Math = Love: December 2017

Monday, December 11, 2017

Monday Must Reads: Volume 22

Happy Monday! I absolutely adore the time I spend each week putting together new volumes of Monday Must Reads. Throughout the week, I stumble on so many great ideas on twitter, and I always make sure to hit the like button. But, I find that by the end of the week, I've already forgotten these awesome ideas. The act of going through my likes once per week and summarizing them in this manner is a great time for reflecting on what I would like to change in my classroom/do in the future.

Here are this week's Must Reads!



Dave shares some fun Christmas activities which practice transformations. These are adorable and make me wish I was teaching geometry so I could use them. He has graciously uploaded the files on TES to be downloaded for free!

Image Source: https://twitter.com/d_e_humpty/status/939519892256157696
Teaching calculus and need an idea to make related rates come alive? Andrew Wille has you covered.

Image Source: https://twitter.com/afwille/status/931192948179505154
Cass Lowry shares an interesting puzzle from AAMT2017 that only requires the use of five digits.

Image Source: https://twitter.com/cass_lowry/status/884962749037420545
You also need to check out this idea by Cass Lowry. Act out the Bridges of Konigsberg problem using plastic cones!

Image Source: https://twitter.com/cass_lowry/status/934903489980805120
Jzitzka offers up a new-to-me activity for practicing combining like terms. I used to love the dot game as a kid, so I can see my students really getting into this. A quick google search shows that this activity can be downloaded here.

Image Source: https://twitter.com/jzitzka/status/939257649404751872
Mark Kaercher combines straws and fuzzy sticks (pipe cleaners) to create a giant sierpinski pyramid. How awesome is this?!?

Image Source: https://twitter.com/shskaercher/status/939206983676317697
Mark posts some great illustrated instructions for doing this yourself below:

Image Source: https://twitter.com/shskaercher/status/939197972176429058
Jen Winne inspires with the idea of including lab-based questions on tests. This is #scienceteachergoals.

Image Source: https://twitter.com/biobythemathmom/status/939231010109173761
Amanda Atkinson shares some ideas for engaging students after finishing an assessment. The Star Wars System of Equations Problem was featured in last week's volume of Monday Must Reads. The Compound Inequalities Treasure Hunt is a new one for me. I found a version online here. I'll definitely be adapting this for my inequalities unit next year. 

Image Source: https://twitter.com/alstechs/status/939241858395492352
Liz Mastalio makes brilliant use of a highlighter when teaching solving systems by substitution.

Image Source: https://twitter.com/MissMastalio/status/939200752928641025
Another great math teacher hack from Liz Mastalio: print tasks involving graphing ON graph paper.

Image Source: https://twitter.com/MissMastalio/status/938479483362971648
Ms. Kuney shares the results of what looks to be a fun holiday-themed systems of equations project.

Image Source: https://twitter.com/mskuney_math/status/939200169832312833
Mark Chubb poses an interesting problem involving the area of concentric circles.

Image Source: https://twitter.com/MarkChubb3/status/938901221590564864
Ilona Vashchyshyn shares a winter-themed WODB problem.

Image Source: https://twitter.com/vaslona/status/939132644159188992
Amie Albrecht shares a great activity for sparking discussions regarding vertical alignment. We need to be aware of what students are doing before they enter our class and what they will be doing after they leave our class.

Image Source: https://twitter.com/nomad_penguin/status/938927280520249344
I've blogged before about using Panda Squares with my students. But, how did I not know that David Butler had also created Panda Cubes?!?

Image Source: https://twitter.com/DavidKButlerUoA/status/938970471395074049
Halcyon Foster shares a holiday-themed brain teaser. I always find these kinds of puzzles to be a bit tricky! Be sure to check out the other Mathvent postings here!


Image Source: https://twitter.com/halcyonfoster/status/938963147808948225
Inspired by the puzzles I've been typing up for my classroom, Sarah Witt has started to do the same. Check out this awesome puzzle from Jumbo Book of Puzzles: The Ultimate Collection that Sarah typed up! She has uploaded the file here for you to download and print for your classroom.

Image Source: https://twitter.com/ms_witt/status/938513510958592006
Until next week, keep sharing!

Sunday, December 10, 2017

Introducing Discrete vs. Continuous in Algebra 1 with a Card Sort

It's Sunday evening. Today can be summed up by this equation: Sunday = Church + Wal-mart + Dishes + Baking + Function Notation. I've been doing my best to tackle the mountain of dishes that has a tendency to grow out of control when you've spent the past week being sick and recovering from having your wisdom teeth removed. It also doesn't help that the husband has now caught my cold...

Just to make my pile of dishes even larger, I decided to do some baking. Tomorrow is Cookie Club, so I always spend Sunday doing at least a bit of baking. For that, I decided to change things up a bit and make a sour cream bundt cake. Then, I had some bananas that were looking very sad, so I whipped up a loaf of banana bread. This will make the trek to school tomorrow because the high school teachers are responsible this week for keeping the teacher's lounge stocked with goodies to eat. Last week, the middle school teachers provided a week's worth of snacks, so it's our turn.

My husband and I watched the first two episodes of The Great American Baking Show. We watched them make lamingtons which are a traditional Australian dessert. Despite visiting Australia three times, I still haven't had a chance to eat one. Shaun mentioned that they are one of his favorites, so as I type this, I have a cake in the oven to make into lamingtons tomorrow.

Enough about today. I want to share a file I created a few weeks ago to introduce my Algebra 1 students to the idea of discrete vs. continuous. I've been finding blogging a bit harder than normal the past few weeks because I keep getting this feeling that I don't have any ideas worth sharing. I know this isn't true. Hello, I've written over one thousand blog posts now. But, that doesn't stop my mind from trying to convince me otherwise. Hopefully, the upcoming holidays and break from school will give me a chance to recharge and get back to blogging more regularly.

Anywho. Let's get back to discrete vs. continuous.


Students were given six cards. Each card had ONE of the following filled in: situation, variables, or sketch of graph. As a class, we filled in the missing information and classified each card as discrete or continuous.


Before beginning our sorting activity, we did a quick note page summary of discrete vs. continuous.


Here's what our finished product looked like after A LOT of discussion and debate and more discussion. It took a lot longer to complete this activity than I expected, but it was a productive use of our time.


I was afraid that my finished product wasn't going to live up to my expectations when I was creating this activity. But, I absolutely loved how this activity turned out.

Domain and Range went so much smoother this year than it did in years past. I think a big difference was that we had discussed discrete vs. continuous BEFORE talking domain and range. In the past, I tried to introduce both ideas simultaneously. Sometimes our students just need to digest one concept before starting the next. 

You can download the files for this activity here.

Saturday, December 9, 2017

Pyramid Challenge (and Thoughts on Puzzles)

So, I started this post earlier this week, but it has sat unfinished due to the fact that I've been sick and had my upper wisdom teeth removed. Thankfully, I am recovering from both. I didn't have to miss any school this week which was a real blessing because we all know it's way more work to miss school than actually be there...

I've been doing a lot of thinking about puzzles lately thanks to the addition of a puzzle table to my classroom this year. Each week, I place a new puzzle on the table for students to work on.  A new puzzle is placed out every Monday morning and packed up every Friday. I have really enjoyed both of the past two week's puzzles, but my students have shown a clear preference for one of the puzzles. This has got me thinking about what makes a good puzzle.


Last week, we tackled the color square puzzle from Puzzle Box, Volume 1 (affiliate link). This book is my current top recommendation for teachers who are looking to incorporate more puzzles into their classroom. Or, maybe you want a challenge yourself. What I love about this book is that the puzzles are accessible but still challenging. Many puzzle books start with too difficult of a level of puzzles, and it can be easily frustrating. These puzzles seem doable but often turn out to be trickier than you first expected.

If you missed last week's blog post with instructions and a printable version of the color square puzzle for your classroom, you can find that here.


My students tackled this puzzle all week long between classes and after finishing their work. As students worked at the puzzle, their struggle brought other students to the puzzle table to see what all the fuss was about. This engaged even more students. A handful of students succeeded in solving the puzzle. My students were engaged ALL week long for the most part.

Some students would make comments about how I was "torturing" them with these puzzles they couldn't figure out. But, those same students would be back at the puzzle table day after day trying to tackle the puzzle.

Due to last week's success, I decided to tackle a similar puzzle from Puzzle Box, Volume 3 (affiliate link). This is Puzzle 170 in the book, and it was authored by Peter Grabarchuk.


You are given a pyramid shaped board and nine squares. There are three squares of three different colors. Additionally, there are three different symbols possible for each square.


The task is to arrange the nine squares into the pyramid so that no two squares with the same color or same shape touch each other ALONG AN EDGE. Last week's puzzle didn't allow pieces to touch at a corner. In this puzzle, pieces CAN touch at a corner. They just can't touch at an edge. So, the X pieces in the picture above are in an allowed arrangement.


I've uploaded the files for this puzzle here so you can download and play along. The game board is designed to print on 11 x 17 cardstock (affiliate link). The game pieces are designed to print on three different colors of letter sized paper. You will need to print the same page three separate times on three separate colors. If you don't have access to 11 x 17 paper, you can scale the print job to fit on letter sized paper. Remember what scale value you used so you can scale the game pieces by the same percent. Otherwise, the game pieces will be too large for your downsized gameboard!


When the new puzzle was set out on Monday, many of the same students who had tackled the color square puzzle last week, tried their hand at this puzzle. Something different happened, however. On Tuesday, students started solving it. Then, they didn't want any more to do with it. More students didn't get sucked in. Instead, it just sat there, basically untouched, for the last part of the week.

Last week, they vented their frustration about how hard the puzzle was. This week, they vented their frustration about how they would be bored for the rest of the week since they had already solved the puzzle.

Here are my thoughts. As you can see, I have many more questions than answers.

Both are great puzzles. I solved both and enjoyed solving both.

Students enjoyed solving both.

Frustration is not a bad thing. Students would rather be frustrated than bored. Though, I'm not sure a student would admit that...

I don't think the problem is with the puzzles but with my puzzle table. When a student finishes one puzzle, they need another puzzle to tackle immediately to prevent boredom. But, how do I pull this off? At the moment, I have a limited number of puzzles ready for my puzzle table. I can't put them all out. Should I place multiple puzzles out at the same time? Should I just accept the fact that some week's puzzles will engage students for longer than others?

What implications does this have for how I run my math class?

Monday, December 4, 2017

Monday Must Reads: Volume 21

Hello, Monday! I'm still getting over a very inconvenient cold, so today will most likely be a VERY long day of school. But, I can't imagine a better way to kick off this Monday than a new volume of Monday Must Reads. Each Monday, I post a quick recap of what awesome stuff the rest of you have been up to.

In other exciting news, this is my 1000th post on this blog. I have to say that I never thought my blog would make it this far when I started it back in 2011 as a student teacher. I'm usually the one to start a new project that only lasts a few months before moving on to the next new project. But, it turns out that being a part of the #MTBoS isn't just a fad. It's a lifetime of friendships. Thanks to everyone who reads this blog and encourages me to continue posting. It's because of you that my blog has come this far! 


I hope you enjoy reading through the ideas I found most inspiring this week.

Allison Hartwig shares some awesome student work from a geometry project where students had to evaluate advertisements and slogans. Any assignment that gets students thinking critically (and mathematically) about the world around them is a huge win in my book.

Image Source: https://twitter.com/ahartwigmath/status/916415535033847815
Malke Rosenfeld inspires with some beautiful mathematical art. I'm thinking this would make a perfect Christmas ornament project for every math class! Check out this blog post for more information.

Image Source: https://twitter.com/mathinyourfeet/status/937061565865570304
Lita Stanton combines creativity and slope with a fun practice activity. I love the idea of combining twelve small graphs to make one large picture! If you create an assignment like this, please share so I can steal it!

I've never been a Star Wars fan, but I still love how Mrs. Richardson combined Star Wars and systems of equations to make an awesome task. She even graciously uploaded the file for all of us to use here.


Image Source: https://twitter.com/CBHSRichMath/status/936705911221051393
Michael Moore recently penned a blog post about an idea called "Math is Fun Fridays."  In this post, he includes a link to a google doc full of ideas to show students the more fun side of math. I loved scrolling through this list. Many items are the list were old favorites, but I did run across some new-to-me ideas. For example, have you ever thought about how long 10! (ten factorial) seconds is? Michael is encouraging everyone to "Take an Idea, Leave an Idea." So, be sure to check out instructions for how to add your own ideas to the google doc!

Image Source: https://cohort21.com/michaelmoore/2017/10/28/math-is-fun-fridays/


Amanda Atkinson shares an inequality activity by Sarah Jurhs. I didn't do the best job this year of teaching my students the difference between AND and OR compound inequalities. I think this hand-on activity would be the perfect intro to AND versus OR. Plus, I already have some play money in my cabinet that I've had for years without any idea of what to use it for! You can download this stations activity here.

Image Source: https://twitter.com/alstechs/status/936419767421988864
Connie Schaef shares some awesome ornaments her chemistry students created. Each ornament represents a different element. These are absolute gorgeous!

Image Source: https://twitter.com/connie_schaef/status/936381529575579648
Usually, I think I made the right decision in choosing to teach high school over middle school. But every once in a while, Casey makes me doubt my decision by posting her sweet students' creations.

Image Source: https://twitter.com/cmmteach/status/936372335807905792
Joe Cossette shares a brilliant teacher hack: hide words in the answers to make grading easier!

Image Source: https://twitter.com/cossettej/status/936349398702940161
Toni Madison coined an awesome term I look forward to using in the future: "craftivity." Aren't these fraction/decimal/percent Christmas trees adorable?!?

Image Source: https://twitter.com/MATHwithMADISON/status/936345500542005251
Ms. Grove shares a brilliant way to make a linear equation out of five six-sided dice.

Image Source: https://twitter.com/MathyMissGrove/status/936322092794089472
Elyssa Stoddard's compass construction project makes me wish I taught geometry!

Image Source: https://twitter.com/math_stodd/status/935963095289167872
Adam JW Craig offers up a fun, hands-on activity for piece wise functions. I love the idea of having students build their own piece wise functions!

Image Source: https://twitter.com/ajwcraig/status/936181077340835842
Morgan Stipe shares an awesome visual for understanding where the formula for the area of a circle comes from. I've never seen this one before!

Image Source: https://twitter.com/mrsstipemath/status/935918629819858944
Have extra window space? Maybe you should take advice from Sarah Martin and post a weekly problem on your window for students to solve.

Image Source: https://twitter.com/Sarah3Martin/status/935905276426964992
Liz Mastalio has created a BRILLIANT introduction to systems of linear equations. Students have to roll two dice to form an ordered pair. Then, they have to test that ordered pair to see if it is a solution to their system of equations. You can read more details on Liz's blog here.

Image Source: https://twitter.com/MissMastalio/status/935907363881717760
Sally Cosgrove shares a fun application activity involving Coke and Mentos.

Image Source: https://twitter.com/Momma_Cos/status/935889792218353665
Randi Munchanitis offers up a creative use for wikki stix (affiliate link) in calculus. The use of color coding here is brilliant.

Image Source: https://twitter.com/Munchanitis1133/status/935594376452902912
Primary Maths shares a fun net activity to pose to students.

Image Source: https://twitter.com/MathsPrimary/status/935438978588794880
DCDSB Math offers up a fun weekly math problem on their twitter account. I especially like this one:

Image Source: https://twitter.com/DCDSBMath/status/935171727495118848
Ashley Tewes gives students both choice and lots of practice at the same time with this distance formula project.

Image Source: https://twitter.com/ATewes3/status/935477750562947077
Teaching solving absolute value equations? You MUST check out these notes from Math by the Mountain. I love the emphasis on special cases. Totally stealing this idea next year!

Image Source: https://twitter.com/MathByTheMt/status/935352441326919680
 Until next week, keep up the awesome idea sharing!