Math = Love

Saturday, July 21, 2018

Sequences Interactive Notebook Pages - Algebra 1

Due to a number of circumstances (losing days due to the walkout and other events during the year) during the last school year, I sadly did not make it all the way through our Algebra 1 standards. I ended up having to skip over data and probability which is especially heart-breaking because I had a lot of fun building those units last year.

So, the last unit in our interactive notebooks for the year in Algebra 1 was Sequences.

We began by talking about different types of sequences.  In retrospect, I think I should have began this unit with a card sort where students had to create their own methods of sorting sequences. I wonder if their sorting methods would be similar to the way we classify sequences as mathematicians.

Once we had definitions for each type of sequence, we spent a lot of time classifying sequences and finding the next value(s).  Sorry for the finger in the photo!

More practice thanks to Mathspad! I love this website. 

Next, we focused on our efforts on arithmetic sequences. I used almost identical notes to last year with the exception of adding the table for students to fill out. The table really helped this lesson go much smoother!  Silly me added the table to their notes but not to the quiz, and I definitely heard some frustration over that move!

After figuring out how to find the rule using a graph, we tried our hand at finding the rule for an arithmetic sequence without using a graph. Some of my students caught on right away. Others took a bit longer to catch on. 

Now, it's time for geometric sequences. We did this notebook page over the meaning of the different variables in our equation. 

We completed a similar table for geometric sequences. 

Then, we did some graphing to show that the graph of a geometric sequence is very different than the graph of an arithmetic sequence. I really struggle with how to set up the graphing for this notebook page since exponential functions grow so fast. :( 

This past year, one of the big things I emphasized in Algebra 1 was whether our graphs should be discrete or continuous. In the past, when we did these notes, I would draw in the curve to emphasize that geometric sequences form an exponential relationship when graphed. This year, I realized that because the sequence only includes discrete values that we shouldn't connect the dots. This was hard for me. I feel like it's much harder to see the exponential relationship without the line, but it led to a great conversation in class when a student asked if we could connect the dots. 

 Files for this unit are uploaded here.

Friday, July 20, 2018

Solutions, Roots, Zeros, and X-Intercepts, Oh My (Free Poster Download!)

Yesterday, I started doing some serious planning for teaching Algebra 2 in less than a month! I'm at a new school that has adopted new textbooks, and I'm not exactly the biggest fan of the chosen Algebra 2 book. I wouldn't say the book is necessarily bad, but I would say it's not as aligned to the Oklahoma Standards as it tries to make you believe. Of course, this view is also coming from the teacher who has made it a point to not use a textbook for the most part over the past six years.

I guess you could say I've been silently sulking and avoiding all planning for Algebra 2 as a result. Yesterday, I decided to change my attitude. Instead of focusing on what I don't like about our textbook, I decided to look through the textbook for something I did like. I skipped over all the examples and stuff and went straight to the questions. Guess what, there were some great questions there! Once I started looking for the things that would be helpful instead of the things I hated, my mood turned completely around. For the first time this summer, I was able to start thinking about exactly what I want my Algebra 2 class to be.

Looking through the second unit on quadratics, I got distracted. I remembered reading something on twitter that I had included in one of the early, early, early volumes of Monday Must Reads (Volume 4 to be exact!)

What I said about teaching my students that roots, solutions, zeros, and x-intercepts is definitely true. I didn't know that there was any difference myself, so I never thought to teach my students that these words meant slightly different things.

And, I went on with teaching and life not knowing any better until this tweet ran across my radar. Of course, by the time it did, I was no longer teaching Algebra 2. So, I saved it away in a Monday Must Reads post until it would come in handy once again.

Now that I'm teaching Algebra 2 and Pre-Calc next year, I'm thinking once again about these topics AND I'm thinking about how to decorate my new classroom.

Matt shared an awesome visual last year that also made it's way into my Monday Must Reads post.

The more I teach math, the more I realize the importance of teaching students to use precise vocabulary. And, I want to continue this with my Algebra 2 and Pre-Calc classes this year.

So, I set off to take Matt's visual and make it into a poster that could decorate my new classroom.

Here's what I came up with.

I was feeling pretty proud of my poster design, so I decided to share the posters on twitter. And, wow, what a response! 19 Replies, 78 Retweets, and 362 likes later (as of the time of this writing), I now realize that this is a very contentious topic. Most people seem to be okay with solutions, zeros, and x-intercepts. Roots, though. Peoples' thoughts on when you should and shouldn't use the word "roots" is all over the place.

From what I can tell, there isn't a clean cut, right or wrong answer. People pretty much use the words however they want. And, we're all pretty attached to our opinions.

Until I know better, this is the version I'm going with. And, I think that's the approach we all need to have in education. We teach what we know until we know better. Maya Angelou said it better: Do the best you can until you know better. Then when you know better, do better.” 

That being said, I'm about to share my posters both as a PDF and as an editable Publisher file. If you use the terminology slightly differently in your classroom, please feel free to edit these to match what you believe to be best. 

No matter how you decide to use these words in your classroom, I think we would all benefit from thinking critically about the vocabulary we use and ask our students to use in our classrooms. 

So, poster files. You can download them here. The font is Century Gothic. I made two versions of the posters in two different sizes. Normally, I would print posters like this on 11 x 17 cardstock (affiliate link). But, I'm not sure if I will have the capability of printing on that size of paper at my new school. So, I've also created an 8.5 x 11 version. 

Saturday, July 14, 2018

Absolute Value Graphs and Inequalities Interactive Notebook Pages - Algebra 1

My quest to get caught up on posting INB pages for Algebra 1 for last year continues. Today, I present to you my unit on Absolute Value Graphs and Inequalities. I'm almost hesitant to post this unit because it features little to no changes from last year's Absolute Value unit.

The unit started off with a divider. You can read more about these dividers here.

This unit featured only three skills. It was nice to have a short unit because the previous unit (linear graphs and inequalities) took FOREVER. 

We began by using an x/y table to plot absolute value relations. After we plotted the graph, we identified the slopes, vertex, and orientation.

My goal for this was to have students try and make predictions about what the slopes/vertex/orientation would be based solely on the equation/inequality and the previous results. 

My students were able to figure out pretty quickly how to tell if the graph opened up or down. It also only took a few examples for them to figure out how to find the vertex of the graph. What they really, really, really struggled with was figuring out which way to shade on the inequality based solely on the equation.

Next, we switched things up a bit. Instead of asking them to produce the absolute value graph, I provided them the graph and asked for the equation/inequality and the slopes/vertex/orientation. 

I had students work through this on their own or with partners (their choice) and check their work with Desmos along the way. It was a beautiful lesson to watch them make the connections we had started making with the previous lesson. 

 We closed out this short unit by looking at transformations of absolute value relations. I gave students two absolute value relations. The students had to identify what transformations were required to go from the first relation to the second relation.

I have uploaded the files for this unit here

Friday, July 13, 2018

Five Things Friday: Volume 20

How is it already Friday once again?!? This summer is FLYING by! Here's a small peek into what I've been up to of late.

1. I went to my second ever footy game. And by footy, I'm referring to Australian Rules Football. Before this, my only ever footy experience was watching my brother-in-law play a game in Australia. But, Shaun discovered that Tulsa has an AFL team known as the Tulsa Buffaloes. Since we've moved much closer to Tulsa, it's much more convenient for us to go and watch them play. We had a lot of fun watching them play. Though, I will admit that I did get a little bored during the second half and started focusing more on my kenken book than the game...

2. The hubby and I have been playing quite a few board games and card games of late.

After talking about Prime Climb (affiliate link) at Math Teachers' Circle, I realized that Shaun had never played despite the fact that we own a copy of the game! This was quickly remedied by him winning ALL three rounds that we played!

Next, we tried a game that was new to both of us: Mille Bornes (affiliate link). This is a card game that I picked up at a garage sale last weekend for only one dollar. "Mille Bornes" is french for "1000 Miles." The goal of the game is to lay down cards to represent exactly 1000 miles. You can prevent the other player/team from laying down mileage cards by causing them to have an accident, run out of gas, etc. The rules were a bit complicated to learn, but Shaun and I really enjoyed playing it once we learned how it worked.

Wednesday night, I challenged Shaun to a game of Hedbanz (affiliate link). I picked this up at a thrift store months ago with the intention of possibly using the head bands from the box in my classroom with some math versions of the game that I had intentions of creating. Well, that still hasn't happened yet. The game box said it was appropriate for ages seven and up, but as two adults we found the game to be super tricky! Maybe we're just bad question askers/guessers...

3. Even though the house we bought is much bigger than the house we were previously renting, organization is still proving to be an issue. As a result, I had to turn to Amazon to purchase some organization solutions. In the past week, I have purchased two 18 inch over the door organizers from ClosetMaid to bring both our pantry and our bathroom closet to order. I feel like just adding these two shelving units to the doors has more than doubled the storage space in each of these areas! Maybe after I get some more organizing done, I'll feel comfortable showing you what my cabinets and closets actually look like inside!

4. I recently marked an important task off my summer to do list. I got new glasses! 

5. Tuesday, I had the privilege of spending the day with Shelli at an EngageOK workshop. My favorite part of the workshop was a sorting activity where we looked at student responses to a common formative assessment. Our group had to decide how to sort the responses.

We decided on three piles: ????, Misconception, and Correct. 

I also enjoyed watching my group explore Liar's Bingo. I have experienced this activity twice as part of Math Teachers' Circle, so I tried my best to keep my mouth shut about how the activity worked. I'm looking forward to using this "magic trick" in my classes somehow. You can download your own set of Liar's Bingo Cards here

Thursday, July 12, 2018

Systems of Equations and Inequalities INB Pages - Algebra 1

I just realized that I haven't posted any more INB pages since February! Since I'm not teaching Algebra 1 next year, I've decided I need to try and finish up all of the Algebra 1 posts sitting in my drafts folders before I delve into the world of Algebra 2 and Pre-Calc in a couple of months.

This interactive notebook unit covered both systems of equations and inequalities. We started with a divider just as we do with every other unit. You can learn more about the dividers I use here.

There were only four skills covered in this unit. SY1-SY3 covered systems of equations. SY4 covered systems of inequalities.

We began our unit on systems by looking at solving systems by graphing.

In the future, I think I would want to modify these notes to have a specific box for students to write the ordered pair of the solution in.

Next, we addressed solving systems of equations by both substitution and elimination. Last year, I had these as a single skill of solving systems of equations algebraically. As a result, most students chose the method that they preferred and used that method every single time. This meant that I had a lot of students that became really good at solving by elimination but were rubbish at solving by substitution.

This year, I decided to make separate skills for solving by substitution and solving by elimination.

Each method of solving had its own graphic organizer which spelled out the steps.

Here's a closer look at the word problems we tackled for substitution.

And, now the same for elimination. By far, students definitely preferred elimination over substitution.

Addressing systems of inequalities let us spend some quality time coloring!

I found that having my students use two different colors (one for each inequality) helped them find the overlapping area.

Files for this unit have been uploaded here.