Reflecting from a Distance

I’m not sure about y’all, but the transition from teaching in my classroom to teaching from my home office while wrangling a 4 year old was…well, let’s just call it “interesting” and leave it at that.

I survived the transition to remote learning with the help of the amazing online group of educators I’ve found and friended on Twitter. We shared our victories and our defeats, what was working and what was definitely not working, our hopes and our dreams, and our worries for what comes next. The community shared Desmos collections of eLearning activities, technology tools to aid in online collaboration, suggestions for physical math packet making/content, productivity hacks to keep track of all of the things, and methods for checking in on our students and keeping communication open with families of our students. My twitter feed became an overwhelming collection of things that looked amazing, but I no longer had the bandwidth to follow along as my school year came to a close. I suspect I was not alone in wanting to try to collect all of these resources while teaching, and that’s how this idea got started.

The Goal:

The goal of Reflecting from a Distance is to continue the sharing that started on twitter during this transition to remote learning as we look towards starting a new semester with a lot of uncertainty with regard to what the semester will look like. Will we be face-to-face? Will we be remote? Will there be a hybrid model of face-to-face and online? Will we start face-to-face and then have to abruptly re-transition to remote? Honestly, we don’t know; what I do know is that planning for what’s next will ease a lot of my anxiety, and from what I read on twitter, I’m not alone.

The inspiration for this initiative comes from a question asked by @druinok on twitter:

The tweet collected a lot of traffic and had some really good ideas from those of us whose students have access to the internet and a device. The thread had more teachers with synchronous learning environments, and the responses skewed towards high school teaching, with a few middle school teachers. To quote @mrsstipemath:

The tweet reads: “Middle school distance learning is not equal to high school distance learning is not equal to college distance learning” [person shrugging emoji]

So, in the theme of learning from this online community and implementing that learning through action: I asked, “Whose experiences are missing?” I noticed a lot of white voices and a lack of representation from teachers of students without internet or devices, in asynchronous environments, and the responses provide little to how experiences changed across elementary school and higher education experiences.

This blog doesn’t serve as a critique of the thread as much as the motivation for why we need to move the conversations from twitter, and its inherent silos, to a platform that is actively working to amplify the voices of under-represented teacher groups online and has experience sharing the amazing work that educators from around the world are doing daily in their classrooms: The Global Math Department.

While we are on the thread of thinking towards our next steps and navigating the tension between teaching in a pandemic while living in a pandemic I want to make sure we focus our energies on how we can humanize our students’ experience in our remote classroom. Back in November 2019, in what feels like a different lifetime, Hema Khodai (@HKhodai) participated in Making Math Moments Matter Virtual Summit (the summit was free at the time, but now requires payment to participate) and gave a session titled Who is a Mathematician.

The talk was an exemplar of how online learning could be structured to engage students, but more importantly Hema cites Dr. Rochelle Gutierrez (@RG1gal) in the need for math teachers to have multiple types of knowledge: content, pedagogical, political, and of diverse students. Math is not neutral and, as math teachers, we are not apolitical. Then, Hema shared a quote that I come back to over and over again in my daily planning, which has been at the forefront of my mind in these remote learning days:

“How can a fractured educator teach the whole student?

               -Hema Khodai, November 2019

Hema and Dr. Gutiérrez were referencing the internal work educators need to engage in to ensure that we are routinely confronting our own personal biases while actively questioning our practice of teaching and the impact that those actions have on our students. As educators, we need to view our teaching through a critical lens to ensure that we are not inflicting harm on our students. Use of instructional methods or practices that disregard the intersectionality of the identities of our students, that fail to see our students as a whole, actively cause harm. It is our work of learning (and unlearning) to continue to shape our practice in ways that allow us to see all of our students as whole.  This same reflection is needed as we critique our remote teaching practices to ensure they are addressing our students holistically.

So I challenge you to think of all the things that are draining for you, as the educator, right now in your remote teaching. If we, the adults in the remote classroom, are having a hard time with the over-abundance of Zoom meetings, the bombardment of emails and notifications, the cluttered calendar, and feeling like the foundation of our teaching practice is fractured, how do you think our students are feeling?

Collecting Videos:

We are working with the Global Math Department (GMD) to collect short videos (5-6 minutes) and blog posts of what you learned from our remote learning experiences from January 2020-June 2020 that worked for you and your students so we can be better prepared for what’s next in our teaching. 

Did you, in your experience of remote teaching, find success with:

  1. Tech Tools: You can go big picture and show us a learning tool (like EdPuzzle, ClassKick, SeeSaw, or some other platform) or show us how you create content within a tool (like pacing on Canvas or your LMS, creating assessments with Google Forms, or something else).
  2. Tasks: Did you redefine what a mathematical task looks like, for learning or assessment, during the remote learning phase of teaching? Is it something you want to share with the world?
  3. Productivity Hacks: Remote learning posed a whole new mountain of stuff for teachers and students to balance. Did you find a system for organizing your thoughts, documenting student communication, helping students stay on top of their work, or some other productivity hack?
  4. General Big Picture Take AwaysIn harking back to Hema’s virtual conference session, what ways have you found to help humanize the remote learning experience for your students? Have you found a system of checking in with students on their emotional health and well being that you will continue to use next semester? 

If you, or someone you know, has done something during this remote learning phase of teaching that you think others may find informative or useful, encourage them to submit their video(s) and tell us a little bit about their remote teaching experience on the google form linked here (and also available at the end of the blog post).

We ask that all video submissions contain closed captioning for those members of our community who would benefit from having a text transcript of the contents of the video. Apple Clips, a free app for recording that works with iOS devices comes recommended from our #DeafEd community. If you record with Screen-Cast-o-Matic and the Camtasia suite of video creating tools there is an automated closed captioning feature in the edit feature (Speech to text) that is very easy to use. Kapwing is another option that is web-based for creating closed captioning in your videos.

We are accepting submissions until June 30th, 2020 at 11:59pm EST. The videos will be tagged with descriptors and then added to the Global Math Department’s Youtube page. 

Thank Yous

Thank y’all for reading this post to learn about how we can continue lifting each other up as we move forward into the unknowns together. If there is one thing I know for sure, it’s that:


Google Form for Video File Submissions:

Online Teaching with Desmos: Self Checking Tasks

UPDATE: July 24th, 2020

Howdy new-to-this blog post friends. I’ve noticed a lot more traffic here so I wanted to clarify a few things about this self-checking template that I made: It was made out of a need to continue the formative assessment structure I already used in class, NOT for summative assessments. My school, when we shifted to remote learning, went asynchronous, and I had students across 21 hours worth of time-zones spread out all over the world. I needed a quick way to get the instant feedback my students were used to from doing card stacks and other self-checking in class practice of content (see my blog post here on my 1/2 and 1/2 structure for a face to face classroom). So I guess that’s my long-winded way of saying, “I threw this together quick with little regard to pedagogy” cause the quick shift to pandemic remote learning was HARD.

I wanted to clarify the above because I think people, myself included in this for what it is worth, have been using these templates in a way that doesn’t really align to the best practices of Desmos usage. I made these templates in a rush. Using the CL knowledge I had to survive pandemic remote learning when I, naively, thought we’d get back to campus in a few weeks. I really did think these templates would get used 3 or 4 times, and then we’d all be back together and mathing in my classroom. I was wrong. We are not over Covid, and we teachers need to find ways to use Desmos remotely AND still uphold using Desmos as more than a worksheet with solutions you know? What I love most about Desmos is it is interactive with my students, I want to think critically on when I want Desmos to be a checker instead of a collaborator with my students learning.

I made these templates before Desmos introduced the chat feature (which is amazing!!). I didn’t know that I’d be able to communicate with my students INSIDE a Desmos AB when I pieced together the CL to make this happen. Desmos evolved, and so will my use of Desmos next school year.

So, if it helps, here are my thoughts on planning for the 2020-2021 school year, which will be a combo of hybrid and online in all likelihood, and in which I will retire the templates from my teaching practices (I’m not deleting this post, or the templates because I believe in modeling growth in learning and changing of ones mind):

It is with that, if I haven’t convinced you that we can do better as math teachers than just my self-checking templates, you can keep on reading friend. I get it. Sometimes you just need kids to know if they did a problem correctly. But know that I’m not going to use these as is next year because I think I can do better by my students and I encourage you to join me in thinking on that. How can we use self-checking code for a better-than-worksheet-checkers?

Howdy internet friends,

It’s been a while. That’s mostly because I haven’t really been overtly proud of anything new I’m trying this year. I’ll blame it on having spent most of the semester solo-parenting a toddler, but its really just that when life gets hectic this blog is the first thing I let go of.

That being said, right now everything is feeling very uncertain with the Covid-19 pandemic and I find comfort in helping people. So here it goes, I want to offer to the internet world something that’s been helpful for my classroom when I want to leave students with work, that provides feedback, when I am absent.

I do a lot of Card Stacks (see @MathEqualsLove blog post here) in class so students can practice new skills and get immediate feedback on how they are doing. Due to parenting a toddler and needing to be out often I started creating Desmos Activity Builder versions of these card stacks. I thought that perhaps people would like a template they can copy and edit to create their own.

Desmos Activity Builder Self-Checking Template: Card Stack Version

If you are semi-familiar with the computer coding access that you have in Desmos called Computational Layer, then you know the drill. Go ahead and edit away and be sure to adjust the input CL’s correct value.

If you’d like a tutorial, keep on reading:

Step 1:

Log into Teacher Desmos and click on the arrow by your name in the upper right corner.

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Step 2:

Check your Desmos Lab Settings. Click on the triangle by your name. Then click Desmos Labs. We need the Desmos CL box to be on (checked)

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Step 3:

Okay, now navigate to my activity here. We want to create a copy for you to edit

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And you will be redirected to a new window with the editing features of a Desmos Activity Builder.

Step 4:

I made the activity so you only need to adjust two parts on each slide to have the self-checking feature work. The first thing we need to adjust is the CORRECT ANSWER. Click on the gear by the input component.

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You will see a new window appear for editing Desmos Computational Layer code that looks like this:

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You only need to change the BLUE number. Please change the blue number 1 to what ever you want your answer to be for the question. Once you’ve completed the correctness edit, click Done. 

Step 4.5: UPDATE from 3/18

So as I am making an activity I’m realizing that I want directions in the note component. Here’s how to do that:

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Then replace  the text “Enter 1” with what ever you want the directions to be for the students. Leave the code at the bottom alone.

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Step 5:

Adding your question. This AB assumes that you will be taking screen shots of questions and posting the image inside of the graph component. So have all screen shots ready to go before you continue.

Click on the Graph Component

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And then add the image to the graph. You will need to re-center the image and scale so it can be seen.

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Click done once you are happy with the image. Congrats. You’ve edited one slide!

Step 6:

Do all of that again for all of the slides you want to use. If you don’t need 10 questions, delete the slides you won’t use.


Duplicate a slide, then you will need to adjust the LABELS on the components (note how mine said input9, you’d have to make an input11 for slide 11) and then update the numbers in the Cl for the NOTE (click the gear by the note) accordingly.

Have questions? Tweet me. @JennSWhite

1/2 & 1/2 Classroom

So for those of you who know me, you know that I love coffee. Like, LOVE COFFEE. I don’t drink it black, even though I know I should. It needs a dash of sugar and a splash of 1/2 & 1/2 to reach perfection.

Why did I mention this? Well because my brain is dead and the title had 1/2 & 1/2 in it and I needed an intro. Let’s focus on the point: What 1/2 & 1/2 has to do with my classroom.

The other day I got into a convo on twitter here (oh and look at that. It starts with a GIF about coffee. So #onBrand and makes this into look planned) about why I like routines in my classroom. In particular how smaller routines fit into a larger routine that is the 1/2 and 1/2.

The Large Routine- a.k.a. The 1/2 &1/2:

I strive, for each period with my students, to spend 1/2 of the class period practicing math or actively doing math and 1/2 the class period learning new math. I teach on an hour block, and do have daily warm ups and, if my pacing/timings work out, a debrief/closing. Now here’s the “weird” part:

  • First half of class: Practice from previous day(s) classes.
  • Second half of class: New math learning. Either from a lecture or student exploration/discovery activity.

In 2018 I finally got the chance to make it to one of Anna Vance’s Make It Stick sessions at TMC18 in Cleveland where she presented alongside my now co-worker Alli George. Their presentation convinced me that if I wanted my students to actually learn the material in my classroom I needed to make sure that I structured the learning sequence in such a way that I am actively fighting the forgetting curve.

If the forgetting curve is new for you, its basically this pretty scary looking exponential decay function that represents the amount of knowledge retained (remembered) as a function of time assuming the content is taught only one time. Here’s a graph with an x-axis that does cause some concern for a math teacher given the non-linear nature of the x-axis…but let’s not focus on that right now as the visual still gets the point across: we forget stuff pretty quickly.

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And if you don’t believe that curve. Ask someone for their phone number, don’t write it down, go think about something else for 10 minutes, and then try to remember the number. You probably won’t remember the number.

So here’s the main idea between Make It Stick, and another book I’m almost done reading called Powerful Teaching:

Interrupt the forgetting curve by: Lagging (delaying) practice from when the content is learned, come back to the content often, and mix up the content with other content so that students are seeing more than one topic at a time.

Now, if you are like me in 2017 when Anna first told me that, you’re thinking, “NO WAY! That sounds miserable as a learner! They’ll never get to get into a ‘groove’ of practicing problems and they’ll be frustrated!”

EXACTLY! THAT’S THE WHOLE POINT! If we allow students to semi-forget something, have them do practice that requires retrieving that stored information from their memory and use it over and over again they will be more likely to remember it!

Back to the phone call analogy. Remember the days of analog phones? Like the pre-speed dial phones connected to the wall but new enough to have push buttons. What’s was the phone number of your best friend from those days? Funny, I bet you remembered that one! Wanna know why? Because you had to think about recalling(reviewing) the number and dialing it every time you wanted to talk to them.

Screen Shot 2019-07-23 at 8.21.37 AM

Have I convinced you? If not, seriously go read Make It Stick. It changed my life and I thank Anna and Alli for that.

So that is my long-winded way of saying “here’s why we practice old material first and then learn new material second in class.”

The Smaller Routines-a.k.a. The Instructional Routines:

While routines are wonderful in the sense that they make us comfortable by removing the unknown, doing the same thing over and over again can get boring. One of the things I find most amusing about myself, and I’m going to guess this is true for you all reading this blog as well, is that I despise change, but I also hate being in a rut.

The large routine of 1/2 & 1/2 stays the same, but I like to cycle through the routines that occupy each 1/2 so that we all get a bit of variety in our lives. Here’s what I used last year:

Practice Routines as First 1/2 of Class:

I like things where the answers are either given or can be self checked so that my time is spent with students who are stuck/struggling and not with students who just want me to check their work.

  • Question Stacks: These can easily be made from existing worksheets or worksheets found online. Sarah Carter (@mathequalslove) has a blog post explaining how to make them here.
  • Add ’em Ups: Where you take 4 problems and format them into quadrants on a piece of paper. Then in the center you place a circle with the SUM of the answers to the 4 problems. Students can check their work easily to know if they got all the answers correct. Groups have some pretty stellar convos about finding the errors together. Sara VanDerWerf has a blog about them here. (full disclosure I found that sometimes 4 problems can be a bit much when we get into some time-consuming content, so I will do 2 or 3 problems instead)
  • Partner Problems: So these have a bunch of names, and I’m not sure what you may call them. But the idea is you make a handout with 2 columns where each row has a different problem BUT where the problem on each row has the same answer. I first read about them on this blog and in finding it again to cite it I noticed they have linked to Julie Ruelbach’s rather large google drive of existing problems (SCORE!)
  • Two Truths and a Lie: which I heard about from Jon Orr here and are pretty much exactly what they sound like and can be morphed into different levels of sophistication for a task.

Note that I do not grade the practice. I even explicitly tell students that the goal is not necessarily for them to complete the entire activity in the 20-25 minutes we are working on this. We WILL see the activity again (because we spiral back with our practice) so don’t worry about working quickly, worry about working accurately.

 Capstones As First 1/2 of Class:

Sometimes I want to collect work from students. Not just because I need to grade something from them (I’d love a day where I am not grading work…but today is not that day) but because I want the opportunity to give them thoughtful feedback on their work. I call these days “Capstone Days” because it means I’m going to give them slightly more time (30-40 mins) to work on a problem or a set of problems that synthesizes some learning from the previous week(s).

Sometimes I ask them to work with peers, other times its individual work. It really just depends on where we are in the learning process. If the capstone is on relatively new material I tend to let them work with a peer (but each in a different color pen) so they feel more relaxed. If the content has been around for a while I tend to have them work individually.

Here are two examples:

Note these are still just problems you could find on any existing worksheet but they’re more time-consuming so turning them into a Question Stack would just be too much. My goal for this year is to have one Capstone a week. I’ll keep you posted on my progress with that.

The Learning in the Second 1/2 of Class:

The learning part looks really different throughout the year. Sometimes it is a lecture via direct instruction. Sometimes it is a Desmos exploration activity with a debrief to make sure the whole class got the material we needed to see. Here’s an example of a geometry Activity Builder I’m really proud of that we did for quadrilateral properties to build off an activity from Michele Torres I edited for parallelograms.

Other activities that you’ve probably heard of that fit in this chunk nicely: 3 Act Math tasks,

Sometimes I have students do a Sometimes/Always/Never card sort which usually results in some nice mathematical arguments in class. We then debrief the sorts over the next day during the second 1/2 of class.

Here’s the thing I love about this structure: Let’s say you have an exploration that’s naturally a 2-part thing (when operating in 20-25 minute parts): You can do that activity over 2 days and then use the second day’s practice 1/2 to review OLDER material. It creates this natural space for older content review. Its so lovely.


This is the part where I admit that there is student push back to this structure over the first 3-4 weeks of class. Every year. The pushback is hard. Usually from both parents and students. I pushback with explaining cognitive science to students and to parents. This year I think I’m making an “Intro to Cognitive Science” letter to parents to send out the first week of school just to front load my reasonings. And here’s the thing. Every. Single. Parent who pushed back with me in those first few weeks, later takes it back. They see the growth in their child. The student starts to feel like the “get the math more” and begins to like the practice structures. They realize this works. And I’ll take 3-4 weeks of pushback if it means there is smooth sailing the rest of the year!

So this blog post wound up WAY longer than I had anticipated, but I hope it helps wrap your head around the 1/2 & 1/2 class structure and possibly convinces you that its a relatively simple instructional shift that yields some pretty good returns in student learning.

Desmos Fellowship Recap 1: Desmos Hacks

So This past weekend I traveled to Desmos HQ in San Francisco, California for 2.5 full days of being a Desmos-Math-Nerd with ~40 other Desmos Fellows from all around the US and Canada and another 15 Desmos Teaching Faculty and Desmos Staff. The words I can use to describe this weekend include, but are not limited to:

  • incredible
  • overwhelming
  • anxiety-inducing
  • wonderful
  • exhilarating
  • revitalizing

The weekend was equal parts me trying to get over imposter-syndrome/social-anxiety and me wanting an infinite amount of time so that I could talk math with my new in-real-life friends.

Because I’m way better at technical explanations in comparison to emotional unpacking, let’s start with some Desmos Hacks I discovered that were MIND BLOWING for me:

Shading Between Two Regions:

Melvin and I were tasked with playing Point Collector and we were both in the mood to try some fancy Desmos equation writing. We both were familiar with the piecewise notation for Desmos and knew that we could use the piecewise functions with some more range restrictions to create regions that would collect points like so:

Screen Shot 2019-07-16 at 7.06.15 PM

BUT the problem was, for those of you who have played point collector in the past, was we needed to EXCLUDE some regions in our graph. And he and I were at the end of our Desmos rope so we did what any good digital citizen would do, we googled it*. And by we, I mean Melvin.

*Update: Melvin didn’t google, he just remembered seeing this graph.

Here’s what we found worked for us:


BUT I had no idea why this worked. I knew it did. So now that I’m back home I’m thinking and here’s what I’ve gotten so far:

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So let’s say you want to shade between two lines, the way I had figured out how to do this in the past was to write the linear equations as functions, and then on a third line write a range restriction for all the y-vales above one function but below another function. It works really well for lines, but when you get to some more complex functions or non-functions line the equations for circles and ellipses things can get tricky with my old method. My students did a lot of Desmos art projects over the past 6 years, so we’ve banged our heads into the wall in the past trying to make the image shade the way we want.

The new way: Take your equations and algebraically set them equal to zero. So y=2x+3 becomes y-2x-3=0, and y=2x+4 becomes y-2x+4=0. Then multiple the equations together and create your inequality to shade either between or outside of the two equations. (NOTE this also means if you set (equation 1)(equation2)=0 it will graph the two equations for you at the same time using only 1 line of desmos!)

Here’s an example of using this formatting for shading between an ellipse and a circle:

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If you, like me, are wondering why this works, well I do not have an answer for you yet. When you have graphed something like:

(y-x-1)(y-x-5)=0 I get why you produce 2 lines. Because either y-x-1=0 or y-x-5=0 and you have those two conditions. What I’m still unsure of and thinking on is why when you graph (y-x-1)(y-x-5)<0 the area between the two graphs is shaded. My initial thinking is that the shaded area is all the ordered pairs that satisfy the conditions that make y-x-1<0 or y-x-5<0. But then I loose that train of thought when I venture out of function territory and think about the above purple ellipse and circle again.

Either way I love this new shading hack in Desmos and will continue to think on why it works.

How to Animate a Slider in Activity Builder: AKA Make a GIF without GIFmos:

If you don’t know who Jay Chow (@mrchowmath) is, go fix that right this instant. My blog can wait. Seriously, I’ll wait here while you go follow him.

Did you follow him? Good. You won’t regret it.

I’m not really sure when I first internet-met Jay, but I do know he started doing Desmos Computational Layer (think computer coding that makes Desmos ABs more fancy) webinars around May 2018 and I was super interested in learning more. So once I got over the Hawaii time is not equal to North Carolina time (I may have accidentally missed the first two webinars because I was asleep…) I started to dip my toe into CL. Here’s the first tweet interaction proof of the many ways in which Jay saves my Desmos big ideas:

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Within the week he’d made an activity builder with 4 different ways to do the color code checking things of my dreams in addition to showing me a better way to do this so the function appears when the solution a student entered is correct.

So freaking cool huh? Yeah. Jay is the best.

Well while we were at Desmos HQ we had some down time to work on a Desmos project of our choosing. I decided to think on an exploration on AB that would result in students discovering the coordinate rules for transformations. In order to do this I wanted a GIF of shapes moving around the plane but ran into a problem with GIFmos doesn’t export labels from graphs. No worries. Jay can fix that.

In two lines of code he got my graph to animate. He did it using my messy pre-determined variables in the reflection slide.

The basics of the animation feature is to create a graph that has ONE slider that determines all of the movement. For the first slide that is the slider t that travels from 0<t<1.

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To animate the slide, go to the AB dashboard, click on the cog by the graph component and enter the code shown:

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Where the animationDuration is the length of the slider (so here that is 1 because the length from 0 to 1 is one. BUT if you had a slider that travels from -2 to 8 you’d need to set animationDuration to 10 in that case).

And then tell CL which variable is the slider in the second line of code.

Easy as pi. Here’s a link to a simplified AB with the CL to grab from Jay.

Another simple thing Jay showed me was how to “turn on” the lanes of points once the transformation was over. It was so easy I’m not sure why I hadn’t thought to try it:

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See those restrictions inside the points? In this slide the a-value is the slider and it travels from 0-2 to make the reflection happen. So when the slider gets to 2 the labels appear. Cool huh?

So there are my two new things I learned about Desmos from Fellows Weekend! More blog posts to come I’m sure, but for now my brain is still very confused by jet lag.

Mandatory Desmos HQ Photo:


Its Been a While

**Taps the microphone**

“Hello, Can you hear me? Anyone out there?”

**Taps Mic**

Hi y’all. So every year I have the goal of blogging more, and then every year, without fail, life throws other obligations/slightly more urgent things for me to do other than blogging. I did a fairly good job at my #Teach180 last year (take one photo from your class every day of the school year), and I hope to keep that up this year here.

As for why I’m dusting the old blog off is to recruit new people to Twitter at the M.E.L.T. conference I’m attending at App State. I’m here taking a course on Discrete Math and it is working as a crash course in all things Discrete. Some of you remember that I’ve been lobbying to end AFM and replace it with a course that is not algebra-based and more open for students of all mathematical backgrounds. WE DID IT! This upcoming 2019-2020 school year will be UNCSA’s first year of Discrete math. So like the good Twitter user that I am, the very first thing I ddi was go to the #MTBoS Spreadsheet of Classes Taught to find my Discrete people…

And I noticed there wasn’t even a Discrete Tab.

So, I then started searching hashtags. On #DiscreteMath I found mostly an unpopulated hashtag with the exception of some GeoGebra gold (pun intended) from John Golden (@mathhombre) with graph theory puzzles and fun.

Not to be dismayed I sent out a tweet:

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and got some responses that I then collected in a list (that I will continue to add onto as I find more people). So now I have a new mission:

Get as many Discrete teachers online as I can find so that we have a place to share ideas, tasks, and general math fun with each other. I’m starting with the 6 lovely individuals I’ve had the pleasure of learning with and from this week at MELT.

So, if you’re new to Twitter and you don’t even know where to start, I have a few suggestions:

  • Pick a handle (Your Twitter @NameGoesHere part) that you can easily say out loud or remember. I choose my name because that way people know who they’re talking to and its easy to remember if you meet me at a conference and want to tweet me.
    • Avoid a bunch of numbers, people are inclined to think you’re a “bot” and may block you.
  • Profile Info add it.
    • Put a picture of yourself on there. Or your dog, your favorite __insert the thing you like__, anything. Just don’t leave it that grey silhouette of a person.
    • Put some things about yourself in the about you section.
      • What classes do you teach?
      • The hashtags you follow
      • What your hobbies are/non-math interests
      • Your website or blog (if you have one)
  • Find your Twitter Friend Group. Not sure who to follow? Search some of the hashtags. The existing hashtags are aligned to the main topic standard in the CCSS as opposed to course:
    • General Math #MTBoS (The Math Twitter-Blog-o-Sphere) and #iTeachMath, #MathPuzzle
    • Algebra 1 #Alg1Chat
    • Geometry #GeomChat
    • Algebra 2 #Alg2Chat
    • PreCalculus #PreCalcChat and #PreCalChat
    • Stats #StatChat, #StatsChat and #APStatChat #APStats
    • Calculus #APCalcChat, #APCalc
    • Middle School Math #MSMathChat
    • Elementary Math #ElemMathChat
    • OpenUp Math Curriculum #OpenUpMath #LearnWithIM
      • Free online MS and HS math curriculum. (alg1/2 and geo coming this summer)
  • Don’t be Shy. Okay, I get it. Engaging with strangers on the internet is a really weird concept. Most of you reading this blog grew up being told not to talk to strangers. Its engrained in our subconscious to be wary of these interactions.
    • Do more than just read tweets.
      • Scared to talk to that human? Okay, like the tweet or Re-Tweet it. This accomplishes 2 things: It stores the tweet on your like-list or timeline for future-you to use, AND it tells that person you liked their stuff and to keep it coming.
      • Ready to talk to that human? Awesome! If you see a task you like, as follow up questions. What worked well? What would they change? Were their any misconceptions by the students? If they could improve one thing what would it be? We’re on here to reflect and learn from each other. The only way to do that is to communicate with each other.
    • Share what you’re doing in your classroom. Don’t be afraid of needing everything to be perfect. The way we all make twitter a less-scary place is if people put out their less-than-perfect things as well as their perfectly awesome things. Want to see examples, check out

And if you need more reasons for joining in on the online fun, here’s my blog post from a few years ago about why I made the jump from Twitter Lurking (being a passive reader of twitter) to a Twitter Contributor (talking about math with other people and sharing things from my class) here.

Need more convincing? Okay:

  • I plan my geometry course with teachers I’ve never met in real life who live all over the county and the world. We talk at least a handful of times a week. We have a google document where we put ideas for lessons. We bounce ideas off each other constantly and are vulnerable about where are weakness are as teachers and help each other in improving in those areas.
  • The math family I have met on twitter have changed my life. When I found twitter I was an overwhelmed beginning teacher (BT) with no textbook, no subject-specific mentor (but an amazing BT mentor), and no idea of what I was doing. Twitter gave me free lessons filled with rich tasks for FREE. Twitter gave me a supportive professional learning network and has helped me grow into a teacher who strives to learn more from my peers.

Join me on Twitter family. Its the best PD I’ve ever had the opportunity to be a part of. There are legitimacy teachers on Twitter 24 hours a day 7 days a week thanks to our Twitter friends on the other side of the earth from where we are.

Geometric Wrapping Paper

A few days ago I posted on twitter about a project I did in geometry this year, which was unoriginally, called the Geometry Fall Semester Project- Wrapping Paper.

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When friends ask for a blog post, I have to oblige. So here I am proctoring a fall semester final exam and blogging. To whom ever stumbles upon this post know that I like this project enough that I am 100% doing it next year. I also want to adjust a few things about this project because I learned a few things and think I have a way to streamline some student issues/misconceptions that occurred in the process of the project.


So the idea for this came to me when I stumbled across this video on the internet from SkillShare. While watching the video a million things few through my mind of possible uses in my math classroom, but I landed on turning it into the final cumulative skills task for my geometry students.


My geometry course starts out reeeeeaaaaally slow. Like. We have only learned the Basics of Geometry (points, lines, and planes), Logic, parallel lines cut by transversals, perpendicular line problems, transformations, and proofs of parallel line things. I spend an awful long time on proofs. I can do this because I have the luxury of teaching at a school with no state exams. Also, I have this (unproven) idea that if I hit proofs really hard first semester it will make them go more smoothly second semester (initial research seems to agree with me based on student feedback and assessments). So the final project didn’t have many skills in a list to choose from. So I opted for Transformations and parallel lines with transversals.

Students were told to create a grid via parallel lines and transversals. To find a 1″ by 2″ image to transform around the plane (translations, rotations, reflections, and dilations). They were also asked to find a small image (1/2″ by 1/2″) to put in special angle pairs on their parallel line/transversal plane (like alternate interior angles).

Once students had their main template completed to their liking with the foundation for their wrapping paper with all the transformations and small image placements where they wanted it to be we followed the video tutorial on how to create a self-repeating space. The Cliffs Notes is cut the paper in half long ways, reattach the paper so the middle (where you cut) is now on the outside and the outside edges are now meeting in the middle of the page. Add any image you like to the empty space. Repeat the process by cutting horizontally and adding images to blank space.

Here are all of my student’s designs. 

Here is the project paper I gave students. I want to re-do it for next year

Things I’d do differently/better next time:

  • I need to change the wording of the handout to say that we want to create a GRID with parallel lines and transversals. This will aid in having translations that make sense if their transversals are all also parallel to one another.
  • Yell from the clifftops that images cannot run off the edges of the paper you use for the template (aka the before you cut and paste the paper part of the project). This prevents decapitated Snoopy’s from repeating all over your design.
  • Also yell from the clifftops that students should record what transformations they are doing AS THEY WORK on the template. Its really difficult to remember what you did three days after you drew it.

Anyways, I hope you like the project. Let me know what recommendations you have for improvement or if you use it and make it better.

Iteration Number 6 with Standards Based Grading

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So some background on me. I apparently wrote in a journal at some point in high school, in-between angsty “omg they are so dreamy” entries about some crush the following:

There is no way in hell I’d ever be a teacher. It’ll be a miracle if I made it out of high school and there’s no way I’d ever come back.

Well aside from teenager me was wrong about my life trajectory I wasn’t the best student. I didn’t learn how to be a decent student until half way through college, and by then I knew I really didn’t want to be a teacher. So I looked into other job options–mostly the type where you sit in front of a computer all day crunching numbers to determine if a process is optimal. Not what I wanted to do with my life. So, like any post-college-I-Have-No-Idea-What-To-Do-With-My-Life person, I joined the Peace Corps. According to a former teacher, in 5th grade when we learned about service branches of the government I stated that I’d join the Peace Corps one day–but I didn’t remember that, I just knew being a health volunteer sounded like fun.

In Peru I realized that, in fact, I did want to be a teacher. I stepped in and taught a few math classes in my town and fell in love with teaching rural farm kids the math needed to budget for and build their future house. So I applied to Duke for their Masters in Teaching Program.

In grad school I was partnered with a mentor teacher, Mr. Belcher (true story, that is his name…he taught freshman. There were jokes.) who got on board the standards based grading bandwagon early. This was Fall 2011 and the man rocked my world in telling me that we weren’t grading things out of 100%, each course objective was worth 10 points, so a test might be 60 points and cover 6 topics. The 10 points weren’t on a rubric–it was more a give students problems for that standard that you will grade on a 10 point scale. Like, 2 points for the correct slope, and 1 for the correct y-intercept… kinda thing. Not full-scale SBG, but it was what I was told he did, so I did. Students could reassess–as many times as they wanted before the end of the grading period. So basically I never learned how to grade, as a teacher, in a traditional setting.

So when I got a classroom of my own I did what Belcher did, because its what I knew. And I kept on doing that, with minor tweaks, until I moved schools. By the time I moved to UNCSA I had been lurking on the #MTBoS for long enough to piece together I needed to get to a rubric based grading system a.s.a.p. instead of the 10-point method. So I did a 10 point scale (what can I say, it translates easy into a traditional grade book) along the lines of:

  • 10-essentially correct
  • 9-non-content-based, yet mathematical error (dropped negative in a solution, added wrong, so on)
  • 8-minor content error (example is in a transformation f(x-6) a student says that’s a shift 6 units to the left)
  • 7-semi-importatnt content error
  • 6-very important content error
  • 5-OMG what did you do??
  • 4-No. You didn’t get the content but you wrote something.

As you can tell. This isn’t a very…objective…rubric. Like, in my mind when I stole it and adapted it for use in my classroom the distinctions between a 8 and a 7 and a 6 were obvious. But when I actually got to the grading, it was really hard to make that distinction. Like. I found myself making a per-standard-conversion for all the possible errors a student might make and what grade I’d give it based on some rather subjective ranking on my part.

If I didn’t grade ALL of my assessments in the same sitting (uninterrupted without taking even a bathroom break) I found I wasn’t consistent with my rubric. So over the next 2 years I tried to refine my 10 point rubric to be less subjective and more objective. I think I would up using someone from TMC17’s 10 point scale rubric here:

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Much like before, if felt like it would work better, because it seemed less subjective. But, alas. I didn’t feel any better.

Then a teacher from North Carolina School of Science and Math, our sister school, came to talk to us about how he does SBG with Interleaving and Spacing (if those last two words are new to you, I’m going to direct you to Anna Vance to learn more). In his class standards earn:

  • 2-Essentially correct
  • 1-Content Error–Not Yet
  • 0-You left it blank

His course is structured so that in class students will see each standard 3 times (i.e. will have three opportunities to show mastery) and the most recent assessment goes in the book. After those three in class assessments, a student can ask to take another reassessment, if they prove they have been actively working to improve the skill by doing extra HW or redoing problems from class or their notes, then they can sign up for a student-initiated reassessment.

The thing I liked most about his set up is that he divides the standards into two categories: Core Content (rote skills) and Advanced Skills (interpreting type questions, or justification, more complex synthesis of CC skills). Then the average of the CC and AS skills yield a traditional grade:

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My department has made a few tweaks to get full buy in, namely that we are going to average the two CC-averages and AS-averages together before converting to a traditional grade.

So its not perfect. But it feels more perfect than my last few iterations of SBG. The part that I really, REALLY, enjoy is that the grade feels 100% objective. Either you got the content, we’re getting there but not yet, or you have no clue. There isn’t a grey area…

Then again, I’ve said that before…like 5 other times…so…yeah. Here goes nothing!

Bridging My Worlds–Twitter For Everyone

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I have a new goal in my professional life. I’m not exactly sure when I decided on this goal, but I think it has a lot to do with the conversations around #MTBoS and #iTeachMath that occurred at Twitter Math Camp 2017. I wrote a post on it here if you wanted to read it–its about making the leap from “Lurker” to “Participant” in the #MTBoS, the group I call my Math Family.

So sometime during TMC17 we decided to take a #MTBoSNC photo. It was a photo of all the wonderful NC teachers who found a way to pay for a professional development in Atlanta. We either paid our own way, of somehow convinced administration that sending us to a Twitter Math Camp was a good use of their resources (it was).


Somewhere on this stairwell the idea to get together once we were back in NC emerged. I mean, there were SIXTEEN of us from NC at one conference and most of us hadn’t met the others (in real life or on twitter). So we did. We planned a Tweet Up for the Fall of 2017 at my school on a Saturday in October. We had about 20 educators come to join us, we shared “My Favorites” and some people piloted their NCCTM sessions for later in the fall with us. It was nice. But I knew it could be more.

I tried to plan another on in the spring but between Spring Breaks that didn’t overlap, NCCTM regionals, and me being in the process of moving for the third time in a school year it didn’t happen.

Fast forward to this years TMC. I’m ready to get the wheels turning on planning another Fall Tweet Up. I have a dream for what I want #MTBoSNC Tweet Ups to become, but if I’m going to be 100% truthful, I haven’t a clue as to how to authentically do this. So hey there internet friend, help me and share your thoughts.

Here’s what I want for the #MTBoSNC Tweet Ups:

  • Tweet Ups would be an opportunity for an active Twitter participant to bring a colleague who is:
    • New to Twitter and feeling overwhelmed
    • Not sure if Twitter is worth their time and energy
    • Pretty sure that Twitter is the death of American politics and culture.
    • Unaware that people still use Twitter

and to show that new person the power of this platform for professional growth.

  • Involvement from all grade bands in Education, from Kindergarten to University level courses. I’m not sure how to accomplish this as I will admit to surrounding myself with mostly high school teachers. After Megan’s “My Favorite” session this year on teaching in her Elementary school daughter’s classroom one of my goals this year is to go observe elementary school teachers and to add them to my learning network.
  • For Tweet Ups to occur 4 times a year, alternating from the Mountains, to the Triad/Triangle, to that section of NC between Fayetteville and Southern Pines that doesn’t have a short name, to the Coast. I want ALL teachers in NC to have the opportunity to attend a Tweet Up without feeling like they have to find a way to stay overnight in a city far from their home.
    • Call for help: Let me know if you’re school is in one of those regions and you’d be interested in hosting. I can tell you more about what my school does.
  • A diverse group of participants. I was reading a post today by Lauren reflecting on her experiences at #DesFellows weekend this summer as a black woman. How she was hesitant to go to Desmos (Yes, to Desmos, the math-teacher-holy-grail-of-free-tech) because:

Adding me adds “diversity” to their group. Prior to coming to DesmosHQ for the weekend, I had to psych myself up about not being the token black female and not fitting any particular role that they needed me to fill to match their agenda. I wanted to belong as a math teacher, not as a black math teacher.

She said that when she arrived at DesmosHQ and found herself in a room filled with people actively working to disrupt the systems in our education process that automatically favor the majority (whiteness) over the minority, that “they are doing the work and not pretending like these inequities don’t exist.” Only then did she feel as through her invitation to Desmos Fellowship became belonging in the Desmos Fellowship.

Before Lauren’s post I can say that I didn’t understand the differences people were noting during the TMC17 discussions on #MTBoS vs #iTeachMath–Those who felt the #MTBoS was uninviting/intimidating and those who felt loved and supported by the #MTBoS. I, naively, thought you could just invite someone to belong in your community. Lauren’s post has shaken (in the best of ways) my understanding of how to expand your community. I have much to learn. I am eager to learn. How can we make #MTBoSNC Tweet Ups achieve this goal–of inviting bringing sharing with people unfamiliar with the #MTBoS community the wonders of belonging to the community? I’d love your help with this.


So there it is. My thoughts on what the future of #MTBoSNC could look like. I’m going to need your help. I took the first steps today, I introduced my Facebook World to my Twitter World to try and get more people I know to participate in our wonderful math family, won’t you do the same?
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Full Text:

Hey NC Math Teachers,

I’m going to bridge my two universes for a second. So hi! If you are reading this you are on Facebook and I know you in-real-life somehow. But I want to introduce you to my other world, my Twitter Math Family. You see, Twitter is THE BEST place to go for teacher development. Trust me. There are people there tweeting 24hr/day about math (thanks to the Australian cohort holding it down while we sleep on this side of the earth).

We tweet about math. About math lessons, math projects, math plans, wonderful successes and epic failures. We tweet about good days, we tweet for love on bad days. We are vulnerable, we speak our truth, and most importantly we raise each other up. Twitter is where we can talk about the practices that make our classroom ours so that we can learn from each other.

Now I know many of you are familiar with Teachers Pay Teachers (for those of you who aren’t, no worries. Don’t waste your time or money), go ahead and burn that log in. You don’t need them anymore. My Twitter Family (#MTBoS if you’re searching for us online) will give you things for FREE. You want that lesson? Cool, tweet me. You want an answer key so you can make sure you remembered probability correctly? No problem, we’ve got you. The teachers on Twitter are sharing EVERYTHING in their classroom. This community is centered around open source classroom design. We share so that we can get feedback on how to improve what we’re doing.

My Twitter family has shaped who I am as a teacher–They make me constantly strive to be better and to do a better service to my students. In an effort to get more NC teachers on Twitter (which apparently is my new mission in life) I want to invite you, my Facebook friends, to come and meet my internet friends.

I’m going to host a Tweet Up at my school this fall. We’re narrowing down a date, and I’d love for you to share your availability on the form I’ll post below so that we can get you to join us. A Tweet Up is an informal day-long professional development where Math Twitter Family can share their favorite lesson/project/routine/structure with the rest of us. A time to recharge those teaching batteries that may begin to run low before Thanksgiving Break rolls around.

I’m making this post public. So share it with anyone you think might be interested. I hope to see you there friends!

Fake It Until You Make It–PlannerLife Lite

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So I want to be one of those teachers who can flip open a plan book, turn to week 8 from two years ago and remember what activity they did and even have notes as to what went well and what didn’t. I’m not that teacher. I’m the one who can’t remember what we did last Tuesday let alone where on Earth I left the copies for next period. I’m that teacher that when you see my desk you make some joke like, “well you know what they say about people with a cluttered desk right?” No. No I don’t. But I know somewhere under a stack of papers there is an empty roll of Scotch tape I can throw at you if you’ll give me a second to find it…

Have I painted an accurate picture of my teacher-planner-life for you? Don’t get me wrong, I plan. Up to this year I will make a Unit plan something that looks like:

Unit “Blah de Blah”

  • Week 1: Topics A, B, C
    • Desmos Thing from here and here on days __ and __
    • Card Sort here
    • Group White Board practice on days __ and __ after __ and ___.
  • Week 2: Topics C, D, and A
    • Yada Yada
    • You get the point

Its usually done on scrap paper. It stays around just long enough for me to create guided notes that go with that chapter. It then disappears into the abyss of papers on my desk. Months later being tossed into the recycling because “What was this for again?” means I don’t need it and to toss it.

So back to why I want to be that #PlannerLife teacher. Its not because I want to do the same thing every year. Lord knows I’d get bored with that. Or I’d find some amazing thing that someone on Twitter did that was WAY better than what I did and I’ll want to steal it and change my plan (Heck that happened twice already this year once I made photocopies of my Unit 1 notes for AFM). I want to be that organized and to know what I did last year for the analysis. Being able to go back and read a note to myself that says something like: “Trig Ratios Intro went okay, make sure to not show an accidental almost-isocelese triangle next year …” I want the #LifeHack tips to my future self from my past self.

So to that end I’m trying to up my planning game. I’ve got a Google Doc for AFM and Geometry with spaces for each day of the year. I’m writing down what I’m going from warm ups to class closures with links to activities. My hope is that this becomes a living and breathing document that will help me grow as a teacher. I am going to add a row for reminders to future me.

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I also bought a non-dated planner (Live Whale) on Amazon that I’m in LOVE with. Mostly because if you forget a week its no big deal, just pick up where you left off and no worries about a ton of blank pages to remind you that you suck at this new habit you’re trying to form. I even found out that the 0.5″x0.75″ Avery labels fit perfectly in the daily view for one class period. So I’ve color coded them Green for Geometry and Blue for AFM. I’m using labels because then if plans change I can peel the sticker off or put another over it.


So its a start. I have routines set up to try and stick with it. Mainly Sunday toddler naps are for laying out the next week or two and putting in stickers. Try and write a brief “here’s what happened today” in the Google Doc before I leave school each day. Wish me luck!

When I’m not Mathing, I’m Cooking

Its Saturday, my parents are over for a visit with my daughter (is there anything better than a grandparent play day? I don’t think so.) and I’m trying to stay out of their way by attempting to finish the Advanced Desmos Geometry portion of the scavenger hunt (here). I’m currently stuck on number 8, but I’m sure if I walk away for a bit and come back I’ll re-remember how to do this. It occurred to me that I should blog, but its Saturday, and like my last real Saturday before school’s back in session, so I don’t want to talk school today, instead I will talk about food.

I am an avid baker. My husband says he can tell how stressed I am in any given week by what I bake. If its a light stress then we get something quick: Pizza for dinner one night, maybe a focaccia, or a chocolate chip cookie. Something that’s quick to make and no real fuss. If its a heavy stress week thats where the butter get involved–cue the pasty. Its involved, tedious, ample opportunity for kneading dough and the taking out of frustrations while beating butter into submission and folding it into flaky layers. I’m also a stress eater, so high stress=I eat WAY too much food.

In an effort to avoid stress eating I do a few simple things during the school year that both help keep the over-eating-tendencies at bay:

  • I don’t buy chocolate chips in a Costco sized bag. Yes its cheaper than buying a small bag at the store. But when I only have 1 small bag I don’t run into the kitchen to grab a handful of chips to snack on as I grade the quiz where all my students somehow forgot how to expand a binomial (is it just me?). When its just the one small bag I’m more inclined to save the chips for cookies. When I need cookies. (need haha)
  • I buy veggies to snack on and cut them into snacking sizes Sunday evening while the hubs washes dishes and we listen to a Wait, Wait, Don’t Tell Me podcast. That way if I want to stress eat my only options are veggies. Yes, its never what I want to stress eat, but when its the only option you do what you gotta do.
  • I throw fruit into a jug of water in the fridge so I have tasty water. I hate LeCroix–its fancy bubble-filled-water that tastes mildly like the aluminum can it comes in with a weirdly fruit-ish aftertaste (I know, I just lost 1/2 my blog readers). I like the idea of LeCroix, just not the execution. So I make my own fruity water in an attempt to make myself drink more water. Favorite combos are:
    • Watermelon and Mint
    • Strawberry and Mint
    • Orange and Blueberry
    • Cucumber and Strawberry
  • And I do a Lazy Person’s version of Meal Prepping. So before I had a kid I did the full on meal prepping–like the spend all Sunday making food for the whole week’s worth of breakfasts/lunches/dinner. But then I had a kid, and let me tell you how impossible it is for me to spend more than an hour doing anything without having my toddler throw a fit that I’m ignoring her and not drawing with crayons at her table. So now I do a lazy meal prep:
    • The kid goes to bed by 6:30pm (#iAmSpoiledAndIKnowIt) and hubs is on nighttime routine duty so I can cook.
    • I double (or sometimes triple) the recipe. It usually takes the same amount of time to double a recipe, just use a bigger pot/pan/container thank you usually would.
    • Eat the meal as usual, freeze the leftovers in 1-2 serving containers for use later.
    • I usually cook two days a week and then once on the weekend. We eat leftovers the rest of the week. My husband eats triple the amount I do and my toddler eats almost as much as I do and this plan feeds us all well and keeps down the amount of times we order take out because we’re too tired to cook.
      • On a related note, you Need to go and buy an Instant Pot. Like now. It’ll cook a whole fryer chicken in 45 minutes, 3 racks of ribs in an hour, or a pork loin in 40 minutes. It’ll turn a dozen eggs into hard boiled perfection in 10 minutes (or soft boiled in 7). It is worth it’s weight in gold.
      • Favorite source for recipes is SkinnyTaste-her blog has weekly meal plans that are great if you’re not a good planner, her recipes are simple and cheap, and require nothing that you can’t find at a local store. She also has two cookbooks with a third on the way. She’s my hero.

So thanks for reading about how I cook/bake during the school year.

If you need baking recipes, ones that I guarantee will work if you follow the directions, from cookies to bread, from pies to pastry, go to King Arthur Flour’s site and drool. They also will help if you tweet them. And as a community of avid tweeters, that’s an important tool for us 🙂