say how you know its true in a proof. We ran out of class time here. Students took photos of their white boarding work and we picked up the next class.

The next day students then wrote up, as a group, the two proofs that were true and peer-edited them before turning them in. I gave groups feedback, and we then moved, in the following days, to more individual proofs.


Groups working on their proof write ups.


Peer Editing the proofs


Proof Writing


Did I mention on day 2 of this my kiddo had an ear infection and couldn’t go to daycare so she spent the day in my class? 


My Digital Filing System

I had the pleasure of attending NCCTM this past week in Greensboro. It was a breath of fresh air to surround myself with teachers striving to improve our teaching practices–I just love having the opportunity to put myself in the learning seat for a while. Not that I don’t enjoy teaching, I love it, but I also love learning…which come to think of it is probably why I like teaching.

But anyhow, when it comes to teaching I do tend to assume that almost everyone else has a better handle on it than I do. I’m on year 6 and every year I have a list a mile long of things I wish I had done better/could have improved/need to improve for next year. The internet Gods gave me the Math Twitter Blog-o-Sphere (#MTBoS) when I was in grad school and their sharing of the happenings in and out of their classroom that have kept me afloat in my time teaching. My online math family keeps me bettering my practice and I love everyone of them for all they share.

At NCCTM we were recruiting newbies to Twitter and it was brought to my attention that some of my MTBoS family don’t have a good system for storing the wonderful things we have borrowed from our friends. I’d say I spend about an hour on Twitter in a day, mostly while I’m cooking dinner or waiting on photo copies to be made…and often when I’m procrastinating from other things. But my MTBoS family post really good stuff that I don’t always have time to read at that moment–I have a two year old after all, time is something I never have enough on–so I store it away for later. This way I can re-look through the goodies when its on my mind or I have time.

So here is my system:

Screen Shot 2017-11-04 at 3.57.12 PMI use Evernote to store all of my internet findings. It is free to sync across two devices, and you can pay for a premium account of you want more devices. Evernote is meant to be used as a digital notebook–I originally got it to try and keep myself paperless in grad school, but quickly decided it had a better use: Storing all the goodies I find on the internet.

So, I’m not sure if this is the best way to use Evernote, but its the way that works for me:

  • Download the Evernote extension in your web browser. I use Safari, so I got the extension here. This allows you to be one button click away from storing the site.
  • I also use the app for my computer, but that’s because I like its layout better than the web-based view.
  • So, let’s say you find an awesome resource you want to save. Click the WebClipper Extension (elephant icon) and the magic window of storage will open in the top right corner of your browser.

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  • You can then choose what notebook you want to store the website in. I’ll talk more about how I set up notebooks in a second.
  • Then you add tags, these are storage labels that you might use to find the webpage later. For instance, “Desmos”, “Linear Equations”, “Linear Systems” These are words that you can search through later on to re-find things.

So somewhere along the way I decided to organize my notebooks by standard clusters. So things like “Linear Equations”, “Quadratics”, “Trig Functions”,  or “Triangle Proofs”. There’s still evidence of my first filing system, it was by course, but things got far too cluttered for my mind.

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Now that things are organized by standard, if I’m gearing up for a linear equations unit, I just click on the linear notebook and I can see all of the goodies I’ve stolen borrowed from my MTBoS family.

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This is what my Linear Equations Notebook looks like. The middle column has small snips of everything that I’ve saved. The right column will preview any of the sites that I’ve saved. To go to the website I simply click the URL at the top of the application by the date.

Can you save other things to Evernote? YES! You can save screenshots, which is the easiest way to save tweets. When you save a screenshot you are given the option to add annotations like arrows, lines, shapes, you can blur out faces, and add text with the built in editor (which is also available for your phone in app form).

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(Sorry Julie, I couldn’t resist this screenshot hehe).

You can save PDFs, you can write your own notes to save. And my favorite feature is to add text to a page that I’ve saved. So let’s say I found a 3-act task I LOVE but might want to add a reminder to future-me that it requires computers, or extra materials for class. Its a mental reminder for “YOU NEED THIS STUFF BEFORE YOU USE THIS” feature.

I’m hopeful this helps you. I’ve been told I should write a proposal to chat more about this at NCCTM in 2018, but I thought I’d get a blog out in the meantime. Also…I really need to get better about long blogs. My 180 blog has been more successful this year as I LOVE to take photos 🙂


First Day Plans

Its the Saturday before school starts and I didn’t finalize what I was doing for one of my classes until well into my second cup of coffee of the morning. I’ve had geometry planned for a while. I was easily able to select The Marshmallow Challenge for them. Partially because I taught half of them last year and didn’t do a wonderful job of establishing group working norms, and partially because it is one of my favorite start of school activities.

Geometry Day 1: The Marshmallow Challenge

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For those of you unfamiliar with the task, you give your students 20 pieces of spaghetti, a yard of tape, a yard of string, and a large marshmallow. They have 18 minutes to construct, with their groups, the tallest free standing structure that they can. The catch is that the marshmallow needs to be on the TOP of the structure.

I like this activity for three reasons:

  1. It pushes students through the phases of group dynamics quickly. They move from the “oh hey, its kinda awkward working with these people I don’t know” to “hey, you, yeah, what’s your name? Ok [insert name] hold this pasta for a sec so we can tape it” to  “OH MY GOD WE ONLY HAVE 3 MINUTES LEFT WHO HAS THE MARSHMALLOW?!?!?!”
  2. I really get a feel for how my students think through a task. These towers have varied from elaborate to simple tri-pod-like.
  3. The debrief possibilities are endless. There is a wonderful Ted Talk by Tom Wujec that I use every year I do this challenge. Spoiler alert: Kindergartners are better than most adults at this challenge. Its a GREAT launching point for talking about the prototyping process and how we can mirror the practice in a mathematics classroom.

AFM Day 1: String Structures

This is the ideas I re-discovered after some of my morning caffeine boost. I had saved this image in Evernote filed under my “MTBoS” & “Group Work” tags”

Screen Shot 2017-08-12 at 9.00.32 AMI can’t remember what the exact instructions were for the construction, but I know what I am going to make them:

Your group has been given 2 yards of string. Your task is to create each of the shapes shown using only your group members’ hands to maintain the structure. Each group member must play an active roll in creating and maintaining the shape. 

Once your group has created a shape, call Mrs. White over to document your awesomeness and then start another shape.

So it goes without saying that I have no idea how this activity will go as it is my first year trying it. But I have hopes for how it will go. For most of my students in AFM they have, as one parent put it at Open House yesterday, “a fair amount of unpleasant mathematical baggage.” Something that feels overtly Math-y isn’t a very user-friendly start to the school year for them. So I want something that feels un-math-y but that falls into the Math category of geometry–I have found that my AFM students tend to have pleasant memories of geometry, so I’m using that.

I am going to give my students 20 minutes to try and construct as many of the shapes as they can. We’re then going to debrief and create some class group work norms. I then want to do a Talking Points activity from my morning Twitter Math Camp session, Talk Less, Smile More.

Things I left out of this plan because the 3rd cup of coffee is just now being consumed and my brain takes a while to wake up on the weekends:

  • My classes will be doing Sara VanDerWerf’s Name Tents because it is the most amazing “get to know your students and help the name-forgetting-teacher learn your names” thing I have ever found. I haven’t finalized the questions I’ll ask each day.
  • I will be sending my students home with one assignment: To complete a student info sheet (which includes preferred pronoun so I can add that to my roster) and log into the web-based tools we will use this year: Canvas, Desmos, DeltaMath, GoFormative.

Week 1 in Review

This year marks my third at UNCSA and I have never looked forward to, and dreaded, the start of a school year so much. I’ve had the pleasure of staying at home for the past six months since the birth of my daughter. That being said, I am not cut out to be a stay at home mom. I’m not organized enough, I’m not good at keeping my brain engaged and working, and I developed a bad case of cabin fever. So in one way I was REALLY looking forward to the start of the 2016-2017 school year. But I dreaded the start of the year because I have felt behind since August. I didn’t get the lesson planning done during maternity leave I (naively) had promised myself I’d do before my daughter started daycare. I haven’t spent the time I feel that I should at home lesson planning because I’d rather be holding my girl and planing peek-a-boo (do you blame me?). And as luck would have it, she got an upper respiratory infection the week school started, so I’ve spent the past few nights up at all hours rocking her to sleep, which left me no choice but to be highly caffeinated to survive the teaching day. I have never felt so shaky at the beginning of the school year, but I think I did do a few things right (or at least I am calling them a win) from my maternity leave to-do for the 2016-2017 school year:

Get better about learning names:

I used Sara VanDerWerf’s Name Tents to aid in both the learning of my students names, and in getting to know them a little better within the first week of school. It was the best decision I could have made, I may never have to try another way to learn names. It was super awesome to get the chance to have a private conversation with each student. They kids responded to the prompts:

  • What do you want me to know about you?
  • Give me your 6 word math memoir.
  • What’s your favorite thing to do outside of your art area? (I teach at an arts school)
  • Doodle me something about yourself and explain the significance.
  • What is your most vivid mathematical memory?

My favorite was the doodle, you’d think that in a classroom with a few visual artists and a ton of dancers, musicians, and actors that the kids might be shy on doodling. Nope. I drew them a picture of my stick figure family on the screen with the prompt, so I set the doodle-bar kinda low intentionally to set their minds at ease.

Don’t go Over the Syllabus in Class

Some where along the line, someone told me to go over the syllabus on the first day. That it sets expectations/demonstrates norms/ya-da-ya-da. I hate syllabus day. Even last year’s attempt at making it bearable (each slide had an internet meme and/or GIF), you know the ones:

Screen Shot 2016-08-24 at 6.10.13 AM Screen Shot 2016-08-24 at 6.10.37 AM

But it was painful, the kids stopped listening 3 slides in (once I was done talking about my story and started talking about “class rules” kinda things). So I ditched it. My syllabus lives on Canvas, our online learning platform. My students are all sufficiently good enough readers to handle reading it on their own–with the exception of a few ELL students who I made time in the first week to talk to about the syllabus to ensure they were up to speed. So my first night’s HW assignment was to read the syllabus and to take my online Student Information Quiz (in Google Forms format). Students then logged into Canvass and posted three questions they had regarding the syllabus in a discussion forum, and answered one peer’s question. I addressed any further concerns on the second day of class and it took less than 10 minutes. Win!


Focus on Group Dynamics, Not The Math

I know, I know. “You’re supposed to do Math on the first day” to set the tone for the year. Yes, I agree, but I wanted the focus of the first week of my class to be on the group work dynamic so that when we step up the math, they are already comfortable working in groups. The first math problem I did with my students I sawn on Fawn Nguyen’s blog that she got from Don Steward:

Screen Shot 2016-08-24 at 8.45.33 AM

The problem was more successful as a day 1 task in my PreCalculus and Advanced Functions and Modeling classes than in my Algebra 1 class. But they all had some pretty stellar math talk going on and eventually (with differing levels of hints) got the final answer. On a related note: America needs to get on board with the metric system.

Day 2 we did a task I first read about in Designing Group Work and Sarah Carter was so kind to provide already made up on her blog: Rainbow Logic. The idea is that the students use strategic questioning to infer the color pattern on a peer’s tic tac toe board. The kids got WAY into it. I should have taken pictures, but several groups were convinced that their facial expressions were giving away information, so they hid behind the file folders I gave them to separate the “game keeper” from the players. We did four rounds of the activity. Three of the rounds were with 3 colors and the last round was with 4 colors. So far my students record for number of questions to get the correct color combination was three.

  • They asked for the first row’s colors
  • Are there more than two of each color in any given row?
  • Is the center color blue?

I didn’t witness the whole thing go down. But I am to understand that there was an educated guess on one square placement that yielded success.


It was a good first week. And it only took me until half way through week two to get around to reflect on it…

I Have a Plan: Cleaning Up My ‘Dirty Words’

Julie (@jreulbach) is awesome, but I’m pretty sure anyone reading this was already well aware of that fact, and has gathered all of the Algebra 2 teachers of the internet to join together in a blogging initiative. While I’m not teaching Algebra 2 this year (I had to give it up in order to get a first period planning in order to have a little more flexibility in the mornings with getting my 6 month old daughter to daycare), I am teaching Advanced Functions and Modeling. A course which is currently Algebra 2 version 2.0 for most portions of the curriculum. There is little to no new information presented to students, and most of the current design has a computational focus instead of an interpreting and analyzing focus. As the course is designed AFM is meant for those students who need a math beyond Algebra 2, in order to be college competitive, but who aren’t ready for the rigor of PreCalculus.

AFM’s current course description:

Advanced Functions and Modeling is designed to further strengthen algebraic manipulation and graphing skills while introducing a selection of other topics and application. Additional topics may include trigonometric functions, sequences and series, and probability. Concepts will be applied to real-world situations and technology will be used regularly. Prerequisite: Algebra II

I inherited this course description and a problem set/note packet for the course from my coworkers. While I am not a huge fan of the layout, mostly because it follows the Alg 2 curriculum very closely, I have just now had time/energy to try a re-write.

The old curriculum mapping went:

  • Introduction to Statistics (measures of center, spread, comparing data, and normal curves)
  • Linear Functions
  • Quadratic Functions
  • Transformations
  • Exponential and Logarithmic Properties and Functions
  • Sequences and Series
  • Trigonometry (Triangles and Functions)

Given that students I teach in AFM are the same students who struggled with Algebra 2, this ordering has never felt 100% right to me. If they struggled with Algebra 2 material when it was in Algebra 2 is it really effective to just re-package the same content in a new course and call it AFM? I understand the need for students developing an actual understanding of key material from Algebra 2, especially if we want them to go on and be successful in any math classes they may take in college, but I wasn’t okay with presenting the material in the same way they had seen it before. As compartmentalized chunks of math that are always taught in the “here’s the rule”, “now here’s the practice”,”now here’s the ‘real world’ applications” structure. After much #MTBoS lurking during the first 6 months of my daughter’s life/my stent as a Stay at Home Mom, I think I’ve found a sequencing that I can finally support. Shout outs to Mary Bourassa’s blog for giving me the spiraling content idea.

  • Unit 1: Introductions to Functions— functions vs relations, function notation, domain and range, family or functions.
  • Unit 2: Introduction to Modeling— a mixture of Linear, Quadratic, and Exponential functions. The focus will be on justifying the choice of a function as a model for a given situation (from a table, graph of points, or verbal description)
  • Unit 3: Introduction to Statistics–Reading tables (%s), Measures of Center, 1 Variable statistics and data visuals, Normal Curves and z-scores, and for the first spiral: Regression (linear, quadratic, and exponential).
  • Unit 4: Transformations of Functions— Spiral from Unit 1 with a lot of Domain and Range descriptions. I know I’ll do a few Marbleslides in here.
  • Unit 5: Sequences and Series— I will start of with Visual Patterns as an informal “find the pattern that works and prove it” exercise, and then move into a more formal definitions of arithmetic and geometric sequences (spiral from Unit 2 with Linear an Exponential)
  • Unit 6: Geometry— I’m still in the brainstorming mode for this one, but I know I want right triangle trig in addition to some review from their Geometry course. I have been told by the SAT prep teacher that the geometry sections of the SAT are more rigorous than in the past and that my kiddos will need the refresher. I would like to bring in some of the IB Math problems I did at my old school, they were really good for getting students to think outside of the box and talk about the math.
  • Unit 7: Trig Functions— Focus on using information about a situation to create a function to model the situation (max/min values and period), spiral with the transformations unit.
  • Unit 8: Financial Math— A good portion of my students are seniors who go straight to a dance company, music chamber/conservatory, or the work force, instead of college. So they need a crash course in how to ‘Adult.’ I have talked about credit cards, monthly budgeting, leasing-vs-buying a car among other ‘adulting’ topics.

So far I’ve only made it through actually planning half of the first unit. I’m trying my best to move away from the “I do, we do, you do” style of teaching of the materials I inherited. Last year I didn’t change them because I knew I’d be out for half the year on maternity leave, I didn’t want to rock the boat and cause a headache for my maternity leave sub.So, I fell into the habit of drill and kill style instruction. I hated it. The students hated it. I don’t think they had any ‘ah-hah’ moments with the curriculum, and most importantly, I don’t think I changed their mind on math. Math was still hard. Math was still boring. And Math is nothing more than a combination of formulas you’re supposed to remember.

That is not the math classroom I want. In the past I have taken great pride in taking the students who hate math, and through modeling and problem solving activities, I slowly changed their hatred to mild distaste. Which for the time span of one school year, I’ll consider a victory. I, for selfish reasons, shifted my focus in my classroom and I need to get back on track. So I promised myself I’d do better by my students this year. I’d make worksheets/kill and drill practice a dirty word in my instructional vocabulary. I need to get back to my instructional happy zone: using math to ponder our world, model things we see happening, and answer questions we have about our surroundings.

My goal for this year is to have one day of instruction, some of which will be self guided, discovery style learning, and other parts will have to be direct instruction because I haven’t found a better alternative yet (let me know if you have one, until then part of my instruction will have to be the well timed curse word in my dirty word worksheet world). The instructional day will be followed by hands on practice, some sort of combination of Desmos activities, group activities, and 3-act problems/labs. I’ve found a bunch of interesting problems thanks to #MTBoS that I plan on using and/or altering to suit my needs to achieve this goal. Fingers crossed I can help improve my potty mouth. Both figuratively speaking with the change in instructional practices, and literally. I’m not cut out to be a stay at home mom, and my boredom did lend to a rediscovery of my love for colorful language…I need to work on that s*@#t before my daughter starts to pick up words…

Goal Setting

Okay, I’ll be the first to admit. I’m god awful at setting routines. I thought to myself approximately 6 months ago, as I sat on the sofa 41 weeks pregnant trying to convince my daughter to make her grand entrance to the world, that I would be ‘productive’ during maternity leave. What’s that? Did I just hear the collective mothers of the internet laugh at me? Yeah, I was naive and operating under the misguided belief delusion that I would get some school work done while lil one slept. Fast forward to present day, and I’m one week away from the official start of the school year. I need to get my act together. Lil girl is in daycare two days a week, so I want to utilize this baby-free time effectively and set up some routines for the 2016-2017 school year.

My goals small, all things considered. I will have, in essence, three new preps this year: Algebra 1, PreCal, and Advanced Functions and Modeling. While I’ve taught AFM before, I am redoing the curriculum. Trying to officially make the move from Algebra 2 2.0 to a unique course that prepares my students for either college level math or the real world, depending on their plans post high school. My math department has decided that PreCalculus needs an overhaul (I agree with this sentiment) to better align with the PreCal topics taught in other (read: Traditional) public high schools in the state. And I haven’t taught Algebra 1 since my student teaching days. Bearing that in mind, for the 2016-2017 school year, I promise myself that I will:

Promise 1: Actually use a paper planner to record thoughts/deadlines/important dates

I tell myself every year that using the calendar app on my computer is sufficient. Its not. I never go back and look at the notes I leave myself because, well, its just too tedious. I have to remember what day I taught what, and then double click, no wait, wrong day…scroll…scroll…what was I doing again? So after much thought, and finding the concept of a Bullet Journal online, I have created my own planning template. Inspired by a tweet from @mathequalslove I just placed the online order to have it printed up on nice paper and bound at Office Depot. I figure if it looks nicer than what I could do with the copy machine at school, and not in a 3-ring binder, then I will be more inclined to use it.

The planner starts with the a year overview. A place where I can write down important dates for the school year like faculty meetings, math department meetings, exam days, and holidays.

Planner. Year Overview

I’ve then got a weekly overview for each course. My math department likes to use this table-format for pacing purposes from year to year. Since we all switch courses so often, it is a courtesy to a future teacher of the course with a general guideline for the year. Because we are in North Carolina, and an inch of snow will cause sheer panic and destroy any pacing template I’ve done in the past, I decided to make my pacing guide big enough to fit Post-It Notes Page Markers so I can move topics around without the need for white out/an eraser.

Course Pacing

And then I have a weekly lesson planning section where I can put in more detailed notes about the day’s lesson, what went well, what I need to fix, and what plans I have for the next time I teach the topic. Consider this section a place for mini journaling (which will help me with my next promise). I decided to leave the section for the dates at the top blank so I can use the same template year to year without the need for editing. Also, it is WAY cheaper to get a black and white cop of the planner made, and I have plenty of pretty colored pens that will add the date nicely!

Weekly Planner

Then the attendance sheets

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Files: Attendance Sheets, Planning Template


Promise 2: Become a Blogging Member of #MTBoS

I think it was Sam Shah who posted about the types of #MTBoS participants. I have fallen into the category of ‘The Stalker’. That is to say, I read a LOT of blogs by MTBoS tweeps. I steal borrow a LOT of their lesson ideas or handouts. I mean half of my interactive notebooks for Algebra 2 last year were inspired by Sarah Carter’s (@mathequalslove) notebooks she posts about. Not to mention my, hands down, favorite end of the year lab for AFM which I outright copied the concept for from Jon Orr. His CSI Crime Scene Lab was such a great idea, one I couldn’t dream of having, that I couldn’t resist making my own version of the hook video.

When I read about all the wonders Desmos had created by adding the Activity Builder feature I could resist and had to try it out. With some success, and failure (earlier blog post). I think I audibly giggled with delight when I got an email from the, one and only, Dan Meyer asking if Desmos could use a version of my activity. *Swoon* #MathBloggerIdol


So I started dipping my toe in the #MTBoS water this summer. Replying to some tweets. Joining in a few conversations. Testing a few Desmos Activities when asked and providing feedback. But I’m ready to take the next step: I’m going to promise myself to blog at least once a month. I have been hesitant to blog about my lessons in the past because I’ve felt like they aren’t worthy of the #MTBoS. I mean, I’m relatively new in the game of teaching, and my lessons aren’t all something to write home about. But a thred I read from Dan and Meg Craig really stuck with me:

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So here I am #MTBoS. Ready to start blogging!

Promise 3: Have first semester planned out by the start of school

This is my slightly unrealistic goal, but I’m trying to set my goals high, well at least for the two courses I am sole responsible for: Algebra 1 and AFM. I’ve already paced out the first semester of AFM and started on the notes packet for Unit 1 (Prerequisites to Modeling with Functions). And I’m hopeful that I can reuse most of my departments resources for Algebra 1 this year. So if I use the next 15 baby-free days (thanks to Daycare!) between now and the start of school. I hope I can get this done!

That Time I Face Palmed in Algebra 2

It has happened to us all. You have a great idea, scratch that, you have a WONDERFUL idea. An idea for a lesson/activity/warm up that you are so stoked about sleep is difficult the night before. And then, during class, that idea falls flat. So flat that you’re not even sure it has a cross-sectional area. It is the definition of a line with a slope of zero. It hurts. So I’m not going to say this this lesson fell that flat, but we’re talking a slope of 0.125 (1 out of 8 kids understood the task at hand).

The Original Task: Desmos Activity Link

The stage for the activity had been set the day before. We had spent the day reviewing how to write the equation for a linear function when given either a slope and a y-intercept, a slope and a point, or two points. The kids seemed to be on top of it. The exit ticket I did had 95% of the class able to do all three. I knew I wanted to try the Desmos Activity Builder that week in class. So I figured I’d give it a shot. The goal of the activity was to have students, while working in pairs, learn how to use Desmos while demonstrating their ability to create the equation of a linear function when given some basic information. The activity then ended with asking students to recall the concept of Domain and Range from the previous chapter to draw one of the letters of their initials using linear equations and domain restrictions.

The concept was okay, the scaffolding was NO WHERE NEAR what it needed to be. The things that I did wrong/the universe did wrong with this first task:

  • I introduced too many new things at once. It was our first day using the iPads (new tech for some of my kids), it was our first Desmos Activity, and it was the second day of writing linear equations.
  • The Wifi hated us. The school had just upgraded a server (or something like that…I don’t speak IT fluently) and had inadvertently kicked everything Mac related off the network. I had noticed I lost printing capabilities earlier in the week, but didn’t think to check the wifi status of the iPads before beginning the activity…oops. The students weren’t able to stay online for more than 3 minutes at a time and they only had access to the guest network which was running slower than molasses.
  • I didn’t set my expectations for their behavior during the activity. What to do if you’re stuck (ask someone else first), what to do if you understand and want to help someone, who to let me know you’re hopelessly lost and need me ASAP.

Fortunately, this mess up of mine was on a Friday. I had all weekend to think about what to change about the activity and how to make amends to my students for causing them a 40 minutes of on-again and off-again frustration. I decided to keep the Desmos Activity platform, but to upgrade a lesson from my early days of teaching: Linear Putt-Putt to an interactive experience. I had written down comments students had made, constructive and otherwise, from the failed activity and tried to do better.

The Upgraded Activity: Linear Equations Putt Putt Desmos Activity

Linear Putt Putt Screen Shot

The idea was to give students 4 holes on a putt putt course with a variety of obstacles in their way. Students would need to create 3 linear equations (for a par 3 course) to successful navigate the course and end with a line through the hole. Students were to use domain restrictions to ‘cut off’ their lines so that they represent the path of a ball for each putt. We assumed that the balls would stop where the domain restrictions stopped (I would love to extend this activity one day to have actual angles of impact hold true for hitting a side wall…but we didn’t have time for that).

The things I changed from the Original Activity to the Putt Putt Activity:

  • I apologized for throwing too much at them. I realized, in hindsight, that we needed to move slower. I think that this threw a lot of my students for a loop. I think that they had never heard a teacher apologize before, but I asked for forgiveness for the frustration I caused on Friday, and their promise to wipe the slate clean and try a new activity. They agreed and we moved on.
  • I gave the students two movable points that they could drag and drop wherever they desired. One point was the ball, and the second point was the “ending” point for their putt.
    • This gave students more confidence in creating a linear equation. I heard on Friday’s failed day “HOW am I supposed to GUESS where a line is? I’m not a mind reader! UGH.” on more than one occasion. They had a point, you can tell a student to create a letter on a piece of graph paper because they can create the points that restrict the line…but on an iPad, that simple task is made much more difficult without the use of draggable points.
  • I made the points restrict to whole numbers. I’m not against equations being messy, but I was trying to build their confidence, not crush it again. I wanted nice whole numbers for them to play with so that they would feel less intimated by the new online resource.
  • We completed the first hole TOGETHER, as a class. I called on students to tell me where to drop the ball, where to move the second point. Then we calculated the slope between the points and created a line together. A student then pointed out how easy it would be to restrict the domain “since we know the x-values for both of the points!” I had her come up to the computer and show us how to restrict the domain using Desmos. We did the same for the remaining two lines and talked about strategies for completing the remaining holes.

Alg 2 Linear Equations Putt Putt

This went leaps and bounds better than the first activity. Students were engaged, they were trying to complete the holes under par in order to have a ‘better putt putt score’ than their neighboring peers. I even heard giggling this time around. We had great whole-class conversations about how you would draw a vertical line with Desmos (we had not yet talked about the equations for vertical and horizontal lines). There was even one student who was so intent on having his lines follow the “true trajectory of the ball” that he was googling angle of impact and trying to figure out how to get the slope he would need to have the ball “bounce” off a wall and keep on going so that he only used one stroke instead of two. He opted to use perpendicular lines to represent the bounce, and quickly realized that his method didn’t reflect the real world physics of how a ball would bounce, but he did manage to make a hole in one on the first course using his method. So I’ll call it a win.

The Moral

Some times your intentions are wonderful, but your execution needs a little more work before you unleash an activity on the kiddos. A special thanks to Desmos and the #MTBoS community for taking a look at the Putt Putt activity before I presented it to the kids and for the invaluable feedback that made the activity run smoothly the second go round. Y’all rock!