#mathartchallenge Loop Art instructional videos

Many of us are doing distance learning of some form or another these days. I have nowhere near the emotional capacity to write any form of post about how I feel about it right now, but I do have an activity to share with you!

Our district is doing voluntary learning opportunities, so we are not grading what our students do or addressing new content. So my team is trying to do some fun things to engage our students. Just as a human myself who has been missing doing math daily, I’ve been participating in the #mathartchallenge organized by Annie Perkins over on twitter.

Thinking it would be fun for our students to create some mathy art, my team decided to turn the instructions into video form and have students work on them next week. I chose the activity that makes various loops and looks kind of like a subway map when you’ve finished.

So, if you’re looking for something fun to do yourself or with students, here it is:

Video instructions to make your own graph paper if you don’t have a printer at home

Video instructions on how to make Loop Art

The key you will need:

A full video example of me making a Loop Art piece in real time

Example Loop Arts by me, my students, and other people I know


Share your Loop Art on twitter with the hashtag #mathartchallenge if you do some, so Annie, myself, and others participating in the challenge can find it!

If you are looking to go a little deeper into the probability involved, here’s a set of questions I came up with that could be used with the activity for a probability and statistics class or unit.

Classroom Mashup 03: Quick Desmos Activities

First, I’m renaming my “Friday Mashup” series, because who wants to be limited to posting that only on Fridays? It’s a quick rundown of things I want to share that aren’t quite big enough for their own blog post. Here are previous ones:

01 | 02

Today’s is about two quick Desmos Activity Builders that I created, one for my Algebra 1 class and one for Algebra 2.

Polygraph: Polynomial Functions

If you haven’t used a Desmos Polygraph in your classroom yet, you’re missing out! It’s the most surefire way to force students to reckon with their vocabulary understanding. There’s no way for them to pretend here. If they don’t understand it, they have to ask for help or they literally cannot play the game. There exists a Polygraph for pretty much every type of function, but most of them are the graphs of those functions.

My Algebra 1 students are learning terminology for degrees of polynomials and the number of terms that it has, and in past years I have realized that this vocabulary does not stick at all. We finish a whole unit on solving quadratics and they don’t know what the word quadratic actually means! So I made a polygraph, but of polynomial EXPRESSIONS instead of graphs. In Desmos, you can insert a picture into their graphs, so I typed out the equations, screengrabbed them, and inserted them into graphs, turning the axes and gridlines off.

Here you can see an example game from two of my students.

(Sidenote: You can sign up for a free teacher account with Equatio and easily type mathematical notation or create graphs without having to open a Google Doc or Word Doc, for purposes of screengrabbing. I use it constantly to insert equations on things that don’t have a built in equation editor, or for things like this)

Matching Factored Form to Standard Form Polynomials

My Algebra 2 students are just starting to factor polynomial expressions, in preparation for solving polynomial equations. I have a traditional worksheet assignment for them on this topic, but I wanted a bit of practice first that was more guided. I thought initially of doing a question stack, but I didn’t want to do 10 questions and didn’t want to spend the time creating a new template for fewer questions. My next thought was matching, but I realized I didn’t really want to print that out on cards, and then my brain remembered that card sorts are an option on Desmos Activity Builder!

Each polynomial expression has a matching factored form card, which students can drag on top of each other to match together. The answer key is even set so that you can put the teacher screen on the board for students to check their work if you want! I then simply added a graph screen onto the activity, since my students are factoring using x-intercepts on a graph to get them started, so that they could do their graphing without leaving the activity or needing multiple tabs. If you don’t want this screen, you could make a copy of the activity and delete that screen!

I haven’t used this one with students yet, but I think it will be a good quick check of their understanding and a confidence builder before we do more open ended factoring work.

Let me know if you use either of these Desmos Activities, or if you have ideas to improve them (or if you improve them yourself!)

Color By Number: Multiplying Polynomials Resource

My Algebra 2 students are beginning their unit on solving polynomial equations, and as I was looking through my calendar from last year and my files, I realized that most of the practice for this unit ends up being just straight practice worksheets. Which is what they need, once they get to the whole process of solving an entire polynomial equation by factoring out rational roots and then solving the remaining quadratics – just a lot of examples. But not wanting them to have an entire unit with no “fun” activities, I went in search of something fun to start the unit with, when they briefly review how to multiply polynomials.

In my search, I could not seem to find anything that fit what I wanted. There are a LOT of resources for multiplying binomials by binomials, which is the Algebra 1 skill that is the precursor to this, but all I could find for multiplying higher degree polynomials together, or multiplying more than two polynomials together, was…worksheets.

I did find a few color by number activities for multiplying binomial by binomial and that made me wonder if customizable color by number activities existed. A quick TeachersPayTeachers search (on the FREE only setting, I never spend money on that site because I disagree with that practice, but that’s another story) found me this from Pink Cat Studio. I grabbed a worksheet from our Algebra 2 textbook (Holt, Rinehart, Winston Algebra 2 from 2003, we have not updated our textbook in awhile) and chose six problems off of it to match the six colors in the image. I mixed up the numbers so they didn’t go in order on the key, and the Pink Cat Studio site spit out an image file for me to save!

I then just typed the six problems I had picked, and made an answer bank so students could match the colors with the correct problem number!

As you can see, some of my students chose to utilize a distribution strategy, while others chose to utilize an area strategy.

If you want to use this resource, I have the Google Doc, which you can make a copy of to edit, or the PDF version.

Logarithmic Modeling: pH lab and Murder Mystery (Algebra 2/Pre-Calculus)

Last year was my first year ever teaching pre-calculus. Most of the year, my goal for each lesson was to 1) come up with a clear and concise interactive notebook page and 2) teach the content well. I definitely did not always hit #1, and I’d like to think I hit #2 most of the time, but I left myself a lot of notes in my lesson plan spreadsheet to improve for this year.

However, with this being my 7th year teaching Algebra 1 and my 6th year teaching Algebra 2, both of those classes feel nicely dotted with “fun” activities – card sorts, question stacks, puzzles, mazes, row games, scavenger hunts, Desmos activities, etc. Pre-Calc felt pretty lackluster last year. Mostly textbook assignments alternated with notes, interspersed with quizzes. Not that there’s anything wrong with that if it’s done well in a classroom, but I wanted to try this year to spice up pre-calc a bit and incorporate some of the practice structures that I find students enjoy more. Reminding myself that Algebra 1 has become full of these activities over SEVEN YEARS, I am starting slowly and trying to find or create at least one “more interesting” practice activity per chapter this year.

Currently, we are working on Chapter 3 of the Demana, Waits, Foley, Kennedy Precalculus textbook: Exponential, Logistic, and Logarithmic Functions. In our district’s curriculum, we focus solely on the exponential and logarithmic functions here. Section 3.5 of the book covers exponential and logarithmic modeling, aka what do we actually use these types of functions for? There are a couple problems about earthquakes, a couple about pH, and a couple about Newton’s Law of Cooling. I think this content is really interesting to work with, but 6 textbook problems just isn’t going to pique that interest in students.

Last year on twitter, I saw and saved this image from…SOMEONE. SOMEWHERE. Honestly, I’ve tried searching twitter for “pH lab logarithm” and so many other search terms, I’ve tried reverse image searching…nothing. If you know where this image was posted, I’d love to give the teacher credit for the idea!

Now looking at it again, I’m getting more ideas for next year because I see they used colored pencils to show the color their pH strip turned…

Anyways, I asked our science teachers if they had any materials to test pH of things, and my friend Jess Hughes kindly supplied me with some pH test strip rolls that she wasn’t sure even worked, so I went home and stuck them in some vinegar and things and they did!

I put some coffee, Maalox, vinegar, and distilled water in containers and brought them to school. I grabbed a bar of soap (which you have to dunk in water to get the pH strips to work), and filled another container with drinking fountain water from school. Here’s where you can find the worksheet I gave students along with this. Make a copy in your own Drive if you want to edit it!

Then, I swear I had seen a teacher do a lab with Newton’s Law of Cooling and a murder on twitter, so I went to find it. I found this from Jasmine Castanon, this (and this) from Cassandra Valenti, and this from Rebekah Mozdeh (via Sarah Carter). All great ideas, but failing to find something ready made that satisfied everything I wanted it to be, I decided to write my own story. I only have 5 students in my Pre-calc class, so it wasn’t too much effort to come up with a plot line that included each of them. They had so much fun reading the story and laughing about what would maybe be true in 30 years and what they hoped definitely wouldn’t be.

Here is a version of the story with my students’ names removed. I highlighted the information that is actually relevant to Newton’s Law of Cooling, because the rest of the story is just about who did it. I made up the temperatures and have no idea how accurate they are to actual cooling dead bodies – I started doing research on that and realized that it would take me a long time to figure out and decided it wasn’t worth it!

Students definitely enjoyed this more than just a textbook assignment and I think it got the point across how logarithms are actually used in our society.

Book Recommendations (Vol. 12)

2019 has ended! So, it’s time for me to do my quarterly book recommendations post. At this point, I’ve been doing these recommendations for 3 years!

You can read previous posts from this series here:

Vol. 01 | Vol. 02 | Vol. 03 | Vol. 04 | Vol. 05 | Vol. 06 | Vol. 07 | Vol. 08 | Vol. 09 | Vol. 10 | Vol. 11

My final 2019 book total was 65 books, meaning I read 15 in this final quarter of the year. I always make my Goodreads book goal 52 books (1 per week), and even though I have easily beaten it in each of the past several years, I do not plan to raise the goal because I never want my reading to become stressful – it’s for fun!

Anyways, let’s do my top 5 books of the last quarter, and if you scroll to the end, you’ll find my top 3 books of the year!

Middlegame – Seanan McGuire

Rodger and Dodger are twins. They were not born, but created with alchemy to be the embodiment of the universe’s perfection. But they’re not interested in being used by their creator. They want this authority for themselves.

I would gasp while reading this book, and my boyfriend would say, “what happened?” and I would say, “I don’t know entirely.” You reach understanding of what’s happening along with Rodger and Dodger just at the end and it’s a miraculously spun tale fraught with danger and possible ends of the world. The writing is impeccable and every timejump is seamlessly woven to propel you to the next page and the next.

The Boy in the Striped Pajamas – John Boyne

Fences like this exist all over the world. We hope you never have to encounter one.

If you’ve never read this book, grab the tissues. I unfortunately read the end while waiting for an oil change and was very much struggling not to sob hysterically in the auto shop. It’s a remarkably human story of a terrible thing and you should read it.

The Testaments – Margaret Atwood

What happens after the Handmaid’s Tale? How does Gilead grow and change? Find out from the three characters in The Testaments. Inspired by all the questions Margaret Atwood’s been asked for years, plus the society we unfortunately live in right now.

I read the Handmaid’s Tale just earlier this year and so I knew I needed to read the sequel as soon as it came out. It certainly gives you a lot to think about and consider regarding the consequences of some of the laws and actions being taken currently in America. I thought the look at Gilead from the outside was really interesting as well.

Look Both Ways: A Tale Told in Ten Blocks – Jason Reynolds

The story of ten walks home from middle school. The stories of our students.

Jason Reynolds is brilliant. His books regularly appear on my recommendations. Even though this one is middle grade, I thoroughly enjoyed reading it. Especially as a teacher, you’ll appreciate the intricacies of the things that affect our students just on their journeys home from school. Reynolds is a master at giving voice to those who typically are generalized and ignored and he does it again here. This is much less heavy than his typical read, but still important and interesting (and does have a bit of heaviness in there).

Call Down the Hawk – Maggie Stiefvater

The first in Stiefvater’s trilogy about Ronan Lynch and the Dreamers, taking place after the events of the Raven Cycle.

If you read and loved the Raven Cycle, you’ve been looking forward to this book for awhile. For some of it, my opinions are reserved based upon where the storyline goes in the latter two books of the trilogy, but I did really enjoy this. I am also endlessly impressed with Stiefvater’s battle with her health and the work that she produced despite the fact that she like, didn’t know what was happening to her body or mind for several years. Read this post and you’ll be stunned at how she ever wrote Raven King or All the Crooked Saints.

Top 3 Books of 2019:

  1. Red, White, & Royal Blue – Casey McQuiston
  2. Math With Bad Drawings – Ben Orlin
  3. American Gods – Neil Gaiman

2020: Notice. Wonder. Seek.

In the tradition of my New Year’s “theme statements”, it’s time to reflect on 2019 and look forward to 2020.

My theme for 2019 was Multiplying Me, Adding You.

For “Multiplying Me”, I said I wanted to do more of the parts of myself I am proud of. I wanted to bake more, and I really think I accomplished that. I made a Yule Log cake for my boyfriend’s family Christmas that got lots of compliments and made me very pleased! I proudly completed my master’s degree and graduated in December, and also was awarded the Yager Award for Teaching Excellence by UNI. Both of these made me proud of the work I am doing in my teaching. I read lots of great books, listened to good podcasts, watched good shows and movies. I redid my home library and it’s organized beautifully.

For “Adding You”, I’m not sure how I did entirely. At times I felt like I improved in my relationships and communication with family, and at times I felt like it was worse. I feel like I’ve developed a very strong, mature, and honest relationship with my boyfriend.

I do think I’ve reached for my phone less in social situations, or even for example have been more present while watching movies or shows, not trying to multitask always. My friend group in town has gotten busier and played trivia less, but we try to keep up montly dinner parties/game nights. I think I post less on social media, although I’m not going to analyze it to tell, but I have planned for 2020 to attend LeakyCon, a Harry Potter fan conference again, and will get to see many of my internet friends in person again for the first time in awhile.

So, 2020. I thought a lot about the phrase “Hindsight is 20/20” when thinking of what my phrase should be. That phrase in itself is not a great thing, because it implies that you don’t necessarily do things the way you would have wanted, but when you look back in hindsight, things are more clear. So my 2020 phrase goes more for wanting to make things clear from the start.

Notice. Wonder. Seek.

(yes, it’s also inspired by the #mtbos notice/wonder classroom routine name, in a way).

To Notice, I want to pay more attention to my surroundings. I want to notice when students need something else from me. I want to notice when I haven’t called my mom in awhile. Notice when someone is excited about something and join in on that excitement. Notice when someone is upset and be with them in that. Notice other perspectives on things when I’m upset or in disagreement. Think of friends and family at significant times and reach out – maybe write more letters or cards this year. I want to lend my voice to those who could benefit from more voices, and to acknowledge when people around me need to be acknowledged.

To Wonder, I want to question the sources of social media posts. I want to ask friends and family more about things they’re doing and be genuinely interested in them, giving them a chance to share things they’re probably excited about. I want to read more widely and listen more widely and watch more widely, and just take in all of the interesting new content that I typically do. I want to push myself to take the risk and “wonder” if something new could work in my classroom, and just give it a try. I want to open myself to new ways of doing things and not just go with the way I always do it, and to try new things that I’ve never done before.

To Seek, I want to continue learning even though my master’s is complete. I want to read more math and teaching books this year to replace the classes I’m no longer taking. I want to take advantage of opportunities for learning like our yearly tech bootcamp in our district. Maybe I’ll take a cooking class or baking class to improve my abilities there. I want to be involved in the caucuses and election, and make sure all of my opinions are informed.

2019 was a great year for me, and I’m hoping to make 2020 even better. Let’s see how the hindsight turns out 🙂

Google Slides Activities: Algebra 1, Algebra 2, Pre-Calculus

I’ve mentioned in several of my most recent posts the technology bootcamp I attended at the end of the summer. I’m going to mention it again because it really is just such a great PD opportunity – districts take note, when you let the TEACHERS run your PD, it’s actually useful to the other TEACHERS.

Our district, like many districts, is in a bit of a budget crisis. One thing they tried to tell us at the start of the year was to make less copies. I use a lot of copies, because my students do interactive notebooks. I am maybe trying to brainstorm a way to use less paper doing that next year, but I really believe in the INB process, especially for my at-risk students who are often lacking a lot of organizational and note-taking skills. So, I’m trying really hard this year to make as few OTHER copies as I can. I have a lot of card sorts, question stacks, and other activities I can reuse from previous years, but I’m always looking to add new activities and improve my instruction every year.

One of the sessions in our tech bootcamp that I attended was a Google Slides 102 session. You can view the presentation from that session here – it was presented by Evan Mosier. As I was sitting in it, I wasn’t super floored at first, but then I realized the potential some of these ideas had to help me use less copies and still be interactive!

So, I’m sharing a few of these Google Slides activities I’ve made. I’ve linked them so that it will force you to make your own copy in your Google Drive when you open it! That way, you can make any changes you’d like.

For each of these, I assigned them with the “make a copy for each student” option in Google Classroom. Each student has their own copy and changes that they make can be viewed by the teacher through Google Classroom, and it doesn’t change the original document or anyone else’s.

1. Solving Linear Inequalities Critique, Correct, and Clarify

Our district math teachers were introduced to the Mathematical Language Practices in a PD session in August. Our department has decided to focus on incorporating one of these each quarter into our instruction, and this quarter’s focus has been Critique, Correct, and Clarify.

To set up this activity, I gave each student at the end of class the previous day one inequality on a post it note. We had just worked some example inequalities together as a class. They solved their one inequality and gave it to me. I put all the post it notes on a page of my Rocketbook (which we received for free at the tech bootcamp PD!) to digitize all their solutions. I went through each solution and selected some that were correct, and then several that were incorrect for interesting reasons (ex: they forgot to flip the symbol, they combined like terms across the symbol, they combined unlike terms, etc.). I took a screenshot of those from the Rocketbook pdf and pasted them onto each slide. You’ll notice those are not part of the background, so you could delete them and replace them with your own students’ work! Then, we did the first one together, going step by step and at each step either typing something in the “done well” box or “mistakes” box. If there was a mistake, students re-solved the inequality on a whiteboard and typed the correct solution in the purple box.

This was very difficult for my students, but I think it was very beneficial as well. They are not used to critiquing completed work, they just go through a process by rote and then that’s their answer. Our department is trying to work on getting them to analyze their own work. It’s going to be a long process but I think this was a good step.

Tip: you have to make sure to tell students they have to click the textbox icon before they can start typing – almost all of mine tried just clicking in the boxes forEVER until they finally asked how to type!

2. Linear Function “I Spy”

I stole this idea from a tweet I saw sometime last year that unfortunately I only saved the image from and not the actual tweet, so I cannot remember who it was – if you know, let me know so I can credit them properly!

There’s a lot of vocabulary when starting to work with linear functions: function, linear, slope, x-intercept, y-intercept, domain, range…it’s hard to keep it all straight! So this was just a practice using all those terms. There are relations in each green bordered box to the side (they’re all sets of coordinates), and in the center there are descriptions. Students drag the the relation underneath the description that matches it.

I had students list all of the relevant information for each relation, then search for the description that matched it, but I feel like the reverse would be better – read a description, then search for the relation that matches it.

3. Quadratic Transformation Matching

As we started our discussion of function transformations in Pre-Calc, I wanted to practice by starting with a function they were really familiar with. I found this card sort online (again, I can’t remember where, so maybe someone knows so I can credit the person!) but decided to make it a digital card sort instead. There is a set of parabolas, a set of equations, and a set of written descriptions of the relevant transformations. Students simply drag a parabola, equation, and description that all describe the same transformation on x^2 to the same row of the background.

This was a perfect way to introduce transformations and get them comfortable with which numbers did what to the equation. There were a few typos in the original card sort I had downloaded, which of course made things difficult, but I think I have corrected them all.

4. Logarithm Properties Memory

Last year, I did this Logarithm Properties domino activity that was pretty good, but ended up being confusing because apparently my students don’t know how to play dominos? Looking for more activities this year, I found a memory activity that was intended to be printed out and the cards flipped over in the traditional memory matching style. In my bid to avoid printing, I googled to see if there was a trick to creating a memory game in google slides that I could use and there is! So I took this memory match game and the logarithm dominos and combined them to make a Memory game of my own. Links to both original activities and the blog post I read to discover how to make Memory on Google Slides are in the activity file!

This is the only one so far that I haven’t used but I am excited about it. A subtle element of competition is good for the students I have in Algebra 2 this year, but it needs to be not so much competition that a student who is behind just gives up. I think this will be the perfect mix, because it also isn’t about speed – they have to take turns anyways, and I’m going to encourage them to help each other with the problems as they go. If I remember, I’ll come back and update once I’ve done this with students!

Have you made any similar Google Slides type activities that you’d like to share? Any ideas for other activities that could be adapted in this way? I’m excited to continue making activities like this as I go through the school year.

Oh, and another cool thing: when you go into the files to look at them in google classroom, you can insert a comment on a particular item that a student dragged to say, “hey, this function has a RANGE of {0}, not a DOMAIN of {0}”, etc, and it’s much easier to give quick feedback to each student. If you wanted, you could even do this live as students are working (or of course, you could just go talk to them). Another teacher I know also suggested that if you were home sick but still able to be on a computer, you could assign one of these with your sub and give live feedback to students throughout the day from home! (When I take sick days, I’m typically far too sick to be typing coherent comments, but maybe you’re home with your sick kid or something and could make it happen!)