Math = Love

Tuesday, January 16, 2018

Algebra 1 Unit 3 - Relations and Functions Interactive Notebook Pages

Before Christmas, we finished one of my favorite units of the year in Algebra 1 - Relations and Functions. With regards to pacing, we are WAY behind where I would like to be, but there's not much I can do about that. Last year, my pacing was off in the other direction. We spent a full two months of the school year on data and probability because we got through the rest of the standards too quickly. I do know that this year's students have a much better handle on solving equations and inequalities than last year's students, so I'm hoping this more solid foundation will allow us to progress more quickly during the second semester.

Here are our notebook pages for Relations and Functions. There are some old favorites which I reuse every single year and some new pages as well.

Each unit begins with a table of contents divider. I've blogged about these before here. The first side contains a section titled "Top Ten Things to Remember." Students complete this either as we work through the unit or right after we finish the unit. I encourage my students to flip back through their notes and decide what the ten most important things we learned were.


The other side of the divider contains a list of our SBG skills for the unit. Students are required to record their initial score for each quiz and any updated scores as a result of retaking quizzes.


We started out the unit by refreshing our memories of the various ways to represent relations. For my Algebra 1 students, they were already familiar with ordered pairs, input/output tables, and the coordinate plane. Mapping diagrams were completely new to them. Each representation got its own flap on this foldable which is one of my favorite foldables of the year.  






Now that we've reviewed relations, it's time to talk about a very specific type of relation - a function. To introduce the idea of a function, we completed a Frayer Model. 


Next, we practiced writing sentences to justify whether a relation is a function or is not a function. I find that students need explicit practice regarding how to properly justify something like this. 


Now that we know all about functions and non-functions, it's time for a function/not a function card sort. I blogged about this card sort and shared the file for it here



Since I started teaching, I have struggled to teach independent and dependent variables in a way I am proud of. Each year, it seems like I try something new. And, no matter what, the same 60% of kids who intuitively understand independent vs. dependent get it. And, the same 40% of kids who mix up dependent and independent EVERY SINGLE TIME still mix them up every single time. This happens no matter how well I feel like I've explained it.

Here is this year's attempt: 


I'm especially proud of the inside. I think that having students sketch a graph has helped their understanding of independent vs. dependent variables. 


This approach, however, was not the magic cure. I still had a fair number of students who switched the variables every single time.

Now, let's take a closer look at discrete vs. continuous functions. 


This discrete vs. continuous card sort still makes me so happy. I blogged about this activity here last month. 


Once again, I chose to pull out the good ol' DIXI ROYD mnemonic device for Domain and Range. 


I was feeling really uninspired when it came time to type up domain/range practice problems for our notebooks. Luckily, Math by the Mountain came to the rescue! These next two booklet foldables are her work. You can learn more about her relations and functions unit in this blog post.

Domain and Range of Discrete Relations:



Domain and Range of Continuous Relations: 



Up next: Domain and Range Restrictions. I simply edited my booklet foldable a bit from last year to update some of the examples.



I added a new graphic organizer this year for rate of change. This resulted from making the decision to NOT introduce the term "slope" during our relations and functions unit. Instead, I decided to wait until our linear graphs and inequalities unit to begin referring to rate of change as slope. 


Rate of Change Practice. We did four problems and stapled them together so they only took up one page in our notebooks. 





After looking at graphs with a constant rate of change, we shifted to graphs that have various rates of change.  I'm a bit disappointed that both graphs I chose were distance-time graphs. This is definitely an area of improvement for next year!



 It's graphing story time! This was my second time using popcorn graphs with my students. The conversations were awesome this year as well!


I was a bit short on time, so I just ended up using the same graphing stories foldable as last year. 



Here are close-ups of the two tasks inside. I found both of these tasks online. 




I created this puzzle to motivate my introduction of function notation. I really liked the concept, but my presentation could use some work. All of the values I picked as my examples could be found on the same linear graph (despite the entire graph not being linear). So many of my students thought that the function notation just meant to multiply by 6. :( It did lead to some interesting conversations when some students had interpreted the puzzle as multiply by six and others had interpreted it as look at the ordered pairs that the graph goes through.


Another big change I made this year was introducing evaluating functions by only looking at graphs and tables FIRST. Once my students were comfortable with evaluating this way, then I introduced evaluating from an equation. In the past, I did it backwards of that and started with equations. I think it was too much too soon. This year seemed to work a million times better!

Evaluating Functions From a Graph:


Evaluating Functions From a Table: 


Evaluating Functions From an Equation: 


Now, it's time to practice writing functions and using them to solve problems. My students found these problems to be a bit difficult. I think we should have spent more time practicing these than we did. 



For graphing functions, I chose to do the Win Some Cash task again from last year. Again, my students got super sucked into the scenario. 


While doing the task this year, I realized a mistake I had made last year. :( Last year, I had my students connect the dots to more easily see the shapes made by exponential, linear, and quadratic functions. This year, I highly emphasized discrete vs. continuous graphs and when it makes sense to connect the dots and when it doesn't. This is actually a discrete function, so we couldn't connect the dots this year. With this in mind, I'd like to edit the activity a bit next year to bring out the general shapes of different types of functions more clearly.

Also, note to self: make the graph bigger. I made a note about that last year, and I forgot to fix it before printing it again for this year! 


We lots of graphing practice. Students had to graph each function by making an input/output table and classify each function as linear, quadratic, absolute value, or exponential.  My students really struggled with knowing how to connect the dots. When I instructed them to connect the dots from left to right, this just confused them even more. Not sure how to remedy this for next year. Maybe I should make some sort of connect the dots puzzle for them to work out that goes left to right...



This year, I meant to make a summary page that discusses key points about each type of function, but we ran out of time.  It's definitely on the list of things to fix for next year. 


This two page spread in our notebooks just makes me smile. 


A Frayer Model for "Linear." Students had to create their own examples and non-examples. 


Our last notebook page of the unit was a linear/non-linear card sort.

You can download the files for this unit here

Monday, January 15, 2018

Monday Must Reads: Volume 26

Happy Monday! It's a three-day weekend here, so I'm especially enjoying this Monday that feels more like a Sunday. Today, I have knocked out our grocery shopping (a much-hated chore) and stopped by a few thrift stores where I picked up some new books. I had lunch with my parents and sister, and now I'm sitting on my couch covered up with a blanket while I finish off this post. After I hit Publish, I need to figure out what my Algebra students are doing tomorrow and continue working on a 2.5 hour presentation I will be giving Saturday over interactive notebooks.

If you're new around here, I try to share a new post every Monday of the previous week's "must-reads." It's really just an excuse to scroll back through my twitter likes of the previous week and think about how I would like to apply them in my own classroom. I hope you can take away something useful from this post!


Without further ado, here are this week's must-reads!

One area where I fall short in my classroom is exposing my students to real-world data and real-world situations. It's an area where I'm always striving to improve, but I always still feel like I'm falling short. One of the main reasons this area is hard is because it's hard to find good data to use in the classroom that will capture students' interest. This graph that was shared on twitter by Trooper Ben caught my eye. I'd love to edit it a bit (especially remove the Halloween label) and use it as a What do you notice? What do you wonder? prompt. Would your students be able to tell why there was a dip at the end of February and a peak at the end of October?

Image Source: https://twitter.com/TrooperBenKHP/status/922805701298319361
Jo Morgan shared a common misconception that her students have with evaluating expressions involving exponents. My students have been having similar issues. Despite going over the order of operations in depth at the beginning of the year, they are still making errors like this. I even make my students sign a "Parenthetical Promise" where they have to pledge to always use parentheses when substituting values into an expression. Still, I get responses like this. How would your students answer this question? I think we need to have more conversations about common misconceptions like this.

Image Source: https://twitter.com/mathsjem/status/952222346907127808
Teaching dilations? Check out this idea from Adam JW Craig's coworker. You could easily use a different mystery picture with each class so that one class couldn't ruin the mystery for another class.

Image Source: https://twitter.com/ajwcraig/status/952169248037761025
We're currently working on linear graphs and inequalities in Algebra 1, so I'm especially on the lookout for ideas for this unit. Amy's Special Lines Drawing assignment caught my eye. I've done this with slope before, but I never thought of doing it with writing the equations of horizontal and vertical lines.

Image Source: https://twitter.com/BetweenDesks/status/951927855730122752
The chemistry teacher in me also loves Amy's Which One Doesn't Belong task.

Image Source: https://twitter.com/BetweenDesks/status/951260698545475587
Students often amaze us when we just give them time to think and ponder in class. I love this conjecture about prime numbers created by c_lum dill_n.

Image Source: https://twitter.com/dilloncolum/status/951940067546816512
Paul Jorgens offers a brilliant activity for introducing the idea of linearity. Totally stealing this idea for next year!

Image Source: https://twitter.com/pejorgens/status/951935587769974785
Julia Anker is helping me write my lesson plans for one of my skills later in our linear graphs and inequalities unit with this activity. Each student had either a situation, table, graph, or equation for a function taped to their back. They had to ask each other questions in order to place themselves in groups that represented the same function. What an awesome idea!

Image Source: https://twitter.com/AnkerMath/status/951673505438777344
Jennifer Michaelis shares a link to an interesting NPR article regarding a study involving gummy bears and several related studies which I found to be quite interesting. Do gummy bears of different colors really taste different? Can your students devise a study to test their hypothesis?

Image Source: https://twitter.com/MichaelisMath/status/950567835692163075
Lauren Hannah creates a yearly gingerbread house with one goal in mind: to have her students find as much math hidden in the gingerbread house as possible. I LOVE this idea!

Image Source: https://twitter.com/mathteachZ206/status/937522024120975360
Sarah Leivian shares the results of a "Mystery Footprint Project" that sounds like the perfect motivation to introduce scatterplots.

Image Source: https://twitter.com/leiviansclass/status/925813197139005443
I also love Sarah's project where she challenged her students to come up with a strategy to determine if Zebra Cakes or Christmas Tree Cakes are better. How fun is this?!?

Image Source: https://twitter.com/leiviansclass/status/941045935676755968
Molly Rawding shares a fun twist on Panda Squares. Instead of giving directions at the beginning, allow for free play to see what people come up with. Great idea!

Image Source: https://twitter.com/RawdingMolly/status/951452897883107333
I'm currently in the process of teaching myself physics so I can be certified to teach physical science and/or physics, so I'm always looking for great physics activities. I love this tug of war activity to motivate coefficient of friction from Frank Noschese.

Image Source: https://twitter.com/fnoschese/status/951219916065173504
It is true. Students are stressed. So, I think it's amazing that Cynthia Platou added a de-stress corner to her classroom that features a giant coloring page. Cynthia says she bought her color poster awhile ago at Hallmark. There are some available to purchase on Amazon, though.

Image Source: https://twitter.com/PlatouWorld/status/951195920015806464
Scottie O'Neill shares a great idea for making classroom management more manageable. I think I need to do this next year. I need to pick a couple non-negotiable rules and track them visibly.

Image Source: https://twitter.com/GHS_oneillmath/status/951173248628219904
I'm also intrigued by this twist on exit tickets that Scottie has shared.

Image Source: https://twitter.com/GHS_oneillmath/status/903341826006011904
Looking for a challenge for your play table/puzzle table? Tara Daas has got you covered. This is perfect for me because I just ordered a class set of base ten blocks (affiliate link) earlier this year.

Image Source: https://twitter.com/chatelet0211/status/950877534178209793
Looking to have some snow day fun? Liz Mastalio puts up a calendar and gives each student a chance to guess when the first snow day of the year will be. I know this is probably too late in the yar for most of you, but here in Oklahoma we still haven't had a snow day yet.

Image Source: https://twitter.com/MissMastalio/status/950877868137111553
Jenn Vadnais shares a photo of giant ten frames on a classroom floor. This has my brain churning about what other giant math-y things we could make on the floor of our classrooms...

Image Source: https://twitter.com/rilesblue/status/950779417952833536
Chris Bolognese has came up with a great idea for investigating similarity - expanding creatures!

Image Source: https://twitter.com/EulersNephew/status/950708109378539521
Have any leftover wrapping paper that has a grid on the back? Daniel Knox has a use for that.

Image Source: https://twitter.com/knoxdan/status/950764955686588417
I can't not share this awesome card sort created by my husband, Shaun Carter, for his geometry classes. See why I married this guy?!? You can find the free download for this activity on Shaun's blog.

Image Source: https://twitter.com/theshauncarter/status/950584921042530304
What better activity for the first day back from break than creating and illustrating a graph that describes how you spent your break? Thanks Trever Reeh for the great idea!

Image Source: https://twitter.com/treverreeh/status/950524235386060801
Megan Denman shares an idea for an awesome way to make stoichiometry calculations more hands-on with a card sort.

Image Source: https://twitter.com/DenmanChem/status/950523262349578241
Mr. Knowles shares a great looking geometry task that involves a lot of algebra practice. I would classify this as a very strong first tweet for a beginning teacher! I look forward to following this account to see what other excellent tasks that Mr. Knowles has to offer.

Image Source: https://twitter.com/SK18Maths/status/950452902421782530
I love using algebra tiles (affiliate link), so I was super excited when I ran across a creative algebra tiles art task from Jazmine Castanon on my twitter feed.

Image Source: https://twitter.com/jcast301/status/950514314124939264
Leigh Ann Mitchell shares an awesome project that combined graphing with Desmos and 3D printing.

Image Source: https://twitter.com/MitchellAlg/status/950433605741957120
I love playing Left Center Right (affiliate link) with my students, so I was super excited to see that Sandra Hinckley had math-ified the game a bit using positives and negatives.

Image Source: https://twitter.com/MrsHinckleymath/status/913900339262361600
Amy Hogan shares some fun 2018-themed math puzzles to help ring in the new year.

Image Source: https://twitter.com/alittlestats/status/948281431763103747
Until next week, keep sharing your ideas!