## How-To: Synthetic Division

During my Algebra 2 unit on polynomials, I had asked my (support) class if they would like to stick to just using polynomial long division, which works for every single problem, or if they would like to also learn another method (synthetic) that, while far quicker, only works in certain situations.  It was almost unanimous that they favored sticking to polynomial long division, which was fairly surprising to me. I almost figured they would want a quicker method, but their rationale was sound.  They thought that having another method would just trip them up, and they didn’t really see a point if it could only be used for linear binomials.

However, a few weeks after our unit on polynomials, we had a bit of down time so I introduced synthetic just for fun.  The students caught on quickly, but still preferred long division since it made more sense to them. (I agree that Synthetic is harder to wrap one’s head around.  It feels a bit more “magic.”)  Unfortunately, most of the class was gone that day due to an optional viewing of the school play being offered for students during the first four periods of the day.

As we start moving toward reviewing for finals, I figured I’d make a slideshow for students to view on their phones if they wanted to get a refresher on synthetic division.  Here it is!  I like it because it has a quiz-yourself and work-at-your-own-pace feel to it.

Do you cover both synthetic and long division for polynomials?  Which does your class seem to prefer?

Recently, I reached out to the MTBoS looking for fun ideas for practicing solving literal equations.  I had searched pretty thoroughly to find any pre-existing activities on the internet, but there wasn’t a lot available.  On top of that, what was there, required way more pre-existing skills (SO MUCH FACTORING!) than my Algebra 1 students currently had a month and a half into the school year.   Unfortunately, the MTBoS and I were pretty stuck.

Farther down in this Twitter conversation, however, it was mentioned that someone recently used BetterLesson’s lesson for teaching literal equations.  At that point I had already taught the lesson and most of my students caught onto solving them quite quickly, but I still was looking for a fun way to get a bit more practice in.  While exploring what BetterLesson had, I found this worksheet  that gave me inspiration for a game I could play with my students.  After a little bit of brain-storming, I created what I’m calling a Connect 4 Activity.  Essentially, it’s BINGO, but 4×4 instead of 5×5.

How to play:

• Before game: print enough game cards so each student has one, and cut apart the 16 problems.  I fold the problems in half (the problem number to the inside) and put them into a plastic bin.  (When printing from your computer, make sure it says “print double sided, flip on long-edge.”)
• To start off the game, each student gets a game board, on which they randomly place the numbers 1-16.  Students then pull out a piece of scratch paper, where they will be doing their work.
• The teacher brings the plastic bin containing the 16 equations around the classroom, letting a student volunteer pick a problem at random. (They LOVE getting to pick!)
• The teacher then places the problem under the document camera (or writes it on the chalk/white-board if you’re at a low-tech school) for students to solve.
• After all students have solved the problem, discuss the solution as a class.
• Once all students are silent, the problem number is revealed for students to cross off on their game card. (The excitement levels usually explode at this point, hence the moments of silence in between.)
• Repeat for as much class time as you have available, or until all 16 problems have been solved.
• Each time a student gets 4 in a row, they bring up their card and their work for inspection (they showed their work and corrected any mistakes for each problem), and are allowed to choose a small piece of candy (Jolly Rancher, a Starburst, etc.).

Reasons why I LOVE this game:

1. It is super easy to set up and is so adaptable for other topics.  This has probably been the lowest prep activity I have made for my students, yet it has been one of the most successful.
2. Students felt much more confident about their skills and were able to get nearly-instant feedback about how they’re doing.
3. Students LOVED it. The class begged me to continue letting them play the game through passing time.

(Updated September 2017)
This year I wanted to find more ways to practice literal equations with my Algebra 1 students.  We teach literal equations the week before Halloween, so I wanted to make something really fun and “Halloween-y.”  I made a Carving Pumpkins activity that’s self-checking and SUPER fun!  I couldn’t wait to try it out, so I gave it to my Algebra 2 students mid-September (patience never was my virtue) since they review literal equations in their first unit.  Students though it was fun, and they also found it really comforting that it’s self-checking.  To quote a group of boys, “this is super dope, we should do this for all of the holidays!”

Students are given 12 literal equations to solve for a specific variable.  Depending on what their answer was, they “carve” color the corresponding pumpkin in a particular way. In the end, each of the pictures should end up looking the same, as far as the color and carvings go.

I’ll be making more activities, and will update the post!

This week in Algebra 1 we covered the topic of percent of change, which is one of the many Algebra 1 topics that is covered in middle school but gets revisited in high school.  The concept of percent of change isn’t too challenging, even when working backwards to find an original or final value, but, geesh, it can be boring.  I looked around online and couldn’t find many activities for this topic, and the ones that I could were really geared toward lower middle school grades, so I decided to make my own version that is great for an 8th-9th grade class.

There are 17 problems that are to be posted, alphabetically, around the room (get creative, though!  can you hide any?).  Students work in pairs, each student getting their own work recording sheet.  Each pair of students also gets a path recording sheet, so they can track the order of problems they’ve gone through.  Students can start at any letter, that way you don’t have 30 students starting at the same place (I normally have a 4 person limit per letter).  Whichever letter a pair of students starts at will be the first letter added to their path recording wheel. They will solve the problem at the bottom, and then look around the room at the tops of the other letters until they find the letter with their answer printed on top.  Then, they go to the new letter, record it on their path recording wheel, and solve the problem at the bottom of the page.  The process repeats until the student makes it back to the letter they began at.

You can download the PDF and editable PowerPoint version of the scavenger hunt here.  You’ll need the fonts Wellfleet and HVD Comic Sans if you want to edit the PowerPoint file.  Otherwise, the PDF is good to go!

## My Favorite Resources #MTBoSBLAUGUST #Made4Math

Over the last year or so, I’ve done a lot of work with very low-end students.  Between teaching summer school for two years straight in the inner city, and teaching support classes in my regular semi-rural school, I’ve really been pushed to find other ways to convey information that work for my students.

One thing that I found is that no matter how small and bite-sized of steps I could break a process down to in our notes, many of my ELL students and students with IEPs for processing disabilities just couldn’t follow along and rework through the steps to get themselves “unstuck” on a problem.  Working toward self-sufficiency is really big for me.  I strongly believe that the purpose for high school is to prepare students to be productive once they enter the “real world,” whatever that means for them (school, workforce, military, etc.).  Being self-sufficient and being able to problem-solve on their own is a big part of being able to reach this point.  So, I kept searching and trying new things until I made my first flowchart graphic organizer.  It was a game changer for my class!

Students were able to easily follow along.  Using the graphic organizer, they were forced to read and do only one small chunk at a time and they had enough space to do their work right on the flowchart (it’s hard for some students to go back and forth between where the steps are written and where they’re doing a problem on a separate page of paper).  Students were able to use the flowcharts as long as they wanted.  As soon as they felt comfortable enough without it, they stopped using it.  I have also laminated a class set that we used for practice early on.

I’ve also found that these have been very successful with my older students to jog their memories about a method they haven’t used in a while (such as solving systems by elimination).  For a lot of my seniors, I’m not the only math class that they are taking–many of them are also taking a class called Math Skills that gives them opportunities to take more Work Samples, which are needed for graduation.  Work Samples are an animal of their own and the topics on them can vary widely, so students find themselves needing review on topics that they may have not seen for a couple of years.  I’ve had a lot of these students specifically ask if I had a flowchart for topic _______ that they could look over to remind themselves of the details of how to do ________.

With my younger classes, the first time we learn a method, I have a student working at the document camera as our class’ scribe, and the class (no help from me) discusses their way through the problem.  They determine which path they need to go down (the “yes” path, or the “no” path), and then work in pairs to do that step.  Then, they compare their work for that step as a class, and then move onto the next part of the flowchart and repeat the process.  I love, love, LOVE how student and discussion centered this makes my lessons!  Seriously! LOVE!  It’s almost as if I’m not needed (shh! don’t tell anyone that, because I still want my job).

From there, we do a few examples that we glue into our INBs, and do some practice with dry-erase pens on the laminated copies of the flowcharts.  I find that starting slow and having them work their way through a problem as a class, without me, helps them remember the ins and outs of the process a bit better, since they had to struggle together as a class.

Although I don’t have students referring to their notes quite as much as I would like, I have found that they go back to these flowchart examples in their INBs more than anything.  When I ask my students why they like these so much, a lot of what they say comes back to the fact that they have the steps on the paper, and the space to do the work on the paper, and the flowchart really forces them to go one step at a time.  A lot of them know that they have a tendency to rush through steps, and using the flowchart makes that very difficult to do.  Students then self-wean off of the flowcharts at their own pace, which is great in my books!  They are taking accountability for their knowledge.  If they can do their work straight away, they do so.  If they need a bit more help to get through a problem, they don’t just give up–rather, they walk to where I keep extra copies of the flowcharts, grab one, and work through the problem.  This has really helped develop the no opt-out culture in my classroom.  If students want to learn, there are tools to help them learn.  For my classes, the flowchart has been an instrumental tool for their development, both in math skills as well as self-motivation and persistence.

If you like the flowcharts, you can find them at my TPT store!  Today, they are 19% off when you couple your purchase with the 10% discount code OneDay.

Solving Systems of Linear Equations Flowchart BUNDLE

Solving Multi-Step Equations Flowchart

Thank you so much for reading!

My school doesn’t cover interval notation in its curriculum.  We focus primarily on inequality notation, although I tend to use the more specific set-builder notation.  Each representation has its merits, so I wanted to include interval notation more this year, as an occasional aside.  I’ve made a poster (8.5×14) that I’m going to hang up in my room to help students see the connections between the inequality symbols, the choice of open/closed points on a number-line, and the choice of soft/hard brackets in the interval notation. I’ve also made a color-coded version where students can ask themselves, “Can I include this point?” Green=”yes, include”, and red=”no, exclude.” Half of my classes this year are geared toward students who had received <40% in their last math class, so I’m hoping that the stop-light colors can make this yes/no, include/exclude concept easier to grasp. [NOTE: Thanks to lovely conversations on Twitter, it’s been noted that the green/red combination could potentially be dangerous if you have any colorblind students! I’m working on another, more color-friendly version that you can use, as well. I will update this post when it’s been made!]

Before I hang the laminated poster up (I add posters throughout the year as topics arise), I’m going to print another one and cut up the grid into the 36 individual rectangles and hand one piece to each student in my class (if there are fewer students, ask your class “who wants another piece?”–I always seem to have a bunch of volunteers because this means they’ll get to talk to more people!).  Students will then find the two other classmates who have representations equivalent to their own card. Once a triple has been found, students will check their cards with the teacher.  If they are correct, they will move around the class helping the remaining students.  If they are incorrect, they will review which card(s) in their triple didn’t belong as a group of three, and then go back to finding the equivalent representations.

A while back I made a display for special right triangles, and realized I never shared the files! You can download the PDF and the editable Publisher files here!  You’ll need to download the free font HVD Comic Serif Pro if you choose to edit the Publisher file yourself.

Here’s a picture of the pre-laminated pieces.  I took a few pieces of the finished product on my walls in the classroom, but each one had a nasty glare from the laminated finish.

I just found out that this year we will be having our open house before the school year even starts. This is a stark contrast to having Open House 2 months into the year, like we did last year.

I decided I wanted to make a flyer to send home with parents that goes over the biggest takeaways for the class.  Once school actually starts, I’ll send home a syllabus with all of the nitty-gritty details.  Although a bit nervous for the date change, I am very excited to use this as an opportunity to speak about required materials.  I hope that speaking about them now, when parents actually have time to go buy some of them (and on sale, too!), will help students be more prepared with the tools that they need.  On the back side of the flyer (not pictured), there is some school-specific information about how to access the online textbook.

Here’s the Publisher files for you to edit! You will need to download the free fonts Wellfleet and Caviar Dreams.