## 35+ Ideas and Tips for Teaching Integers

Operations with integers is such an important concept for students to master.  While integers are used often in everyday life, adding and subtracting integers can be a challenge for students.  When I teach a tough topic, I try to collect as many different ideas as I can, so that I have lots of options if my students start to struggle.  Having lots of ideas for teaching integers can help keep things fresh for you too!

So...  Here are more than 35 (THIRTY FIVE) ideas and tips for teaching integers.  Hang on to your hat, because this post is a BEAST!  :)

## Introducing Integers

What is an Integer? - This is a well-done video by kids.  They give lots of explanations with diagrams too.

Where's the Third Wheel? or Introduction to Positive and Negative Numbers - This blog post explains how to use counters to make zero pairs.

Ordering Integers Math Pennant Activity - This activity is a great way for students to practice ordering integers and it makes a cute classroom display.

Discuss Integers in Their Natural Habitat - Students have encountered integers in their daily lives.  Have students list as many different real-life examples of integers as they can.  Checking accounts, the stock market, basement floors in a building, temperatures, there are so many integers in real life!

Integers Song: Learning About Positive or Negative Whole Numbers - This song is a little cheesy, but it gives lots of real-life applications for integers. It's two minutes well spent.

Integers Song: With Introduction to Absolute Value - This is a cute little video by Numberock.

Adding and Subtracting Rational Numbers Foldable - This foldable and practice sheet is great for helping students organize information about adding and subtracting rational numbers.

Teaching Adding and Subtracting Integers - Tile spacers are a great manipulative to help students make zero pairs.  This blog post explains how to help students understand the concept.

Have a Funeral for Subtraction - Subtraction of integers, by definition, is adding the opposite.  @mathwithmeaning had a funeral for subtraction and had her students rewrite subtraction problems as addition.  Having students write their own problems could get funny!

Integers: Addition and Subtraction Square Puzzle - This square puzzle is a fun way to have students practice.  I like to use it as a warmup or as an activity for centers.  I featured it on my instagram account @mrseteachesmath.

Use Money Examples - Integers can feel like an abstract concept for some kids.  However, if you explain adding and subtracting integers using money, it can help!  For example, "Johnny owes me \$5.  He paid me \$3.  How much does he still owe me?"

Integer Operations Graphic Organizer - This free graphic organizer is an awesome visual for students to "see" the rules for adding and subtracting integers.  It would be great in an interactive notebook too!

Adding Integers Square Dance Match Game - This free puzzle is a fun way for students to practice adding integers.

Adding and Subtracting Rational Numbers Mini Unit - These interactive notebook pages are a great way for students to take notes while learning about integers.

Have Students Write a Comic Strip - Sometimes students just need to let loose a little.  Writing a comic strip can be a fun way to demonstrate their understanding!  @thesmartpug has an adorable comic strip!

Adding and Subtracting Integers Puzzle - If you're in the mood to break out the scissors and glue, this cut and paste puzzle is a great way for students to practice.

Adding and Subtracting Integers - If you want to use snap cubes to help your students with addition and subtraction of integers, but you're unsure how to introduce them, this video is perfect.  Here, a teacher explains how to use them to teach your students.

Integer Operations Battle My Math Ship Activity - In this partner game, students play Battleship.  This would be a fun sub day activity!

A Manipulative for Integer Operations - This blog post explains how to use a number line to help students decide the sign of the answer when adding and subtracting integers.

Use Snap Cubes to Play Games - @doyouevenmath played a fun game with snap cubes to practice integers.

Math Antics - Adding and Subtracting Integers - If you will be having a substitute or use a flipped classroom, this video lesson is a good option!

Adding and Subtracting Integers Partner Scavenger Hunt - This cut and paste partner activity is a fun way for students to practice, with a twist.

Integer Rules Visuals - Sometimes kids need to SEE which number is bigger in order to choose the correct sign when adding and subtracting.  This blog post gives a great visual.  @colorado_math_teacher used this same technique to write notes for her students.

## Multiplying and Dividing Integers

Multiplying and Dividing Rational Numbers Foldable - This foldable and practice sheet is great for helping students organize information about multiplying and dividing rational numbers.

Negative Number Multiplication Bingo - This is a math bingo game that involves multiplying and dividing negative numbers.

Multiplying Negative Numbers by Negative Numbers Animation - This is a simple number line animation that helps explain multiplying two negative numbers.  It reinforces a pattern.

Multiplying and Dividing Integers Puzzle - This is a great activity to use in stations, as a small group activity, or as an individual activity!

Multiplying and Dividing Rational Numbers Foldable - These two lessons are great in an interactive notebook!

## Mixed Integer Operations

Positive and Negative Integer Rules Lesson for INBs - I love this interactive notebook page as a review for positive and negative numbers!  It's pretty and can easily be adapted for all skill levels.

Operations with Integers Differentiated Notes and Practice -  If interactive notebooks aren't your thing, this complete lesson is perfect.  I love when things are already differentiated for me!

Integer War - Have students play War, but instead of playing one against one, they play in teams of two.  Instead of the biggest individual card winning, the largest team sum wins.  You could also change this to be subtraction, multiplication, or division.  Red cards are negative, black cards are positive, and you can choose the numerical value of the face cards.  @ms.lyonsclass enjoyed playing too!

Magical Math Solve and Color - This unicorn is adorable!  Students can practice integer operations while coloring a picture.

Operations on Integers Coloring Activity - This is a coloring activity that easily fits into an interactive notebook.  The emphasis is on the math, which is always nice :)

Reviewing Integers - This blog post is a great explanation of how to effectively review integers with students that have a basic understanding.

Integer Operations Solve and Snip Interactive Word Problems - On this worksheet students will show their work and cut out the correct answer.

Integer War - Order of Operations - This fun game combines the game of War with the order of operations.

## Polynomial Division INB Pages

Dividing polynomials usually overwhelms my Algebra 2 students at first.  So over the years, I've found that teaching it over two days helps SO MUCH.  I always teach polynomial long division on the first day and synthetic division on the second day.

As the warmup, I write a couple of fourth-grade style long division problems on the board.  After the initial freak out, I typically have a few students that remember the process that step up and help the class.

This was the first year that I taught this lesson using interactive notebooks.  I thought about creating a fancy foldable for this topic, but I really thought that just going through the algorithm a couple of times would be enough to help everyone catch on.

I created a hamburger book for polynomial long division.  It started with dividing a polynomial by a monomial.  There are additional problems inside the hamburger book.

Then the next day, we worked on synthetic division.  My kids usually have a brain explode moment when I do the first problem.  This year I made them put their pencils down and just WATCH me do the first one.  They seemed to catch on quicker.  I also used a hamburger book for this lesson.

Dividing Polynomials: Long Division Hamburger Book
Dividing Polynomials: Synthetic Division Hamburger Book

## 7 Ideas for Teaching Congruent Triangles

Congruent triangles is one of my favorite units to teach.  I love using activities that help students practice with congruent triangles and proofs.  There are some awesome resources for teaching triangle congruence and you don't even need worksheets!  Here are my 7 favorite ideas and tips for a triangle congruence unit.

### Teaching Congruent Triangles Tips

1.  Use Foldables - This congruent triangles foldable is so helpful for my students to refer to throughout the unit.  It keeps all of the information in one location so that it's quick and easy for them.  I love interactive notebook pages for congruent triangles!

2.  Use Cut and Paste Activities - Anytime students can physically manipulate items they will be more engaged (and retain more!).  I love using cut and paste activities because students are more likely to jump in and not be afraid to make a mistake.  If you want to have students work in groups, this cut and paste sorting activity is fun to have students do on a giant poster.  My proofs cut and paste activities are a great way for students to practice proofs without pressure.

3.  Use Videos to Illustrate - Using videos can be a good way to engage some students and can help break up long class periods in a productive way.  They're also a great activity for a sub day!  This video is a nice explanation of all of the triangle congruence theorems.  This video does a great job of explaining the SSA false shortcut.  WARNING:  It is incredibly boring. (I still show it every year.)

4.  Use Task Cards and Digital Activities - Students need sooo much practice with congruent triangles.  I like to use task cards to practice the triangle congruence theorems and task cards to practice triangle congruence proofs.  If students have access to technology, it can be fun to give them a digital activity too.  This digital activity practices congruent triangles proofs.

5.  Require Students to Mark Diagrams - For a lot of my students, getting them to mark their diagrams is like pulling teeth.  However, students that mark them always seem to do better on tests and quizzes.  I wonder if there is a correlation there...  For congruent triangles, I have my students mark the diagram, but also mark A or S, depending on if it is a side or angle that is congruent.  I find that actually writing it out helps them eventually determine the correct triangle congruence shortcut.

6.  Have Students Practice What ISN'T Needed - Once students have a pretty good grasp on the shortcuts, it's good to give them information and have them determine what isn't needed.  I like to use this extra information activity so students can work together and sort the cards into the correct categories.

7.  Have Students Re-Draw Overlapping Triangles - Many students struggle visualizing overlapping triangles.  If they re-draw the diagrams, they usually do better.  This activity can help students see the different common types of overlapping triangles.

I hope these ideas help in your next congruent triangles unit.  It's one of my favorites in geometry!

## 3 Must-Have Classroom Supplies for Every Teacher

When I first started teaching I bought cheap supplies for my classroom, because that is what I could afford.  However, I ended up spending more money over time because I had to replace the items so often.  If you're on a budget (What teacher isn't?), then it's a good idea to buy quality classroom supplies from the beginning.  Here are three must-have classroom supplies that every teacher needs!

This post contains affiliate links.  That means that, at no cost to you, I make a small commission from these links.  However, I would never recommend a product that I don't believe in.  You deserve the best when you spend your hard-earned money!

### A Good 3-Hole Punch

It drives me nuts when my 3-hole punch jams.  It always seems to happen when I'm in a hurry and then I end up with a stack of papers that are going to be ripped out.  It also drives me nuts when I don't get the paper in evenly and I end up punching the edge of the paper.  That's why it's important to me to have a good 3-hole punch!

As a teacher, you need a heavy-duty hole punch that will easily punch through a class set of papers without eating any.  This hole punch is sturdy enough, that I even let my students use it.  It's definitely a place where I would spend a little extra money on quality.

### A Quality Pencil Sharpener

Recently, Classroom Friendly Supplies sent me one of their pencil sharpeners to try.  I was so impressed!  I usually go through at least one electric pencil sharpener every school year.  Students are so hard on them and don't treat them right.

The pencil sharpener from Classroom Friendly Supplies could certainly hold up against classroom use!  The face of the sharpener pulls away, which prevents pencils from being "oversharpened".

Since it's a hand crank sharpener, I don't have to worry about the motor getting gummed up from colored pencils (which always ruined my electric pencil sharpeners!).  The sharpener works better than I was expecting and it's actually quiet.  I could continue to teach a lesson while a student is sharpening their pencil.  We all know that normally doesn't happen!

It's definitely worth the cost, especially since the company sells replacement parts.  If something breaks, you can buy a new part instead of buying a whole new pencil sharpener.  I was sent a nice blue color, but there are tons of color options to match your classroom decor.

### A Heavy-Duty Stapler

If you're going to be in a classroom, you need a decent stapler.  I usually allow my students to use cheaper staplers.  I've even found some at garage sales.  So many students slam on the stapler and jam it, that I don't want them to use mine.

However, you need a nice stapler for yourself.  I really like this heavy duty stapler.  It staples 40 pages at a time (most staplers only do 25) and is a low force stapler.  If you're going to staple a bunch of student packets or paperwork, it's nice to have a low impact stapler.  This particular stapler has lasted me years and is still going strong.

Check out: 15 Items Every Teacher Needs for Back to School and my Top 5 Classroom Supplies for Secondary Teachers

What supplies do you think are needed in every classroom?  Let me know in the comments!

This blog post was sponsored by Classroom Friendly Supplies.

## Top 5 Classroom Supplies for Secondary Teachers

I get asked all the time for my product recommendations for math teachers.  I've tried many different items over the years and I can't tell you how many things I've thrown away because they've just stopped working.  No one wants to buy something that's poor quality, only to have to replace it halfway through the school year!

Some of these links are affiliate links.  That means I earn a small commission that I use to keep this blog running.  However, I only recommend products that I truly believe in and all the opinions are my own.

Markerboards
I love using markerboards for students to practice.  They erase easily and students like using them.  My FAVORITE marker boards are by The Markerboard People.  They are double sided and last forever.

My two-year-old son even colored on one with Sharpie and I was able to get it off without staining or ruining the board.  Seriously.  They have boards with coordinate grids and unit circle and polar grids printed on them too!  Also, check out their markers and mini-erasers.  They are just as high quality as the boards.

Pencil Sharpener
You need a good pencil sharpener.  A lot of the electric ones just eat pencils.  I hate when I give a kid a pencil, they sharpen it, and half of the pencil is gone.  This pencil sharpener is a hand sharpener, but it is quiet and doesn't eat pencils.   It lasts forever too.

Page Protectors
With so many schools putting teachers on a paper budget, you need a way to save paper.  You can make class sets, slip them into the page protectors, and still let students write on them.  There are a bunch of cheap ones out there, but they get kind of nasty over time.  It's nice to just start with a quality set that won't get grubby.  I like the ones from hand2mind.

Playing Cards, Dice, and Poker Chips
It's nice to have some playing cards and dice on hand to use as manuplitaves or for games.  I know you can find them at the dollar store, but I don't always see them there.  This playing card set on Amazon is nice because it comes with some poker chips and dice.  I also like this dice set from hand2mind.

Timer
You need a good, cheap timer so you can break up your class period.  I also need help remembering how long I've let students work with partners.  You can use your phone, but I don't like to have my phone out in front of students, because I don't want it to get misplaced or stolen.  I really like this timer because it's magnetic and I can put it on my whiteboard.

What else do you LOVE for your classroom?

## Parallel and Perpendicular Lines INB Pages for Algebra 2

My Algebra 2 students see equations of parallel and perpendicular lines in Geometry, but it always seems like they need a refresher at the beginning of the school year.  In Geometry, I've used a discovery lesson and activity and I've also used foldables to teach the lesson.  Since I loop with my kids, I wanted to do something different and not just re-use the same lesson.

I made a flipbook that reviewed the slopes of parallel and perpendicular lines and then had them practice writing equations.  The problems in the flipbook were quick for us to work through because they had seen the material before.  This flipbook is available in the exclusive content area of my Geometry Foldable Bundle and my Algebra Foldable Bundle.

Then, I gave them four practice problems to work on with their partners.

After this, my students felt very confident to start their homework.  One day is all it took!

## Using Songs and Chants to Teach Math

We all know that using little songs helps to memorize.  I mean, can you forget the alphabet after learning the song?  I love using songs and chants to help my students remember different properties and theorems in math.  Check out these videos that show some of the songs and chants that I use with my students!

## Beginning Factoring INB Pages

When I teach factoring, I spend quite a bit of time practicing factoring out the GCF.  I actually spend an entire class period.  If students can't easily recognize the GCF, then they will struggle with factoring polynomials for the entire unit.

First, I used this interactive notebook page to explain finding the GCF and have students practice.  It's very helpful for students to use two different colors to list the factors and circle the common factors.  My students tend to kind of get things mixed up if they don't.

Next, I used this page to help students practice going between factored and distributed form.  I got the idea from Math=Love.  This was difficult for my students.  The most difficult part for them was deciding if the expression was factored or not.  Once we got going, they had a much easier time factoring the expressions.

This lesson takes longer than you would think!  I spend lots of time making sure students can list and find the GCF.

## Solving Rational Equations INB Pages

I really like rational expressions.  Once you can factor, they're easy.  I didn't make a whole bunch of fancy foldables for my rational equations lesson, partly because I was end of the year teacher-tired and partly because I didn't think it was necessary.  Yes, sometimes I do just have students write in their notebooks!

These are the notes I used for my students.  I only did these four problems and then had them start on their homework.  They appreciated having extra time to work on homework.  Semi-interesting note: my students strongly preferred method 2.

Check out Graphing Rational Functions

## 8 Ideas for Teaching Order of Operations

Order of operations is an important concept for students to master before progressing in algebra.  However, students struggle with it and need LOTS of practice. We've all run across the social media posts with the order of operations and seen all of the incorrect answers!

Here are 11 ideas for your next order of operations lesson!

1 - Choose an acronym.  Not everyone agrees on the common PEMDAS acronym.  Some teachers think that PEMDAS reinforces the misunderstanding that multiplication must ALWAYS go before division.  If that acronym doesn't work for you, this blog post may help you find something you like better.

2 - Use a foldable for your class notes.  I love foldables and I've seen them keep students attention better than traditional notes.  These foldables would be great in your student's interactive notebook!  This foldable would be perfect for pre-algebra students and this one is great for algebra students.

3 - Have students practice with a cooperative activity.  Sum 'em activities are AWESOME at getting kids to work together.  I normally have them work in groups of four.  This sum 'em activity for the order of operations is perfect for students that are ready for a little challenge.  If you want to have students work in partners, this clock partner scavenger hunt is great!

4 - Let students work on a puzzle.  I love having students work on puzzles and card sorts at the beginning of class as a warmup.  Students can get settled in class as they are working on the puzzle.  This order of operations puzzle is perfect for students to work on in small groups.

5 - Have students complete an individual activity.  This free order of operations ladder activity is nice for students to work on individually or with a partner.  The squares match together like dominos, so students can check their work without constantly asking "Is this right?".

6 - Decorate your room with the order of operations.  I love a decorated classroom, even in high school!  This blog post has an awesome, free order of operations mobile that just may match your word wall.  If you want to have students help, in this activity students "text" the steps of a problem to a partner.  Then, you can hang the final product on the wall.

7 - Show students a video.  So, this video is SUPER corny, but I totally love it!  It's a rap that explains the order of operations in a clear, concise way.  Hopefully, it gets stuck in your student's heads!

8 - Have students practice in a fun way.  Remember those social media posts that people always mess up?  Well, you can have students practice on those social media posts!  I really like the number sentences that are pictures, like the ones in these emoji task cards.

Do you have something special that you like to do when you teach order of operations?

## Angles and Arcs in Circles INB Pages

I never have time to post my INB pages during the school year!  Today, I want to share the pages that I made for the beginning of my circles unit.

This was the first lesson in my circles unit, so I needed to introduce some vocabulary first.  I gave my students a fill-in-the-blank page with diagrams so that we could discuss the vocabulary as we went.

After that, we talked about arc measures, the Arc Addition Postulate, and congruent angles and arcs.  I compiled it all into one foldable.

I included the explanations on the front of the foldable so that I would have room for examples inside.  Inside each flap, we did two examples together and I had them work two examples with their partners.  This foldable went pretty fast as we worked through it together in class.  Most of my students thought this lesson was pretty easy since I didn't include much algebra in it.

After the foldable, I worked this spherical problem with my honors students.  They were shocked that I was "bringing back trig".  The fact that the radius of the sphere could be drawn to different points blew their minds at first.  I really liked this problem and included it on their test with different numbers.

You can find this foldable here, in my Teachers pay Teachers store.