mtbos – Math by the Mountain

How-To: Synthetic Division

January 17, 2017January 17, 2017Math by the Mountain2 Comments

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?

Download a PDF of the slideshow here: synthetic-division-how-to

synthetic-division-how-to-page-001

Solving Literal Equations “Connect 4” Activity {Student Approved} FREE DOWNLOAD

October 14, 2016September 21, 2019Math by the Mountain6 Comments

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:

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.
Students felt much more confident about their skills and were able to get nearly-instant feedback about how they’re doing.
Students LOVED it. The class begged me to continue letting them play the game through passing time.

Download the game here:More Literal Equations Activities:
(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!

Percent of Change Scavenger Hunt Activity {Free Download}

October 8, 2016October 8, 2016Math by the MountainLeave a comment

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!

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My Favorite Resources #MTBoSBLAUGUST #Made4Math

August 22, 2016November 12, 2017Math by the MountainLeave a comment

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!

Inequality vs. Interval Notation Poster {FREE Download} #MTBoSBlaugust #Made4Math

August 20, 2016March 4, 2020Math by the Mountain2 Comments

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.

Would you like a copy of the reference poster? Get the color and the black and white versions here! (It’s free!)

Special Right Triangles Display {FREE Download} #MTBoSBlaugust #Made4Math

August 14, 2016August 14, 2016Math by the Mountain2 Comments

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.

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Open House Kit for Math Teachers – Editable Freebie

August 14, 2016July 16, 2020Math by the Mountain1 Comment

Back to school season is stressful, can we all agree? I remember when I was a new teacher and the thought of Open House was terrifying to me (I mean, it’s still fairly stress inducing, but I’ve found ways to minimize that). Dozens of parents in one room staring at you (with what feels like a far more critical eye than their students) is enough to make anyone feel the pressure. It was always important to me to make a good impression during Open House so it could set the tone for the year. It is the first point of contact for many parents, after all.

1 Open House Kit Freebie Math by the Mountain

Send me the Open House Kit!

Something that really helped calm my nerves was to make sure that I had an informational and professional looking handout that I could give to parents that gave them all of the necessecary information they’d like to know in one place. It also helped ME by giving my 15 minutes with them during Open House structure and I was really comforted by having something tangible to reference that they could all see with me.

I wanted something parents could physically take home with them because going to open house is overwhelming, especially if they have multiple children. I chose to make a short flyer that covers the biggest takeaways for the class and I wanted it to be something they could look back to over the school year as a reference for the course (where to contact, ways to get help, ect.). This flyer doesn’t contain all of the information for each class, though. Once school actually starts, I’ll send home a syllabus with all of the nitty-gritty details.

Send me the Open House Kit!

Although still a bit stressful, I love open house because I get a chance to meet parents face to face prior to confrences over Thanksgiving (that’s a long, long way into the year), and I like having the chance to speak about required materials before the year begins. I’ve been shopping for school supplies for long enough that I know most of the deals and can let parents know the best places to shop for what. I know money is tight for a lot of people, so this is also a chance to talk about priorotizing and what the school has a limited supply of for students who need it. For example, our school has a small amount of calculators that can be checked out for the year from the library, but a lot of students don’t know about it! This is the perfect thing to discuss prior to the school year starting.

I’m also a fan of Open House because I have the chance to tell parents about the many ways students can get help throughout the year and give them an idea of what the classload will be. On the back side of the flyer (not pictured), I photocopy some school-specific information about how to access the online textbook and I print a HUGE picture of a few calculators I’d reccomend buying/checking out, if they don’t already have one.

Here’s the flyer I’ve used year after year. I’ve tweaked it to work perfectly for each of my classes!

If you’d like to use my open house flyer in your classroom, I’ve got good news for you! It’s an exclusive freebie for the Math by the Mountain Club! It’s 100% editable so you can customize it to your exact needs. Join here!

On top of that flyer, I’ve also made a whole Open House Kit that you will receive, for free! You’ll get a PowerPoint presentation (totally editable, of course) and a sign-in sheet for parents to use and for you to collect up-to-date contact info!

Sign me up! I want the freebie!

I hope that this can make back to school season less stressful for you! I sure know it’s helped me.

-Audrey

Get this open house flyer as well as the perfect open house kit right here!

I want it! Gimme that freebie!

Justify It! Geometry Posters {Free Download} #MTBoSBlaugust #Made4Math

August 14, 2016August 14, 2016Math by the MountainLeave a comment

Throughout the year, I will be adding more justifications as they come along. The next batch that we will come across will be about segments. From there, we’ll talk about angles, congruence, similarity, and more!

Here’s what I’ve got so far! What justifications you most want to include in an edited list? I plan on using these primarily for two-column proofs in geometry.

PDFs: Justify It! Posters (Color) and Justify It! Posters (Black)

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Performance/Mastery Task Checklist Poster #MTBoSBlaugust

August 14, 2016August 14, 2016Math by the MountainLeave a comment

In my state there are a couple of ways to meet the graduation requirement for math. First of all, students need three credits of math. From there, they can either pass the SBAC test, have a high enough PSAT score, OR they can graduate by completing passing Work Samples.

Work Samples are given twice each year, and one thing that I’ve found is that math is not what typically keeps students from passing them. It’s that they forgot to clearly communicate their plan, or forgot to state their answer as a complete sentence, or they didn’t reflect on their answer at the end. There’s so many little places to go wrong along the way.

problem solving steps poster

To help them get used to the process, I decided that this year I would start doing one mastery task each unit as a partner quiz-grade, probably toward the end of the unit as an in-class review activity. I made a poster to put up on the wall for students to reference whenever they are doing these mastery task quizzes. I’m hoping that by doing this with a partner, more valuable conversation will happen to help deepen a student’s understanding of the topic. Additionally, as students start getting used to this process, the work sample will become much less daunting. Instead of having a 40-box rubric to follow along (that’s what the state provides, yikes!), they will have this process ingrained in them, which encompasses the requirements of a passing or exceeding score.

Lastly, I know I have had to give several proposals about how to solve a problem while I was working in a research lab in college, and this is typically the format that my presentations would follow. If I were to give a presentation trying to sell someone that my way was the best way, this is the sequence I would follow and I believe it would suit many professions, not just the inherently mathematical ones. I want students to get into the habit that good work needs to be backed up, and, regardless of what they are doing, good writing will need to go along with it.

My Teacher Planner + Free Download #MTBoSBlaugust

August 3, 2016July 1, 2018Math by the Mountain6 Comments

You can view the full version of my plan book (edited slightly for privacy) here as a PDF or here as a Word document. The first and last page have been printed on card stock and laminated to increase durability, and the whole book is coil bound. I sent it off to my school’s print shop a couple weeks ago and it was printed the same day. Unfortunately due to their limited summer hours and my conflicting schedule while teaching Summer School, I haven’t been able to pick up the finished product, yet. Summer School wraps up this Friday, so I must continue to anxiously await until then.

All right, to move on to the main feature of this post, we need to start with some confession time: I did a real poor job of keeping track of my planning papers my first year of teaching and still haven’t even figured out and logged my PD hours (it’s on the to-do list for summer, m’kay?), so I knew I needed to have a better system this year. I had so many unit plan calendars in so many places (hey, I did have 4 preps), and I had revisions of unit plan calendars in so many places, AND THEN I RECYCLED THEM. What?! What was I even thinking? The best/only explanation I can come up with was I was temporarily possessed. Where were Sam and Dean Winchester when I needed them?

I even took the time to write myself memos about how lesson plans went so I could refer back to them a year later and refresh my memory about what worked, what didn’t, and ideas to make it even better. Those got recycled too, I assume. Fun fact: I went to a university that had 5 different types of recycling bins. Recycling is in my blood. I see paper, I recycle. Reduce, reuse, recycle, #amiright? Well, I was wrong, very wrong to do that. Definitely did not do my future self any favors.

Thus, my huge make-an-all-in-one-resource summer initiative was born. I can’t tell you how many versions and variations of my plan book I have made in the last few months. With each blog post I read from other teachers making their plan books, I kept getting more and more ideas to make a resource that would (hopefully) really work for me this year, and allow me to keep all of my most important planning information in one place.

Without further, ado, let’s get into it:

The front page has my name and the current school year on it. It’s printed on card stock and laminated.

The next page is a copy of my school’s 2016-2017 calendar, available for easy reference. (Wouldn’t want to accidentally plan a great lesson for MLK Day or Memorial Day.)

On the back side of the calendar, I keep a page for “Important Information.” I can’t tell you how many times I had to search for the pin to my office phone voicemail (we have own phones both in our classroom as well in a separate shared office space), or the password for the online textbook, lunch ID number, etc. This page will keep all of the important information that I don’t use frequently enough to remember.

Like I said earlier, I didn’t even keep track of my PD hours this last year, so I’m going to be much more proactive about it this school year and record my information after each PD session since I’ll have this lovely plan book with me, anyway! I have two pages dedicated to this Professional Development Log, which I hope is enough to last the whole year.

Next, I have a 10 month calendar in green for my Algebra 1+Support class (I color code my different preps). Then, I have a 10 month calendar in blue for my Geometry classes, and in purple for Algebra 2 + support. I also do all of the important handouts for my classes in the corresponding color coded papers, throughout the year.

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This calendar section of the plan book is to plan out a from a glance plan of what needs to be done each day within a unit. For example, cover section 2.1 on the 12th, section 2.2 on the 13th, quiz on the 14th, move onto section 2.3 on the 15th, and then finish off the week with section 2.4 on the 16th. This allows me to get more of a “global” sense of what will be going on through the semester. purple
To go into the specifics of each day and week, I will use the next (largest) section of my plan book. Here I break each week down, day by day, into three columns (one for each main prep). On the right side, I have a spot to write notes to myself, reminders, to-do lists, memos about how things went, etc. I wanted to make sure that I could jot down any thoughts and not worry about losing them or having a sticky note fall off (and get reycled).

cal cal

The next chunk of my plan book is dedicated to meeting notes. I can’t remember who it was, but some lovely soul posted about their own plan book and had a note taking template similar to the one that I used. I streamlined it a bit, and am in LOVE. It has room for actual meeting notes, important dates spoken about in the meeting, as well as to-do/action items that came about as the result of the meeting. It’s so visual, which makes it easy to see exactly what needs to be taken care of. meeting notes template

The next thing I included was a student home contact log. I certainly kept a log last year, but I kept it in about three different places, which can’t be called great record keeping, by anyone’s standards.

My classroom has a bit of a weird setup where the phone has to be on the opposite diagonal corner from my desk, so keeping an electronic log isn’t the most convenient. Paper will be much easier, and I definitely preferred it last year. I envision bringing my plan book with me as I contact parents and write down comments as we have our discussion. Additionally, now that I have a dedicated log for this (rather than a section of some 5-Star notebook), I think I will be able to keep a much more cohesive and detailed list. student home contact log

My district has a professional development program called Math Studio–we were graciously given a separate binder to use for these special PD days, but I found myself not applying the information as much as I would’ve liked since I never would see my notes again until the next math studio day. This year, I wanted to keep a section in my planning book where I could easily look back on the great ideas talked about and presented in these math studio days, as well as the goals I have made for myself. I came up with so many great goals during these studio days last year, but I can’t say a lot happened with them. This year, I will definitely be much more purposeful with their implementation.

studio
Lastly, I’ve included a few “miscellaneous” pages for those things that I I’m sure I’ve forgotten to include dedicated pages for. misc

I tried my hardest to not overlook any major day-to-day resources I would need to include, and this has certainly come a long way since my first draft. Let me know if there are any glaring missing items that I should include! Potential unforeseen flaws and all, I am so excited to use my personalized plan book this year…and not recycle it at the end of the year by mistake. 😉

Thanks for reading, and happy Blaugust Day 2!