Math = Love

Monday, January 22, 2018

Monday Must Reads: Volume 27

Happy Monday! I hope you all had a lovely weekend. I had the awesome opportunity to give a 2.5 hour workshop on interactive notebooks on Saturday. It went super-well, and I look forward to sharing lots of files and information about what we covered in the workshop after I give the workshop one more time next Saturday. After the workshop on Saturday, my husband and I went to the restaurant where we had our first ever date to have lunch. It was fun to reminisce about our first date and talk about lots of math and math teaching.



Every Monday, I try to compile a list of the great ideas I've seen on twitter and in blog posts during the past week. Here are this week's Must Reads.

Mashup Math recently tweeted a graph of every shot Kobe Bryant has ever taken in his career. I've seen this data before, but today was the first time that I thought about it in the context of being a math teacher. What trends would my students notice in this data? I had to stop and think a bit about why there was a half-circle section with almost no shots. I felt a bit silly when I realized the reason! 

Image Source: https://twitter.com/mashupmath/status/955220829872238594
 Looking for an interesting opener for solving equations? Goytre Fawr Primary has got you covered.

Image Source: https://twitter.com/GoytreFawr/status/941326955076562944
Working on proportions? I like this task from Bluecoat Wollaton Maths.

Image Source: https://twitter.com/bluecoatmaths/status/449241969802223616
Team Maths shares a fun order of operations puzzle from Mr. Taylor. I need to file this away for next year!

Image Source: https://twitter.com/Team_Maths1/status/751652779199004673
Mr Knowles has hit it out of the park again with two more great tasks shared on twitter.

Image Source: https://twitter.com/SK18Maths/status/955153052478132225

Image Source: https://twitter.com/SK18Maths/status/952625242236702721
I'm always on the lookout for interactive classroom displays. I love this Equation Station from Michelle Courville. This could be adapted for many different grade levels very easily!

Image Source: https://twitter.com/CourvilleM/status/954858041794486272
Some of my favorite things to include in interactive notebooks are calculator tutorials. Students often forget the steps or happen to be absent on the day that we went over the steps in class. With the steps written out in their notebooks, all students are on an even playing field when it comes to being able to take full advantage of everything their calculator has to offer. Shaun Carter has typed up some lovely looking calculator tutorials for the TI-84 that address univariate and bivariate statistics.  You can download them here on Shaun's blog.

Image Source: https://twitter.com/theshauncarter/status/954720908081496064
Shaun also shared a hands-on activity that should appeal to all geometry teachers. I love how this approach gets students thinking about the math behind the formulas instead of just memorizing formulas and having no idea where they come from! You can find the downloads here.

Image Source: https://twitter.com/theshauncarter/status/954111219564150786
All math teachers know that time we are given to teach is never enough. I love the way Casey Ulrich makes the best use of his time by combining two topics: measuring angles and finding the sum of the interior angles of a triangle.

Image Source: https://twitter.com/ulrichedu/status/954502318724206597
Paul Jorgens shares a back-to-back drawing activity that he uses with his students as a type of formative assessment. This could be adapted for so many different topics!

Image Source: https://twitter.com/pejorgens/status/954468182907011072
Jae Ess shares a great card sorting activity for combining like terms. Students have to match all of the cards that simplify to the same expression. I've done sorts like this before, and students always love them. Looking forward to stealing this in the future!

Image Source: https://twitter.com/jaegetsreal/status/954454292634722305
Sigma-Aldrich shared a fun brainteaser with a chemistry theme. I posed this as one of our chemistry warm-ups this past week. I was a bit sad that only one student was able to figure it out. It turns out that the rest of my class claims they have never been taught the words "cirrus", "cumulus", and "stratus." I'm certain this is NOT true. When the answer was revealed, the rest of the class also said that they had never heard of this saying before. This led to an awesome conversation about the origins of various common sayings.

Image Source: https://twitter.com/SigmaAldrich/status/952998889686274048
I am super inspired by this real-world inspired task shared by Regina Dashiell to practice using both the Pythagorean theorem and scale factor.

Image Source: https://twitter.com/rbdashiell/status/872864812967100416
Rachel Blunt shares another awesome activity to address scale factor.

Image Source: https://twitter.com/MrsRachelBlunt/status/927622978078044160
Looking to combine arts and crafts with calculus? Check out this project by Michelle Ott that uses paper lanterns to demonstrate volumes of solids of revolution.

Image Source: https://twitter.com/michelle_ott/status/731216518126686208
Another great idea from Michelle Ott: Give students a set of criteria which they must draw a function to fullfill said criteria. Then, students have to do a gallery walk to evaluate each other's work. Brilliant.

Image Source: https://twitter.com/michelle_ott/status/844258467737165824
I could definitely do a better job of bringing real-world applications into my classroom. It looks like Silviya Gallo has this concept down, though! Check out these stations for law of sines and cosines.

Image Source: https://twitter.com/Gallo_wths/status/941322205442568193
One of my favorite function activities is a telephone game. I love how Liz Mastalio adapted this telephone structure for polynomials. I'm looking forward to adding another activity to my upcoming polynomial unit!

Image Source: https://twitter.com/MissMastalio/status/953736978620706816
Pam Wilson shares an awesome geometry task that I need to set some time aside soon to work out for myself!


Image Source: https://twitter.com/pamjwilson/status/953641381137960960
Looking to improve your school's culture and boost teacher morale? Check out this awesome idea from Kam Renae Koyama. Encourage teachers to write positive notes to one another while waiting for their copies to print!

Image Source: https://twitter.com/KamRenae/status/953096206774763520
Teaching translations can be a tricky task. Lisa Dollar breaks out the transparencies to make the topic slightly less abstract.

Image Source: https://twitter.com/LMoneyMath/status/950848856182460416
Lisa Dollar shares another awesome activity to make reflections less abstract that involves finger paint.

Image Source: https://twitter.com/LMoneyMath/status/951562065189199872
Katie Roznai shares a creative idea for structuring group discussions.

Image Source: https://twitter.com/krozaline/status/840230949006778368
John Carlos Baez shares an interesting mathematical fact regarding on-going mathematical research.

Image Source: https://twitter.com/johncarlosbaez/status/952335645740969984
When will I ever need to use math in real life? Jennifer Michaelis shares a real-world example from the bakery section.

Image Source: https://twitter.com/MichaelisMath/status/955269585976127489
Teaching angles? Julie Morgan shares some great ideas in a recent blog post.

Image Source: https://twitter.com/fractionfanatic/status/954766276097970176
I appreciate Julie's willingness to be open with the world about both the lessons that go well and the lessons that don't go so well. More of us should take a lesson from Julie (check out her blog post) and start sharing our own lesson fails. If we reflect and learn from them, then they really aren't failures.

Image Source: https://twitter.com/fractionfanatic/status/952552187195994112
I'm super excited to see Amy Gruen blogging again! Her exponent puzzles that she recently shared on her blog are awesome. I especially like her use of leveling with the puzzles. Level 1: Find the missing exponent. Level 2: Find the missing base and exponent. Level 3: Use the same base to complete two different equations. Seeing these brilliant puzzles are making me wish I was teaching Algebra 2 again.

Image Source: http://squarerootofnegativeoneteachmath.blogspot.com/2018/01/exponent-puzzles.html
Until next week, keep sharing all the ideas!

Friday, January 19, 2018

Five Things Friday: Volume 7

It's the first Friday in what seems like forever that I've actually remembered to sit down and write a Five Things Friday post. I'm seriously considering taking the Friday out of the name so that I can just post them whenever I finally remember...

Here are five things that I want to mention on my blog, but I don't feel are worthy of an entire blog post. 

1. One of my students chose to draw a math symbol as part of her slope art project. This made me so happy. What didn't make me happy was grading these slope art projects because many of my students did not follow all of the directions. :( 


2. When my husband (formerly an Australian maths teacher) and I were dating, he wrote a blog post where he shared how he used the Sieve of Eratosthenes with students. I was blown away by this post because I'd used this activity with students before but never exactly like the way he explained. Shaun didn't just have students mark out a number once. He had them color-code their work and mark out numbers each time they were a multiple of one of the prime numbers. My math concepts students are currently working on prime vs. composite numbers, so I finally got to try this activity out for myself with this multi-colored tweak. It was awesome! I also appreciated that Shaun has his template extend to 150 instead of the standard 100 often used in math classes.


3. Part of my math teacher identity is defined by the fact that in six years of teaching I have never taught Geometry. Algebra is my comfort-zone. I've branched out over the years to teach other things than Algebra such as Statistics, Physical Science, and Chemistry, but I've never thought of myself as capable of teaching Geometry. My husband, however, does teach Geometry. And, this year, he teaches right across the hall from me. I was thankful for this earlier this week because my Algebra 1 class got embroiled in a big debate over rhombuses vs. parallelograms. One student insisted we didn't need the word parallelogram because every parallelogram was a rhombus.


In the middle of the debate, I left the room. My students thought I was mad about their debate. I wasn't. In fact, I was quite excited. I barged into my husband's room and announced that I was needed to borrow his tub of exploragons (affiliate link). It was an emergency! We used various sized pieces to make a parallelogram that was a rhombus and one that wasn't a rhombus. It was awesome.


I'm realizing more and more that algebra and geometry are intertwined. I need to embrace geometry and incorporate it in my teaching whether I am formally a geometry teacher or not. This is something I want to think on how to do better this summer.

4. I took the plunge and purchased a 100 Chart (affiliate link) for my classroom. I've only ever seen these used in elementary classrooms before. As a high school teacher, this purchase might seem a bit weird, but I'm looking forward to challenging that view. My math concepts class is a class of 9th graders who aren't ready for Algebra 1. We've already used it once when looking at finding multiples of three. I also look forward to using it to play a LOW-TECH version of Julie Morgan's 1-100 Grid Review Game. If you've used a hundred chart with secondary students, I'd love to hear more ideas in the comments!



I was super impressed that it came with different sets of color-coded cards based on which numbers the cards were multiples of.


5. For the first time since September, I have a properly working projector in my classroom. My old projector would overheat and turn itself off every 3-5 minutes. This was not convenient for getting through material in a timely manner during class. My new, fancy LED projector (affiliate link) is so much brighter than my old projector. We can actually have class with all of the lights on! And, it doesn't randomly turn off, so we can actually get stuff done. Yay! My chemistry class was the first to use our new projector, and I was excited to be able to share what plum pudding looks like while talking about Thomson's Plum Pudding Model.


Thursday, January 18, 2018

North East South West Puzzle from Puzzle Box, Volume 1

Just a quick post today because it's already past my bedtime! This has been a crazy week because I've been spending almost all of my spare time prepping for a 2.5 hour workshop I'm giving this Saturday on interactive notebooks. The participants will actually be designing their own notebook pages during the workshop, so I've had to put a lot of time and thought into how to make our time productive and make sure people leave with an INB that they are proud of. I'm looking forward to sharing my presentation slides and documents in a couple of weeks once I've had time to tweak them and perfect them.

Today, though, I want to share about this week's puzzle table happenings. It's a short, 4-day week due to Martin Luther King, Jr. Day. And, I was so frazzled on Tuesday that I never got around to putting out this week's puzzle. So, yesterday was the first day for this puzzle on the puzzle table. With only two days of student attention so far, it has been attempted by several and solved by one pair of students I don't even have in class this year. Two girls stopped by to discuss something related to student council. The website I needed to access to answer their question was having technical issues, so they were forced to wait. They naturally gravitated toward the puzzle table and solved the puzzle. It was awesome to listen to their reasoning.


Instead of just jumping in the puzzle and placing letters in random places, they really reasoned through which letters were used the most and which letters were used the least. Then, they used this information to decide where to put these key and not so key letters in the puzzle. Once they did this, they had the correct solution in what seemed like no time at all. My other students have not been so lucky yet.

This week's puzzle, which I have named "North East South West" comes from Puzzle Box, Volume 1 (affiliate link) from Dover Publications. This is the first book in a series of three puzzle books that are edited by the Peter and Serhiy Grabarchuk. This specific puzzle is by Donald Knuth.


http://amzn.to/2kRduid          http://amzn.to/2kRLtqI          http://amzn.to/2BHqKhf

Each volume has 300 puzzles, and I have found over a hundred puzzles between the three volumes that I would like to adapt to use in my classroom some day. If you love puzzles or if you are looking for resources to teach your students to reason logically, Puzzle Box, Volumes 1-3 (affiliate link) are the books for you!


This week, I decided to give my students a chance to try a word-based puzzle instead of my normal shape-based or number-based puzzles that I tend to gravitate towards. Hello, I'm a math teacher!  


Puzzlers must take the 10 letter cards and arrange them in such a way that NORTH, EAST, SOUTH, and WEST can be traced out by moving one square at a time, horizontally, vertically, or diagonally. Donald Knuth's original wording of the question mentioned moving as a chess piece. I figured that would confused my students, so I chose to reword it.


I have uploaded the files for this activity here. The puzzle board is designed to print on 11 x 17 paper or cardstock (affiliate link). The puzzle pieces are designed to print on letter sized paper.

You can print it on letter sized paper by changing the scale percentage. I had to scale it to 65% to make it fit. Be sure you remember what percent you chose because you will need to scale the puzzle pieces to the SAME percent so that the puzzle pieces fit on the puzzle board properly.

I'm off to bed. Hope you and your students have fun with this puzzle! If you haven't already, I definitely recommend that you check out the Puzzle Box books. You can get a great taste of what types of puzzles they have to offer you and your students by looking at the free Amazon Preview! Just click the "Look Inside" button for each book. If you're logged into Amazon, you can click "Surprise Me!" on the left side of the page. This will let you see quite a few of the puzzles inside the book for free. I typed up my first Puzzle Box puzzle from the free preview. Then, I did some more looking around and knew I had to order it!


Full Disclosure: I purchased Puzzle Box, Volume 1 with my own money. I was sent a free copy of Puzzle Box, Volume 2 and Volume 3 by the Grabarchuk Family.

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