Math = Love

Thursday, October 19, 2017

CPM Function Machine Activity

I recently found this blog post in my draft folder, so I decided I should finish it!

During the Summer of 2016, I attended a section called "Fun Functions" by CPM at the OCTM Summer Conference.  If you're interested in knowing more, I recapped the session and shared the resources here.

One of the ideas shared in the session was to give students a set of four function machines.  Given a starting value and an ending value, students had to arrange the function machines so that if the starting value was used as the input of the first machine, the output of the first machine was used as the input of the second machine, the output of the second machine was used as the input of the third machine, and the output of the fourth machine was the given ending value.  

For my Algebra 1 students, I used the free resource page offered by CPM on their website.  CPM also has an Algebra 2 version available on their website.     

The first challenge I gave students was to start with 15 and end with -6.  They were able to use our new group sized dry erase boards in order to work on this problem.  We've had these boards for about a week now (as of November 2016), and we have already used them SO much.  I'm so thankful for my school's foundation for providing the grant money to buy six group sized boards for my classroom.  They also bought us 75 dozen dry erase markers.  We can do so much more math now! 

Not all of my students were successful at completing this activity.  In fact, I only had two groups of students successfully complete the challenge.  I think this is okay.  The purpose of this activity was to give students lot of practice evaluating functions.  Even the unsuccessful groups tried a ton of combinations and did a lot of practice.

The groups who were successful were asked to complete a second challenge: If the final output is 2 and the first input is 8, what order should the function machines go in? 






I'm looking forward to trying this activity again this year with my Algebra 1 students. I think we will do lots more practice just working with the function machines before we tackle this problem. I'm hoping they will be much more successful as a result.

Wednesday, October 18, 2017

Open Middle Style Problem for Equations with One/No/Infinite Solution(s)

Two summers ago, I created some open middle style problems that have been a hit in my classroom. Both problems use a reusable set of tiles that have the numbers from -4 to +4 printed on them. These tiles are laminated which has helped them hold up to use over multiple years.

The first problem I created reviewed the concept of function/not a function. Students had to create three relations that were functions. Then, they had to create three relations that were not functions. I shared the file for this activity here.


I followed up the creation of that activity with an evaluating functions problem that can be downloaded here.


This year, I'm placing a big emphasis on solving equations with variables on both sides. Though I covered this last year, my emphasis on word problems meant I didn't do a good job of introducing my students to the concepts of no solution and infinite solutions. This year's solving equations/inequalities unit hasn't gone perfectly, but I know it never will. I will always have room for improvement as a teacher.

I decided to see if I could make an open middle style problem for creating equations with one solution, no solution, and infinite solutions.

First, I did a bit of trial and error on a scrap of paper.


My husband had to bail me out because I accidentally created two problems with infinite solutions. Shaun reminded me that I had a lot of wiggle room because the tiles in the one solution problem could be moved around a lot. 


Then, I took advantage of the fact that my freshman students went on a field trip leaving me with almost no students for an entire day to actually type up the activity.


After typing it up, I realized that I only had 8 boxes for my 9 tiles to fit in. Luckily, I just had to make a tiny tweak to the bottom equation.


Students have to place the tiles in the appropriate boxes so an equation is formed that matches each equation type. My students found it pretty easy to get one of the equations correct. They found it much harder to get all three of the equations correct using the exact number tiles provided.

Here are some action shots from my classroom:




You can download the file for this activity here.

Tuesday, October 17, 2017

Updated Evaluating Expressions Question Stack with More Difficult Questions

On Sunday, I shared a question stack I made to review the distributive property using printable business cards. Today, I want to share a different version. I created this question stack for my Algebra 1 classes to review evaluating expressions.

If you've ready my blog for awhile and can keep track of my hundreds of posts, you may be thinking that I've already shared my evaluating expressions question stack before. Yes, I did share an evaluating expressions question stack last year. Here's the post.

The questions looked like this:

Last Year's Question Stack (Download HERE)
There was nothing wrong with this, but this year I decided I wanted my students to do problems at a bit of a higher level. I spent a substantial amount of time reviewing the order of operations this year, so that allowed me to ask much more difficult evaluating questions than in years past where I skipped order of operations review because I assumed all of my students had already mastered it. Let's just say that evaluating expressions went a million times better this year than last thanks to the order of operations review even with the harder problems!

Introducing my new and improved and much more difficult question stack!


I printed these question and answer cards on Avery Business Cards (affiliate link) that I purchased from NAIER last year.
http://amzn.to/2wSMcf6
So, how does a question stack work? Check out this post for the full details, but I'll go ahead and quickly summarize how it works below!


Each group gets an explanation card with all of the rules.

I printed them on peach paper and laminated them so they are handy every time we do a question stack. And, I do lots of question stacks!



Students lay out all of the cards individually with the answer sides facing up. These cards form the "answer bank."

Each group chooses one card to flip over. They lay this card on top of their laminated question stack template so they don't get confused.

Each group member works out the problem. When the group has decided on an answer, they check the "answer bank" to see if their answer is there. If it is, they are (most likely) correct. If it isn't, they have made a mistake. They need to check their work and/or ask for help.

 

If the answer is in the answer bank, this card is flipped over to reveal a new question. This process repeats until the last question is flipped over. The answer to this card should be at the bottom of the pile if all of the questions have been answered correctly.

Here are some action shots from the day I used this activity in class:













You can download the file for this activity here.

Monday, October 16, 2017

Monday Must Reads: Volume 14

Happy Monday! For me, it's an especially happy Monday because it's only a two day school week. Granted, parent teacher conferences on Monday night AND Tuesday night will make for a two day week that feels incredibly loooooooonnnnngggg. I feel like Fall Break is something I definitely need in my life right now. School has been exhausting lately. Friday night, I fell asleep on the couch before 6 pm! I'm looking forward to the chance to rest and recharge so I can be the best teacher possible for my students.

Seeing what other teachers are in their classrooms inspires and energizes me, so I'm excited to share this week's Monday Must Reads with you!


Here are the tweets and blog posts I found most inspiring this week!

Hedge and Cononiah Watson combine a few basic household items to create a powerful visual for students regarding diagonals of 3-D shapes.

Image Source: https://twitter.com/approx_normal/status/918981568366043138
I especially like how David Butler points out the fact that giving students an item of a set length creates the need for taping two of the objects together to create the longer diagonal!

Image Source: https://twitter.com/DavidKButlerUoA/status/918985640988917761

I'm always on the lookout for easy-to-implement classroom routines. I especially like this "Find my Rule" activity from Mrs. J M Clark. This could easily extend to so many topics!

Image Source: https://twitter.com/mrsjmclark/status/913448475316166656

Mrs. J M Clark also shares what she calls a "Back to Back Exercise." Students stand with their backs to one another and describe graphs while their partner draws them. Then, they turn around and compare how close they were.

Image Source: https://twitter.com/mrsjmclark/status/916280777033371648
Sally Watson shares some beautiful, mathematical artwork created by her students. It was inspired by the symmetries found in the Alhambra Palace. What a gorgeous classroom display!

Image Source: https://twitter.com/sallywatson77/status/918884571449569280
I love watching shows like The Great British Bake Off and The Great Australian Bake Off. So, I was super excited to see the twist that Rebecca Owen put on the traditional technical challenge with "The Great British Biology Off." How fun to frame a lab as a technical challenge!

Image Source: https://twitter.com/owen_becca/status/918852196489486337
Stephanie Fote shares a way to embrace the idea of "color with a purpose" while solving equations. LOVE it! I also adore her sign which I'm assuming can be flipped around to tell students whether or not they can use calculators for that day.

Image Source: https://twitter.com/ms_fote/status/918949921440587776
Whenever I've taught trigonometry in the past, angles of elevation and depression have always been one of the trickier topics to teach. I've found that it's hard for students to visualize what the diagrams should look like. So, I'm a huge fan of how Elissa Miller has engaged her students with a diagram matching activity!

Image Source: https://twitter.com/misscalcul8/status/918942676053053440
Mrs. Taylor hosts a bumper sticker design competition. Her chosen topic was lab safety, but this could be used for so many things. I love that each submission is given a number so that votes can be tallied to choose the winner!

Image Source: https://twitter.com/MrsTaylorROMS/status/917442870541520899
Kelsey Fladda shares one of the most awesome scatterplots I have ever seen made in a math classroom.

Image Source: https://twitter.com/MissFladdaMath/status/827214821657604097
I love seeing how math is taught in other countries. So, looking through these Irish geometry posters shared by Card Colm Mulcahy is a true treat!

Image Source: https://twitter.com/CardColm/status/918982845879799808

Martin Joyce shares a photo of a resource he got from Lisa Bejarano. I used number talks for part of last year, and I felt like it was lacking a bit of structure.  I think a handout like this would be PERFECT!

Image Source: https://twitter.com/martinsean/status/919008702706810882
Reena Bhatti doesn't teach math or science, but her twitter feed is still an inspiration to me as a math/science teacher. I would love to take this balloon activity and use it during our upcoming unit on relations and functions!

Image Source: https://twitter.com/reenateacha/status/884865315166924800
I'm also super inspired by Reena's interactive notebook pages!

Image Source: https://twitter.com/reenateacha/status/880720326442799105
Sterling Bristow takes the class cup stacking activity to a new level by having students create their own cup designs!

Image Source: https://twitter.com/BristowSterling/status/918928791551950848
Sterling also shared a great construction activity for geometry students involving the flag of Nepal!

Image Source: https://twitter.com/BristowSterling/status/913880969878401024
Elyssa Stoddard presents a fun activity for geometry teachers to use while working with angles.

Image Source: https://twitter.com/math_stodd/status/918899405830459392
Julie Morgan shares a fun and easy to implement review game on her blog, Fraction Fanatic. I love that this game can be used with ANY topic, and it doesn't require any real prep time. Julie uses questions on cards that do take time to make, but in a pinch you could use any worksheet you found online!

Image Source: https://fractionfanatic.wordpress.com/2017/10/13/maths-game-1-to-100-grid/
Lisa Smith shares a game for working with solving equations and inequalities that I would love to adapt for next year since I've just finished those topics!

Image Source: https://twitter.com/MrsSmithNavo/status/918680819908120576
Amy Klose offers up a fun introduction to polynomial functions. I'm not teaching a class that covers this topic anymore, but I'm keeping this idea in my back pocket for future use!

Image Source: https://twitter.com/amy_klose/status/909844806599356418
Liz Caffrey turns her students into detectives with this fun function lesson. I'd love to see these stations to see how it works!

Image Source: https://twitter.com/AsymptoticLiz/status/918691185689899008
Melinda Golden offers up the most engaging activity I have ever seen for pythagorean theorem/distance formula. Students must drop two paratroopers and calculate the distance between them. It looks like the paratroopers are made out of coffee filters and yarn. How fun!

Image Source: https://twitter.com/Mrs_GoldenLCMS/status/918618329887199242
 Kate McNabb shares her students' awesome models of atoms. I love the variety of materials used!

Image Source: https://twitter.com/k8mcnabb/status/918639832477454337
Kristine Woodford took my idea of a Witzzle Bulletin Board and made it so much better. I designed mine to be a teacher-led activity for when we had a few odd minutes left in class. I love that Kristine made hers accessible to students at any time by offering the target number and a place for students to submit solutions!

Image Source: https://twitter.com/MathWithWoody/status/918499571071717376
Krista shares an engaging, real-world task involving Coke vs. Pepsi.

Image Source: https://twitter.com/kristaworth2/status/804050360046325760
Exploding Dots has been taking over math classrooms all over the world this week. Justin Aion inspires with his reusable exploding dots machine made out of painters tape. Brilliant idea!

Image Source: https://twitter.com/JustinAion/status/918463833437503488
The NGSS Tweeps Twitter account recently shared a new-to-me strategy for promoting voice equity in the classroom.

Image Source: https://twitter.com/NGSS_tweeps/status/915247576735191040
Destinee Johnson gets students up and moving while learning about metallic bonding with a fun tag activity.

Image Source: https://twitter.com/msjohnsonchem/status/918237848951762945
Jen Winne was featured in Volume 13 of Monday Must Reads for her creative mini poster presentations. I was super excited to see the finished product on twitter this week! Plus, she even wrote a blog post with more information which you can find here.

Image Source: https://twitter.com/biobythemathmom/status/918109926546866176
Halcyon Foster uses dice and paper strips to create an engaging activity that has students exploring the triangle inequality theorem.

Image Source: https://twitter.com/halcyonfoster/status/917828280392101888

Here are a few more details about how this activity works:

Gina Ging brilliantly uses a paper plate to teach circle vocabulary.

Image Source: https://twitter.com/KlineGina/status/865586987855728642
Stephanie Ling shares an awesome approach to teaching equation solving. I love the emphasis on solving equations that might look the same at first glance but are totally different.

Image Source: https://twitter.com/ling_stephanie/status/917892323249287168
Rick Barlow shares an awesome slope activity that has students comparing different climbs presented in as different representations. You should check out his blog for more details!

Image Source: https://twitter.com/rickbrlw/status/917873851320508416
Jennifer Williams combines football and functions for a fun activity. I need to get my hands on some footballs before we start functions in Algebra 1!

Image Source: https://twitter.com/jlwilliams314/status/915318281170571264
 Paul shares some awesome growth mindset statements to print on sticky notes.

Image Source: https://twitter.com/tips4teachingUK/status/917116783940816901
Casey McCormick asked her students to write about what a mathematician is. The results are priceless.

Image Source: https://twitter.com/cmmteach/status/917494796519849985

Image Source: https://twitter.com/cmmteach/status/917495465616203776
Gwen Bergman keeps a running list in her classroom of all the uses they have come up with for Desmos!

Image Source: https://twitter.com/gwen_bergman/status/917482015401873414
And, that's it until next week. Keep up the great sharing of ideas!