Math = Love

Friday, November 16, 2018

Twelve Basic Functions Challenge in Pre-Calculus

A few weeks ago, I had my best lesson of the year so far in pre-calculus. My students were engaged like never before, and they became super competitive throughout the activity. They did way more questions than I ever would have been able to get them to do if I had just given them a homework assignment. When they came into class the next day, they begged to do an activity similar to the previous day's activity because it had been so much fun. Yes, students begging to do math. It made my heart smile. 

When students entered the room, they found twelve lime green posters spread around the room. 


Each one of these posters represented one of the twelve basic functions identified in our Demana and Waits Pre-Calc textbook.








Each poster contained the name of the function as identified by our book, a graph of the function, the equation of the function, and an interesting fact about the function.

My goal for this activity was to get students up and moving around the room and talking about the various parent functions. I originally thought about making these posters into small cards for each group to have at their desk, but the copy machine I had to use to do that ended up breaking which put a halt to that plan. So, posters it was. And, I think that ended up being a good plan anyway.

The next resource I created for this activity was a challenge tracking sheet. Each group would have the opportunity to earn up to 16 stamps by completing 16 different challenges. I find that a tracking sheet is necessary whenever I do activities like this, or groups do not end up managing their time wisely or they try to do the same problems over and over and over again. This way, students know exactly what has been finished and what still needs to be done.


After passing out a challenge tracking sheet to each group, I gave each group a ziplock bag containing twelve laminated cards that match the twelve basic function posters surrounding the room.


When I was talking to my husband about my idea for this activity, he suggested that I make the cards double-sided and add a letter to the back to make the activity easier to check. This turned out to be a LIFE-SAVER.


So, you are probably wondering by now what are the challenges?

The idea for this activity started when I was flipping through the textbook and a set of exercises caught my eye. The problems asked students to identify which of the twelve basic functions fit each description. For example, identify "the four functions that are odd" or "the three functions with no zeros" or "the six functions that are increasing on their entire domains." I thought these were AMAZING questions, but I didn't want to just hand them out as a textbook assignment. That sparked the idea for this challenge activity.

Not familiar with this textbook? You are in luck because Pearson has the PDF of this section of the textbook on their website for free! You can find it here.

I especially loved that these questions killed two birds with one stone. They gave my students crucially needed practice with the new vocabulary words we had been learning (even odd, domain, range, continuous, point of discontinuity, bounded, increasing, decreasing, zeros, end behavior, etc.) and it introduced them to a whole bunch of parent functions at once. Some of these were parent functions they were very familiar with from Algebra 1 and Algebra 2. Others (like the logistic, sine, cosine, and greatest integer functions) were completely new.


I typed up the challenges two to a page and printed them and laminated them. I only printed one set of challenges, but in retrospect I should have printed at least two sets so that two groups could be working on any one challenge at the same time. There were a few challenges that students found especially tricky. This meant that other groups had to wait a really, really long time to be able to tackle that challenge since there was only one copy. Given that I had set this up as a competition to see which group could complete the most challenges within our 50 minute period, this meant some students were very frustrated at the groups using the challenges that they still needed.

To kick off the challenge, I gave each group a challenge tracking sheet, bag of parent function cards, and one of the challenge cards (randomly chosen by me) to begin with.

Each group immediately set to work looking at the posters of the twelve basic functions around the room and debating which cards represented the correct answers. When they thought they had the answer, they would send a delegate from their team up to my desk with three things. Their Challenge Tracking Sheet (for me to stamp if they were correct), their Challenge Card (so I could figure out where to look on my answer key), and the function cards that they believed answered the question.


I would flip over the cards that they brought me and quickly compare the letters to my answer key. If they were correct, I would stamp their sheet and let them change out their challenge card for a new challenge. If they were incorrect, I would tell them simply that they were incorrect and send them back to rework the problem with their group.


I didn't really get any pictures of my students in action during this activity because I was CONSTANTLY busy checking students work and handing out new challenges. I overheard so many awesome conversations, and my students were VERY familiar with the basic graphs of the twelve basic functions by the end of the class period! My students were super competitive which was good because it kept any groups from giving other groups the answers which can sometimes happen with activities like this.



I feel a bit weird being proud of this lesson because I don't actually feel like I did much teaching about parent functions. My students did all the learning and teaching themselves. But, those really are the best lessons, aren't they?

Want the resources to run this activity with your own class? I have uploaded the resources to Google Drive as both editable Google Slides and PDFs. You can download them here.

Wednesday, November 14, 2018

Things Teenagers Say: Volume 56

Today marks a new chapter in the history of Things Teenagers Say. It's the first volume of many from my new school. It will be interesting to see how students at my new school take to this tradition. At my old school, Things Teenagers Say went from being virtually unnoticed by anyone to having almost a cult following by some of my students and coworkers in the course of a few years. It turns out that no matter where you work, teenagers still say some pretty crazy things sometimes. 



--

Me: What do we call this type of graph?
Student 1: A uvula!
Student 2: I think that's called a parabola.
Student 1: Oh. Yeah. That's what it's called.

--

Student 1: Why do you look like you're about to go to a baseball game?
Student 2: It's the hat.

--

Student 1: How tall are you?
Student 2: Tall enough.

--

I want you to have to use 30 pounds of shampoo next time you have to wash your hair.

--

He's not a substitute. He's a hero. A national treasure.

--

You don't learn much information from a puddle of goo.

--

I can't English today.

--

I like saying swear words in other languages.

--

Alligator and chicken are not the same thing.

--

I feel like I'm actually a decent person...sometimes.

--

Student 1: We speak American here.
Student 2: Aren't you the president of the Spanish club?

--

Can the pope have a beard?

--

Student: Why should I trust you?
Me: I have a degree in math.
Student: I have degrees on my thermometer, but you don't see me showing it off.

--

Your carrots taste like perfume.

--

Student 1: I need to get Jesus in my life.
Student 2: You just kicked Jesus out of your life.

--

How come is it whenever a girl breaks up with me they always cry?

--

Either my dad is a witch or a pyromaniac.

--

Monday, November 12, 2018

Monday Must Reads: Volume 48

Happy Monday! I haven't spent as much time on twitter lately as usual, so I know I have missed out on some awesome tweets. But, I decided to go through my twitter likes and see what was worth sharing anyway. And, wow, you guys did not disappoint! Sorry to anyone whose awesomeness I missed during my twitter absence, I will try to make up for it later!

I hope you enjoy this collection of Monday Must Reads and can find a useful idea or two or three to use in your classroom! 




Julia Anker shares an awesome way to bring boxplots to life and give them meaning. This is simply brilliant!

Image Source: https://twitter.com/AnkerMath/status/1060735881382780928
Have some hula hoops laying around? Check out this idea from A. Morgan. This could be extended to so many different grade levels.

Image Source: https://twitter.com/PenAndTellHer/status/1060921370475982850
Speaking of hula hoops, I can't wait to see how Jonathan Lind teaches trigonometry using hula hoops.

Image Source: https://twitter.com/lindjonath/status/1057137362734596096
Andrea Perry-Plattsm makes me wish I had a dry erase board in the hall outside my classroom!

Image Source: https://twitter.com/aperry_andrea/status/1060908554704601092
Tori Cox shares a new WODB she created for parallel and perpendicular lines.

Image Source: https://twitter.com/ToriTeachesMath/status/1059484811847450626
Liz Mastalio continually impresses me with the creative activities she comes up with to emphasize thankfulness among students.

Image Source: https://twitter.com/MissMastalio/status/1060268528190808064
Peter Drysdale shares a lovely puzzle for combining like terms.

Image Source: https://twitter.com/pwdrysdale/status/1059610376835219456
rupeleMX shares a photo of an awesome interactive activity he uses with his science students. How could we learn to make math more visual?

Image Source: https://twitter.com/rupeleMX/status/1057262390671302658
Kristen San Filippo offers up the brilliant idea of using bendy straws for end behavior of polynomials.

Image Source: https://twitter.com/LV_sanfilippo/status/1055601786298474497
I love how creative Elissa Miller is with her geometry classes. Who would have thought of playing Twister with transversals?!?

Image Source: https://twitter.com/misscalcul8/status/1055642799016697856
Elissa also shares a great teacher hack for those of us who are 1:1.

Image Source: https://twitter.com/misscalcul8/status/1035282444428173313
Jacob Wagner shares a great summative task for polynomials and rational functions.

Image Source: https://twitter.com/MrWagsMath/status/1053463900518137857
I love how Susan Hewett has students draw an illustration as part of their Frayer Models!

Image Source: https://twitter.com/SusanHewett7/status/1052956769327173632
Stacy Benton shares an easy way to increase student excitement and anticipation!

Image Source: https://twitter.com/sbentonteach/status/1052007931292602368
I definitely want to find a way to fit Desmos jack-o-lanterns into my curriculum next year! Thanks to Patty Stephens for sharing.

Image Source: https://twitter.com/pattystephens/status/1052066818943213569
I love seeing other teachers make creative auctions to use in their classrooms. Check out this exponent auction from Michelle Pavlovsky.

Image Source: https://twitter.com/MsPrzybylek/status/1049378247333629954
This Three in a Row Activity from Math with P Nik is brilliant.

Image Source: https://twitter.com/MrNiksMathClass/status/1048401564732481537
This like terms search makes me really miss teaching Algebra 1! Thanks to Sarah Giek for sharing!

Image Source: https://twitter.com/sgiekAHS/status/1046860223133167618
I love how Grw029 modified the 2018 Challenge to celebrate the Jewish New Year.

Image Source: https://twitter.com/Grw0291/status/1042007775033864192
Chris Prystenski's post about Ultimate Tic Tac Toe inspired me to show the game to a couple of students in my class who I caught playing regular Tic Tac Toe in their spare time. So fun!

Image Source: https://twitter.com/MsCPry/status/1039261447635841024
Mary Ellen Riley shares a new twist on the traditional system of equations puzzle.

Image Source: https://twitter.com/ThisIsMaryEllen/status/1034236654519758855
I adore this "Math is Life" display from Ms. G!

Image Source: https://twitter.com/TheMathGhost/status/1035693220762673152
Mr. Gray shares an absolute beast of a factoring task, and I LOVE it! It is a free download from TES.

Image Source: https://twitter.com/BucksburnMaths/status/1011643805869707264
I love these sentence starters from MPS Secondary Math!

Image Source: https://twitter.com/MPS2edMath/status/923240540510085120
I love how Math by the Mountain modified the 2s-9s challenges to make the dry erase and double sided!

Image Source: https://twitter.com/MathByTheMt/status/1037120585417949184
Todd Feitelson is so creative with 3D printing and implementing the Smallest Positive Integer Contest!

Image Source: https://twitter.com/toddf9/status/1036927718112288769
After this lesson, I imagine Alexis Pleasant's students will never forget the power of exponential growth!

Image Source: https://twitter.com/PleasantMath300/status/1037651368188825600
Until next time (not promising it will be next week since we all know how long it's been since my last Monday Must Reads post...), keep sharing your awesome ideas!



Friday, November 9, 2018

Five Things Friday: Volume 22

Blog posts two days in a row - what craziness is this?!? I figured since it's Friday, I might as well keep up my new-found blogging momentum with a new volume of Five Things Friday. These posts are a collection of things I have been up to of late that haven't made it on the blog. Since I've been neglecting this blog so much, I could probably sit down and write a Fifteen Things Friday, but I will try to keep it to just Five.

1. This has been an extra crazy week. We had a professional day on Tuesday for Election Day. Then, the rest of the week has been a bit out of the ordinary. Wednesday, I was displaced by the Pre-ACT being given in my room. Thursday, all the sophomores went on a field trip. Then, today our schedule has been thrown off by a Veterans Day Assembly. This meant our only normal day of the entire week was Monday!


I had to cover all of my beautiful decorations for the Pre-ACT which turned out to be a real pain. The paper would NOT stay up on the walls. Apparently, some of the paper ended up falling off the wall during the actual test. Oops...


Do you know what else happens when you cover up all your decorations? Every single kid who walks into your classroom for the rest of the day has to ask "Are we having a test?" "Is there a pop-quiz today?" "Why are the walls covered?" Given the fact that I've never once before covered the walls, I don't understand why my students automatically equate that with having to take a test.


I do have to admit that I got tired of telling students the real reason for the walls being covered at a certain point and started telling them that I was in a bad mood. As a result, I decided the room was too colorful and I had to cover up the posters to match my mood. I thought they would realize I was joking, but I heard from the chemistry teacher later in the day that students were talking about the fact that I was in a really bad mood.


2. In used Shaun Carter's ZERO! Game with great success to motivate factored form of quadratics. I presented this as a "game day" after we had talked about vertex form of quadratics and standard form of quadratics and BEFORE we started factoring quadratics the next day. It was PERFECT for an Early Release Friday with shortened, 40 minute periods.


I noticed a HUGE difference between how my Pre-AP Algebra 2 classes and my on-level Algebra 2 classes tackled the strategy aspect of the game. If you're not familiar with the game, students must pick a card. A random number generator is used to generate an integer between -5 and 6, inclusive. If that number causes a student's card to evaluate to ZERO, the student's team earns a point. The strategy comes in from the fact that a team may earn a maximum of one point from any single turn. So, if three students have a card that evaluates to zero, the team still only earns one point. So, if a team is clever, they will figure out how to maximize their probability of earning a point each round.


One thing this activity made me realize is that my students REALLY don't have an understanding of how randomness works. I used the random number generator that Shaun created especially for this game and shared on his blog, and students became very stressed out if a number was called twice or (GASP!) three times in a row.


As we have been solving quadratics by factoring, it has been interesting to be able to reference the game that we played and make the connection between what they were doing in the game and what we are doing as we solve equations.

3. I'm really pushing the box method this year in my Algebra 2 classes, so Christie Bradshaw's area model puzzles were a perfect introduction to the box method before we jumped into factoring using the box method!


4. Shaun and I have really been enjoying attending the Tulsa Math Teachers' Circle this school year. We've always loved attending in the past, but it's super nice to live much closer and not have an hour long drive home afterwards! We tackled some fun puzzles at our last meeting. Our opening task was a new one to me.

Take a standard checkerboard and remove two of the corner pieces that are diagonal from one another. You can see in the picture below where we marked them out with an x. Then, take a standard set of dominoes and cover the remaining squares of the checkerboard.


Afterwards, we discussed the mathematics of the famous Fifteen Puzzle. It was a bit mind-blowing.


4. Years ago, I attended a Common Core Workshop where we did an activity involving rope and systems of equations. It was called "All Tied Up In Knots." Well, I finally tried the activity in my classroom with my Algebra 2 students, and it was an awesome introduction to solving systems of equations. There are a few things I would tweak before doing the activity again, but I will definitely be doing it in the future.


I didn't burn the ends of my rope because I'm a major procrastinator and didn't have time to cut the rope until the morning of the activity, so I ended up having to throw all the rope away. In the future, I will definitely burn the ends of the rope to prevent fraying so I can keep the rope and reuse it from year to year.


The goal of the activity was to determine what number of knots was required to take two ropes of unequal lengths and make them the same length. The students achieved this by collecting data, creating a scatter plot, drawing in lines of best fit for each rope, and finding the point of intersection.


5. Sadly, I'm finding that a lot of my go-to review games from the past six years at my old school just aren't working for my new school. Having 30 students in a class is very different from having 10-16 students in each class. One game that has been working well this year has been ZAP. It has become one of my students' most requested review games. Whenever one class gets to play it and another doesn't, I definitely hear complaints.


I love that now that I have the cards prepped, the only real prep is to find a set of questions to use as a review.



Enjoy your weekend!