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When I first started hanging math word walls on my classroom bulletin boards, I figured out a super roundabout way to enlarge a pdf to print on multiple pages. There were multiple conversions involved and the whole thing took entirely too long. So I enlarged a few things, put them up in my classroom and moved on. 

But I recently revisited this whole free poster thing because there had to be an easier way. And my "revisiting", I mean I asked in our Facebook group and got an answer in 3.2 seconds from a super helpful teacher Ms. Potter. And yes, I had been doing things the hard way!

I could very well be the very last person on Earth to know how to do this but like we tell students, "Always ask your question because guaranteed there is someone else in the room who is wondering the same thing." So if you are like me, here are 3 super-simple steps to enlarge a pdf into a multi-page poster. 

How to enlarge a pdf to print on multiple pages
Step 1:
The first thing to do is download Adobe Acrobat Reader DC. It's free. Definitely uncheck those "optional offers" for McAfee Security. Those seem unnecessary.

Step 2:
Right click on your pdf file and choose "open with Adobe Acrobat Reader DC". 

Step 3:
Once your file is open, choose "print". This will bring up the settings.

By choosing "current page" and "Poster" my printer magically enlarged this How to Be a Math Person poster to 4 pages. 

*You can experiment with Tile Scale (right underneath the Size button) to get the number of pages you want your poster to be. For this poster, 100% worked. When I printed my Quadratic Keywords poster (below), I had to change this setting to 185%. You can keep increasing this % to make a giant poster!

There is some trimming to do, but this is OK because the overlap makes the poster easy to tape together. 

Once I lined everything up, I put small pieces of tape on the edges to hold things in place while I used larger pieces of tape to secure everything.

And here's the finished product! Once the poster is taped and on the wall, the seams are barely noticeable.

Super easy to do. I went on to re-print my parallel lines cut by a transversal poster, too.

And this Quadratic Keywords poster.

I hope this post has been helpful and helps you make lots of fun posters for your math classroom decor! Please always email if any settings give you trouble and I'll be happy to help.

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That glare from a shiny, laminated word wall is killer. Between the florescent lights and the windows, there's always somewhere in the room where the glare coming off the lamination blocks sight of the references underneath it.

I've been on the search for flat lamination pouches for a while now. I even tweeted Staples, who replied that they'd send the idea to their corporate office. To date, there are no flat laminating pouches at Staples. Or anywhere else. 

But there is an easy solution! I finally figured this one out today and I want to share it with you! 

So what's the solution?

Clear, flat spray paint!

Here's the how-to...

1) Start with a laminated word wall. This is especially great if you already have your word wall laminated and are super bummed about it being shiny. 

I used this Testors brand, but I'm sure you can use any clear, flat (or matte) finish spray paint. My husband does a lot of hobbying so happened to have this brand.

laminated only (not sprayed)
This Sales Tax reference is laminated only. I did not spray paint it. You can see how much glare is coming off of it.

2) On a warm dry day, spray a thin coat of clear, flat spray paint on your laminated word wall references.

If the weather is too wet, the spray paint won't easily dry. If it's too hot, the paint will dry before it hits the lamination. I'm one to throw caution to the wind so spray painted today in close to 100% humidity... then used a hairdryer. This works, too, but a lot more work. If I were to do an entire word wall, I'd wait until a dry day.

3) Let dry. It's done!

laminated and sprayed with clear, flat spray paint

This calculating tip reference was laminated and then sprayed with the clear, flat spray paint. The glare is completely gone!

I hope this has been helpful. I felt really bad hearing that teachers were feeling defeated after putting so much work into their word walls only to have the references often unreadable. Spraying everything is a little more work, but I feel the end result is worth it and your word wall will be protected for a long time to come. And be glare-free!

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I absolutely love our math Facebook group! There are so many wonderful, caring, thoughtful, intelligent, sharing teachers in there always willing to help each other. The community has grown way past what I had ever imagined when I opened it in 2017. At that time I had added my husband as the first member because I was so afraid no one would join! 

One of the awesome math teachers in the group is Danielle Fulbright. Danielle posted about the way she uses Google Forms to streamline homework data collection and so many wanted to know more. Danielle doesn't (currently:) blog, so I asked if she would want to write a guest post. And she accepted! So below is Danielle's post.

Using Google Forms to Streamline Homework Data Collection

by:Danielle Fulbright

When I started teaching, finding a homework collection method that worked for me was a real challenge. As a math teacher, I firmly believe that the only way to learn math is to DO math. I actively teach my students that you don’t STUDY math, you PRACTICE math. My students practice A LOT and I needed a way to hold my students accountable, even though I assign homework grades based on completion rather than accuracy.

I decided to try Google Forms with Google Classroom and it was life-changing! Google takes my students’ responses and assesses/presents the data in real-time so I can make on-the-spot instructional decisions.

Here is the link to a Shared Google Folder with photos and video of how I create my Google Forms, copy them when needed, and post them to my Google Classroom!

As a middle school teacher, I have multiple classes. Each class needs to review different concepts, so each class has their own form. To keep everything organized, each class is assigned a color and has their own HW Check folder in my Google Drive. This way I can easily find data on any student for any assignment.

My Classroom Routine:

➤Students come in and check-in their Homework with me for a stamp. This is when I mark absences and incomplete work in my gradebook.

➤Students spend the first few minutes of class the next day checking their HW on Google Classroom. 


➧Checked in pen
➧Star correct answers
➧X incorrect
➧Circle wrong questions we did not go over as a class
➧Correct work for what we went over in class.
➧Fill-out the Google Form (I attached one below)
Rate their Learning Targets in their Interactive Math Notebook. 

Ratings are:

1: I have no clue
2: I can kind of do this (need help to start or get stuck frequently)
3: I can do this
4: I can teach this

➤I look at the bar graphs on the responses and only go over questions that more than 5 students missed. This helps cut down on time spent on going over homework. Students that missed other questions can come see me during class or during intervention time for extra help.

➧Having a different form for each class allows me to tailor this instructional time to the needs of those particular students.

All of their Homework Checks can be found under the topic “Homework Checks”.

*Google has updated all new Classrooms so that the most recent assignment will appear FIRST! Yay!!!

This is what each assignment looks like to students. Heads up, submitting the form will NOT submit the assignment on Classroom. My students don’t use this feature for HW Checks because their names are on my response sheet.

This is a typical Checker for my students. A simple form with check boxes that they can mark what was incorrect.

Important Note: If you don’t want your students to see you answer key, you can create answers to the questions on the Google Forms. Your students can then enter their answer and the Form will self grade! This would save time overall. I prefer to have my kids practice marking their own and looking for mistakes.

The magic of Google Forms is in the automatically generated response sheet!

Clicking the SUMMARY response tab will show you:

1) A list of all students who filled out the form (the names on my form are random and not my students)
2) Bar graph(s) that show how many students select each answer
3) A pie chart that shows the percentage each Learning Target rating was selected.

Clicking the INDIVIDUAL response tab allows you to look at how every student filled out the form.

Google Forms also allows you to create a spreadsheet that organizes the data for you. All spreadsheets generated like this will automatically sort into the folder on Google Drive where the matching form is.

Automatically generated spreadsheet: 

I like to sort by Learning Target Rating so the students are grouped based on ability level.

If you have been looking for a way to make homework data collection easier and less stressful, I hope this post has been helpful! 

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Math Dollar Deals are back for 2019-- our 4th annual celebration! Each Tuesday in July my math friends and I will be putting math resources on sale for just $1. 

Kara from Learning Made Radical (my partner scavenger hunt friend:) is heading things up this year. You can find more info about all the deals in her post:


You can also search #mathdollardeals on Teachers pay Teachers each Tuesday in July to find the resources on sale that week.

I hope you have a great July! 


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A month or so ago, I asked in our Facebook group what the best way to build a list of favorite math books would be, and of course the most popular answer was a Google Form! I wanted to make a go-to list for any teacher or parent to find a new math-themed book to read. The math books in the list now range from books for preschoolers to adults. 

And I hope you will add to the list! Here is the list of favorite math books. At the top is a link to the form where you can add your own favorite math books.

I went for a really long (embarrassingly long) time not reading. I'd find every excuse not to pick up a book, and before I knew it, it had been years. My first book back was Mathematical Mindsets from Jo Boaler, which of course changed my life. It took me a really long time to read because it's so densely packed with so much good stuff. And I read at night, which makes it harder to read for a long time!

I hope you check out the math books list. Below are some of my personal favorite math-themes books.

Zero is amazing. If you like ancient history and math history, this book is for you. I can't even wrap my head around how long it must have taken author Charles Seife to compile all of the information in this book. It feels like it must have taken decades. So awesome. I'll definitely read this one again.

A book I recently found at our public library is this one, Junk Drawer Geometry. Inside are tons of paper-folding, paper-cutting and other hands-on activities to show geometry concepts. 

I haven't even scratched the surface of what is inside. My favorite is the borderline parlour tick of turning 2 paper circles into a square by taping them and cutting. When I showed this to my students, they called it magic. Always a fun day when kids call math magic!

My daughter loves this book Amazing Visual Math. Inside are so many opportunities to explore math in 3 dimensions.

Here, part of the book folds up, making a cube. Kids can think about how many single-units would make this cube's volume. 

The Math Book from Clifford A. Pickover is another one that is so packed full of facts I can't imagine it having taken less than a century to compile it all.

It's a cool reference book. Every other page is another tidbit of math with a picture to go with it. Zeno's Paradox is also mentioned in Zero and took a long time for mathematicians to figure out.

A Remainder of One rhymes as it teaches kids about division and arrays. I get weirdly sentimental reading this book for some reason.

Maybe it's because the Elinor J Pinzes was able to show how 25 can be arranged in a bunch of different ways. I think it's cool how most ways leave a remainder of one. I love this book so much that I made a set of free Remainder of One posters.

Alice Aspinall nailed growth mindset in her book Everyone Can Learn Math. We love this book in the McKay house. 

I think as my daughter starts to hit harder math as she makes her way through elementary school this book will be one that we will re-read (and re-read) and reference during homework sessions.

What is your favorite math book? I hope you will add it to the favorite math book list! And I hope this growing list is helpful to you for finding a new math-themed book for you, your family or your students.

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There are two ways to approach summer school algebra: as a punishment for slacking off all year or as an amazing opportunity to turn math attitudes around. There are solid reasons for taking either approach, but which has the better possibility of changing a kid's life forever?

Having a solid algebra foundation is incredibly important for all math courses that come after it. When I was in grad school, my calculus professor also worked in the extra-help center, which I visited weekly. One night while working on a problem, I made the ultimate error-- I committed the freshman's dream. He pointed it out, I felt a little silly, and he then quickly explained that it's often the algebra that gets in the way of calculus. This reminded me a lot of how arithmetic often gets in the way of algebra for our students.

So who are the kids taking algebra in summer school? There are 3 types of kids who end up back in school in the summer. The first type are there because their parents forced them to go. I learned about this about 3 weeks into summer school one year when it came out that half of my students were there for enrichment. The second type are the kids with truancy issues. These kids have a high likelihood of not meeting the summer school attendance requirement and then needing to retake the class in the fall. 

The majority of kids in summer school will be type three: the kids who came to school everyday but just didn't do the work. Why? Was it boring? Was the class too erly in the morning? Did they miss some unknown, yet critical, piece of information at some point in their past? Did they butt heads with their teacher? It could be anything. These are the majority of the kids who will be taking algebra in summer school. They can do it, they just didn't.

In this post I want to share activities and other resources for making summer school algebra fun and rewarding for both the student and the teacher. 

This post covers:
Solving equations
Slope and linear equations
Functions & domain and range
Systems of equations
Factoring quadratics
Quadratic formula (and word problems)

**Next to each resource below will be a (free) or a ($) to let you know which is which. All of the resources in this post - both free and paid- can be found in this summer school algebra bundle.

Solving equations

When I had kids who just could not understand solving equations, I gave them this solving equations flowchart (free). Instead of like terms, this graphic organizer first focuses on the + and - signs, which are visually much easier to find. From there, a series of questions guides students through the equation solving process, depending on which side of the = sign has variables.

I have a summer goal to write all about the ways to use algebra tiles. Below is an algebra tiles solving mat and paper algebra tiles (free). For kids who function on "why?", algebra tiles work really well. In the post with the mat and the tiles are three examples of how to use them to show equation solving.

Displaying student work is an amazing motivator. On the days my students would say things like, "I can't today," I pointed to their hard work on our bulletin board and it got them past their mental blocks. Math pennants are a fun way to practice math and display student work and remind kids that they CAN do it. This solving 2-step equations math pennant (free) is sent via email after subscribing to my blog.

Multi-step equations can give students a hard time because there is more than one "right" first step. These equations are covered on the flowchart above. This multi-step partner scavenger hunt ($) is a fun way for pairs of students to practice solving. Their equations are different but, if both partners solve correctly, their answers will match.

When I was a kid, I'd freeze in competitive situations. When I played baseball and basketball with my friends, I was the next Roger Clemens and Larry Bird. On the field and on the court during organized sports, I hit no balls or baskets. The pressure and anxiety got to me. It was too much! Kids team up in both the partner scavenger hunt above and the solving multi-step equations VTTT math game ($) below. This lowers the pressure, keeping the anxiety at bay so that kids can show what they really know.

Slope and linear equations

When I think of algebra, I think of slope and linear equations. The problem is, slope is a topic that was introduced in 7th grade as constant of proportionality and unit rate, was then changed to slope in 8th grade, and becomes a review topic in algebra, geometry and algebra 2. My least favorite unit teaching algebra 2 was our algebra review. It wasn't because I dislike algebra-- I love algebra. It was because the kids totally tuned out. "Slope" was a word they had already heard year after year after year, so in their minds they already knew it. 

But did they know slope? Nope. Nope=slope. They did not. By algebra 2 it was really hard to teach the kids who didn't already understand slope how to find it in a graph or even given 2 ordered pairs. It was just too late for a lot of them by then. 

So now that I've totally depressed you and myself, how can we teach slope in summer school algebra so that it is firmy stuck by algebra 2? This slope poster (free) comes in both color and b&w versions.

Coming back around to displaying student work and how motivating it is, kids can practice finding slope on leaves and then display their work on a tree in this slope tree activity ($). On the "I can't" days, this tree serves as a reminder that they can.

Then onto linear equations... these linear equations flippables ($) come in a couple versions - filled in and not - so that they can be used as a reference or as a way to take a quick set of notes on the slope formula, slope-intercept (shown) and point-slope. 

One of my favorite activities to do when I taught Algebra 1 was this linear equations graphing grass project (free at this link). We grew grass in cups and measured the growth daily. Then we found lines of fit, slope, wrote equations of lines, gave the grass a haircut and talked about piecewise functions. This project brings in so many elements of algebra and would work really well during a summer school session.

Additional slope & linear equations resources:

Writing Linear Equations VTT game

Slope Partner Scavenger Hunt Activity

Slope Scavenger Hunt

Functions and Domain & Range

This is one of my favorite units to teach. Domain and range is one of those things that all of a sudden clicks for kids, as long as they keep trying. I had a group of kids one year that needed extra support finding domain and range from graphs, so I made them this set of domain and range practice cards (free). It was all the extra practice they needed to allow us to move on (phew!).

Getting back to functions... this function or not sorting activity (free) is a super simple way to get kids thinking about what does nor does not make a function. There are more ideas for teaching functions (along with the story I tell my students to make functions stick) in this function or not blog post.

This domain and range scavenger hunt ($) is one of my favorite activities. I love scavenger hunts because they get kids out of their seats and working with each other. I included both inequality notation and interval notation versions in the summer school algebra bundle

Additional functions and domain & range resources:

Domain and Range math pennant

Domain and Range matching activity


I love teaching polynomial sketching. It's so fun to see the kids get so proud of themselves the first time they correctly sketch one of these crazy looking functions with parenthesis and exponents all over the place. Talk about a confidence booster! First, I'd give out this sketching polynomials cheat sheet (free) that the kids could use as a reference throughout the unit. 

We'd practice sketching daily using this polynomials quick check sheet (free). I'd give a point for each correct answer on the sheet for a total of 10/10. Once all students were sketching correctly most days, we'd move on.

One of my oldest activities is this polynomials blueprint activity ($). I have used it in just about every class I have taught, from 8th grade algebra to algebra 2, to review adding and subtracting polynomials.

This set of multiplying polynomials task cards ($) is a nice activity to assign as an assessment. I often give activities as assessment grades to lower the pressure so that I can really see what they know.

All Voyage to the Treasure math games come with peer-evaluation sheets so that students can evaluate each other on the work their partners put in. Sometimes during collaborative activities one student ends up doing all the work, so I wanted to stop this in its tracks. You can see the peer-evaluation sheet in the top left corner of this Multiplying Polynomials VTT game ($).

Additional polynomials resources:

Polynomials Math Pennant Activity

Sketching Polynomial Functions Task Cards

Systems of Equations

I was just about to gush about how much I love teaching systems but stopped because I've already gushed a couple times in this post. I guess you can say I really love algebra. My friend Mandy sent this graphing systems of equations math pennant ($) photo to me. A student who usually didn't do much work in her class completed it. This to me is everything.

I made a quick check for systems (free) like the one I made for polynomials. These work great to give kids structure and practice because it lets them anticipate the questions they will be asked.

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There are so many cool ways to use algebra tiles in math. Last week I wrote a post about using them to factor. In this post I wanted to show 3 examples for using algebra tiles to solve equations.

I'm using a set of paper algebra tiles in the photos, mainly so that I could cut one in half for example 2 that involves a fraction. 

So let's get into it!

Example 1: 

Solve 2x + 3 = 11 with algebra tiles.

(This solving mat can be found for free here or here.) 

The rectangular tiles are used to represent x and the small squares are each used to represent 1.

In this photo, the 3 squares on the left got recycled along with 3 squares on the right, leaving 2x = 8.

Here's the fun part! We can split the 2x into x and x and make equal groups of the small squares on the other side.

After recycling one group, we get x = 4.

Using algebra tiles to solve 2-step equations is an incredible way to introduce the topic. 

Example 2:
Solve ½x + 4 = 7 with algebra tiles.

Here is a quick video showing this example:

How to use algebra tiles to solve equations with fractions - YouTube

It's nice to use paper algebra tiles (free here) for this example so that an x can be cut in half. (We still keep the other half for the end.)

First I cut an x in half to show the ½x.

Here we can see our equation set up.

We recycle the 4 squares on the left and 4 on the right, leaving ½x = 3.

Now we bring in that other ½x from earlier. Because we just doubled our x, we have to double the other side. This gives us x = 6.

Example 3:

Solve 2x - 3 = 7 with algebra tiles. 

To get negative tiles with paper, you can print on 2-sided paper, like astrobrights, or glue two pieces of paper together before cutting. 

Here we have 2 x tiles and 3 negative tiles on the left and 7 tiles on the right.

To get rid of that -3 on the left, we +3 to make a zero pair. Then we have to +3 to the right, too.

The zero pair gets recycled since it's 0. Now we have 2x = 10.

And now back to the fun part: splitting into equal groups.

And recycling the extra stuff to get x = 5.

Here is a video showing all 3 examples in this post:

Solving equations with algebra tiles - 3 examples - YouTube


Algebra tiles can be found here.

Solving mat can be found here.

Solving equations activities can be found in this post.

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Slope is one of those super important Algebra topics that just keeps coming around. It even shows up years later in Calculus! I love teaching all topics with tons of activities that get students thinking independently and working with each other. This way everyone gets the practice they need to feel confident.

Every year, our slope and linear equation review in Algebra 2 is a little brutal. I'm convinced that when the word "slope" comes up, my students immediately shut off because they have heard it - a thousand times - before. Then I'll get x on top of y, errors with negative signs, graphed x and y intercepts instead of y intercepts and slope. You name it, I see it. Why? From seeing this same thing year after year, I really think it comes down to how well they pick it up the very first time they see it. 

Fun Slope Activities 
Below are some activities that make slope accessible and fun for all students. (There's also a free slope activity included).

I love sorting activities because they give students lots of confidence in the very early stages of learning a new topic. There are finite categories and answers, so students can rely a little on process of elimination. This can often be the boost kids need to push themselves through tough topics. 

One of my classes this year responds really well to scavenger hunts. If you have never done a scavenger hunt, the idea is pretty simple. Students do the big problem on each slip of paper, record their answer on their answer sheet, then find their answer on the smaller box on another slip of paper. This goes on until all problems are done. 

I hang the papers in random order in the room or in the hall outside of our classroom. The very best thing about scavenger hunts is how super easy they are to grade! Students can start on any slip of paper. From there, the slip number order on correct answer sheets will all be the same! A super quick scan of the side of a student's answer sheet reveals if they got all problems correct. Students also know immediately if they did something wrong because their scavenger hunt will "short circuit" back to a problem they have already done. I added some QR code hints on some of the trickier problems. 

I don't give many tests, which I know may be controversial. What I give instead to summarize understanding are task cards. The way I see it is that I answer so many questions during tests - and then feel guilty about it - that I might as well use the time to give a learning activity where questions are welcomed. 

The other big reason I don't give many tests is that most of my students have failed math tests repeatedly and I just don't wan to be part of that for them. Task cards work great as a way to sum up learning in a low-stress way. This set of task cards includes a fun mystery message.

If you know you're going to be out, or it's the day before a vacation, or you're just in need of some classroom brightening, this slope tree doubles as math classroom decor. 

I took this photo of a sample at home and it's still hanging on my wall months later! 

Math pennants are another great way to engage students and also build classroom decor for days leading up to conferences, Back to School night or holidays. Students love seeing their work displayed, especially when they can personalize it with colors.

If your students like showing off their creativity, I have a bunch more math pennants in this post

This is a quick puzzle with 16 pieces that covers positive, negative, zero and undefined slopes. Students can cut out the pieces themselves, which are all mixed up on the printout. 

Because every class and every year is different, this bundle of slope activities includes all the activities in this post as well as a Jeopardy game, an "I Have Who Has?" game, an additional set of slope task cards, a set of slope notes and a slope quiz. It's super discounted and the activities are sure to meet the needs of all of your students. 

My friend Kara from Learning Made Radical and I have recently started working together on a new type of partner activity. They are partner scavenger hunts where students work on unique problems that yield the same answers.

The partner scavenger hunt above is for finding the slope between 2 points. If partners find the same slope between the unique points they are given, then they know that their work is correct. If their answers differ, then partners can help each other find mistakes. There is more info about partner scavenger hunts in this partner scavenger hunts post.

I hope you have a great school year!

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Algebra tiles are the coolest little things. They are a wonderful hands-on tool that can be used to visually represent so many topics in algebra, from solving equations to multiplying binomials to factoring quadratic trinomials.

In this post, I want to focus on that last topic -- using algebra tiles to factor quadratic trinomials. Algebra tiles are a perfect way to introduce and practice this concept. They take a lot of the guesswork out of factoring, especially for trinomials that are not easily factored with other methods. 

Below are 4 examples of how to use algebra tiles to factor, starting with a trinomial where A=1 (and the B and C values are both positive), all the way to a trinomial with A>1 (and negative B and/or C values).  

Here is a look at the tiles in this post:

In my set of algebra tiles, the same-size tiles are double-sided with + on one side and - on the other. You can get a similar effect by printing this free printable set of algebra tiles on astrobrights paper (or glue 2 different colored pieces of paper together back-to-back before cutting). 

Let's jump into the examples!

Example 1: Factor x2 + 5x + 6
Factoring this trinomial is a nice place to start because the A value is 1 and both the B and C values are positive. We'll be able to get a good feel for how the algebra tiles work with this example.

1 x2 tile 
5 rectangular x tiles
6 + tiles

Here we have all of the tiles we will need to factor this trinomial. Now it's just a matter of putting the puzzle together.

First, I tried (x + 4)(x + 1). This used all of the rectangular x tiles but not all of the + tiles. In order for the trinomial to be factored correctly, all tiles have to fit together to make a perfect rectangle.

Next I tried (x + 2)(x + 3), which allowed all 6 of the + tiles to fit. 

x2 + 5x + 6 factors to (x + 2)(x + 3).

Example 2Factor 2x2 + 3x + 1
Algebra tiles are great for factoring quadratic trinomials where the A value is not 1. I have always liked the AC method for factoring these trinomials, but even I will admit that factoring with algebra tiles in this instance is all around way better.

2 x2 tiles
3 rectangular x tiles
1 + tile

Here we have all the tiles we need to factor this trinomial. With trinomials where the A, B and C values are all positive, we start and finish with the same number of tiles. (In a minute when we factor a trinomial where B and/or C are negative, the approach will be slightly different.)

Arranging the algebra tiles into (x + 1)(2x + 1) allowed all of the tiles to fit together into a nice, neat rectangle.

2x2 + 3x + 1 factors to (x + 1)(2x + 1).

Example 3Factor x2 - x - 12

When we factor quadratic trinomials involving negatives, we may not start and end with the same number of tiles. We may have to add in some zero pairs as we go. In the case of x2 - x - 12, our B value is -1.

Needed (to start):
1 x2 tile
1 rectangular -x tile
12 - tiles

Since there was no way to make a rectangle that fit those 12 - tiles, we needed to add in some additional zero pairs (1 of each rectangular + and - x tile).

We can do this because:

-1 + 0 = -1 or
-2 + 1 = -1 or
-3 + 2 = -1 .... and so on...

By adding in equal amounts of rectagular + and - x tiles, we are not changing the trinomial's B value. It's still -1.

Here we have 3 rectangular -x tiles and 2 rectangular x tiles. Still not enough to fit those 12 - tiles, though the B value is still being represented as -1.

We got it! We needed 4 rectangular -x tiles and 3 rectangular x tiles to make all 12 - tiles fit. -4 + 3 - =1 so we did not change the trinomial's B value.

x2 - x - 12 factors to (x - 4)(x + 3).

Example 4
Factor 2x2 + x - 3

Using Algebra tiles is so helpful when factoring quadratic trinomials where the A value is greater than 1 and B and/or C are negative. The tiles make the process so much more intuitive!

Needed (to start):
2 x2 tiles
1 rectangular x tile
3 - tiles

Right away it's obvious that we do not have enough pieces to make a nice, even rectangle. So we will need to start adding zero pairs to keep B at +1. Here I added a rectangular +x and a rectangular -x. This wasn't quite enough to fill it in.

I added one more zero pair of x tiles and our rectangle is complete!

2x2 + x - 3 factors to (x - 1)(2x + 3).

I had gotten this set of algebra tiles secondhand on Ebay. If you don't have a set, you can print this free set of printable algebra tiles.

Related posts:

Cereal Factoring

Fun with Quadratics

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This is a bit embarrassing, but because I try my best to swallow my pride and embrace growth mindset, I'm fessing up. It was during my first year teaching that I finally realized what a2 + b2 = c2 really meant. 

To be fair, I was teaching algebra and biology and hadn't seen the inside of a geometry book since high school. Geometry students' Pythagorean Theorem projects were hanging on a bulletin board in the hall and when I stopped to look at them, suddenly it all became clear. 

Pythagorean Theorem water proof

If only there had been GIFs when I was in high school!

Back in 2004 Teachergram wasn't yet a thing. If it was, I'm sure things would have been different. These days with social media, the ideas are constantly flying, making us all better teachers. And learners!

Through social media, blogging and TpT, I've also made some good math teacher friends (who I lovingly refer to as my "math friends") and in this post I want to share some of their fun Pythagorean Theorem activities.

If proving the Pythagorean Theorem had been a thing when I was in 8th grade math, maybe my first year of teaching wouldn't have been so... eye-opening. Amanda from Free to Discover made this Pythagorean Theorem Proof Discovery Worksheet to prove the theorem.

Kara from Learning Made Radical has been making these great math bookmark notes that I can just imagine kids referring to late at night while doing homework. She made this set of Pythagorean Theorem Bookmark Notes

It's hard for me to believe that I've made over 100 math pennants. 

Of all of them, this Pythagorean Theorem Math Pennant was one of the most difficult to make because of all of the graphics. Students find missing side lengths of the inner right triangles, areas and perimeters. 

Kara from Learning Made Radial and I have been collaborating on partner scavenger hunt activities that get students working together on their math. 

I had a senior a few years ago who had a boyfriend who she never spoke to face-to-face. This got me thinking about kids and how they need time during their day for meaningful conversation. Kara made this Pythagorean Theorem Partner Scavenger Hunt activity.

Kara also made this fun Pythagorean Theorem Hole Punch Game

Karrie from Mrs. E Teaches Math made this Pythagorean Theorem Word Problem Coloring Sheet

Alex from Middle School Math Man and I have been collaborating on a new math game series called Voyage to the Treasure!

In these new math games, students are on the same team, working through math problems as they try to beat the Math Monster to the treasure. The one above is Voyage to the Treasure! Pythagorean Theorem.

Mel from Secondary Math Shop made this Pythagorean Theorem Cut, Paste, Solve and Match puzzle where students set up and solve Pythagorean Theorem problems. 

Hayley from Activity After Math made this Pythagorean Theorem Color By Number activity where students find a missing leg, hypotenuse, converse or the distance between two points. 

Hayley also made this set of Pythagorean Theorem Task Cards with QR codes. 

Karrie wrote a great post called The Pythagorean Theorem Without Words over on her blog. The image above from her post is Perigal's Puzzle. 

Karrie also pulled together a list of her favorite Pythagorean Theorem resources in her post 7 Ideas for Teaching the Pythagorean Theorem.

teorema de pitágoras - YouTube

If you have Geometry students who speak Spanish, this wordless Pythagorean Theorem proof has some funny outtakes at the end! Actually, they're even funny if you don't speak Spanish. 

Lastly, I made this Pythagorean Theorem math word wall reference so that students won't find themselves in my position at 28 years old! I usually do not duplicate references between math word walls, but I did add this one to both 8th Grade and Geometry.

I hope you are having a wonderful year!

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