Solving equations visually using cut paper algebra tiles

Short videos showing how to use cut paper algebra tiles to visually solve middle school math 1-step and 2-step equations, even when x is a fraction or the coefficient of x is negative.

Algebra tiles help make math visual for students, and paper algebra tiles take it a step further because we can cut them into fractions. In this post are a few short cut paper algebra tiles videos for solving 1-step and 2-step equations that include when x is a fraction.



This first equation is a simple 1-step equation where x is being divided by 4.

 


Next up is another 1-step equation where the coefficient of x is a negative fraction. 



In this 1-step video, x ends up being a fraction. We can show this by cutting the tiles to evenly distribute it.



Last is a 2-step equation where x is a fraction and the coefficient of x is negative.


There are more algebra tiles videos to see in this algebra tiles YouTube playlist.



More algebra tiles posts and resources:


Factoring with algebra tiles (free digital algebra tiles)


Solving equations with algebra tiles


Multiply polynomials with algebra tiles


Middle school math algebra tiles tutorial video (long version)



Algebra tiles resources pack
Algebra tiles resources pack




4 Editable New Year's Math Review Coloring Activities

Editable math reviews for 6th grade math, 7th grade math, 8th grade math and algebra 1


Happy New Year 2026! If you're looking for a midyear review for your middle school 6th grade, 7th grade, 8th grade or algebra 1 students, there are 4 editable math review activities updated for 2026 linked below. Each comes with 20 review questions and a 2026 coloring sheet, and will be updated every year. The math reviews can be used to refresh skills or as semester 1 review when students come back from winter break. 


Each of the 4 math reviews comes with a 2026 coloring page and an editable 2-page worksheet with topics covered between back to school and the new year. 






Topics include:
  • Multiplying binomials 
  • Factoring quadratic trinomials 
  • Finding parallel and perpendicular lines through given points
  • Calculating slope and y-intercept from a table 
  • Converting standard form equations to slope-intercept form 
  • Identifying domain and range of graphs

This algebra activity is editable in PowerPoint and includes 20 questions. 




Students answer the questions on their worksheets, then color their 2026 based on the key. An answer key is included.







Topics include:

Domain and Range Finder Tools


Do your students struggle finding domain and range of graphs? I made a couple printable domain and range tools to help our students this year.



There are directions pointing students to look at x for domain and y for range as they drag each tool across the graphs. There are also directions printed on the tool for what to record for domain and range when a graph has an arrow.




We have always used rulers to find where graphs start and stop, but I wanted something a bit more self-teaching for our students this year. The graph cards in the photo are a free download on my blog here.


You can find the domain and range finder tools here on my website.



I also made a new domain and range of graphs cheat sheet for our students that you can find here in my drive.




UPDATE: A 3rd tool for finding increasing/decreasing intervals of graphs has been added to the file linked below.


> Browse all domain and range activities


Domain & Range Finder Tools


Winter math activities and classroom décor


Printable and digital winter math activities for middle school

We're getting so close to winter break! In this post, there is a collection of winter-themed math activities that hit the standards while keeping students engaged in learning their math before and after winter break. Many of the activities below were made to double as colorful winter math bulletin board displays of student work.


Students review finding slope from a table in this winter snowflake activity. Student work then becomes a festive winter-themed math bulletin board display
Slope winter snowflake activity

The first activity is a slope winter snowflake activity where students find the slopes of lines given a table, then decorate your classroom with their finished snowflakes. Anna L's students called their slope snowflakes "slope flakes" as they worked on the slope review activity coming back from winter break.


multiplication ornaments

These multiplication ornaments make a festive math bulletin board display of student work. Students can decorate their ornaments with bows and holly after calculating their products. There are 4 blanks also included for your own multiplication problems.


Students review proportional relationships in this snowflake pennant activity that becomes a winter math bulletin board display
Winter proportional relationships snowflakes

There's a similar set of winter proportional relationships snowflakes for younger students. students plot coordinates of proportional relationships, then determine the equation of each snowflake's line. 


Students solve 2-step equations, then color their winter snowflake based on the colors in the key.
Winter snowflake 2-step equations

If your students are solving 2-step equations this winter, they can practice their solving on this winter snowflake 2-step equations sheet. After solving, students will need to read the inequalities in the key to figure out which color to color each section of their snowflake.


Students calculate the slopes between cute cartoon animals in quadrant 1 of the coordinate plane in this slope review activity
Slopes between winter animal pictures

This winter slope activity has students calculating the slopes between winter animal pictures in the coordinate plane. The x-axis is in months, and the y-axis is in days of the month. It's a fun, low-stress way to review slope.


Students calculate decimal multiplication problems on black and white mittens that they can color and hang to make a winter math bulletin board display
Multiplying decimals mittens

If your students need practice multiplying decimals, these multiplying decimals mittens make a colorful winter bulletin board display of student work.


Christmas Multiplication Ornaments Winter Holiday Math Activity
Multiplication ornaments activity

This set or Christmas multiplication ornaments have students multiplying multi-digit numbers that then become winter classroom décor. The multiplication problems include: 2x2 digit, 2x3 digit, 1x4 digit, and 2x5 digit. There are a bunch more Christmas math activities here for middle school, high school and elementary school math topics.


This the digital version of puzzle #2 in a winter picture puzzles math escape room game. Students love these highly-engaging math activities because they are self-checking.
Winter picture puzzles math escape room

For a digital activity, this winter picture puzzles escape room has students solving for the values of winter pictures before going on to the next puzzle. 


Printable PDF version of a winter math escape room
Winter picture puzzles math escape room


The escape room is self-checking in Google Forms, and also comes as a printable PDF for days off devices. 


Editable New Year's math review

This is year #2 of updating this editable New Year's math review. There are versions for 7th grade math, 8th grade math, and algebra, and will be updated every year. They're each editable in PowerPoint so that you can customize the activity to your students' needs.


You can browse all winter math activities here: winter math




Free Discriminant Cheat Sheet for your Quadratic Formula Unit

free printable discriminant cheat sheet to help students make connections between the discriminant's value in the Quadratic Formula and the number of real solutions their quadratic equation will have.

In this post, I want to share a few resources for teaching the discriminant as part of a Quadratic Formula unit. 


This simple discriminant cheat sheet helps students make the connection between the value of the Quadratic Formula's discriminant and the number of real solutions the equation will have. It also shows examples of graphs with 1, 2, and 0 zeros and what the discriminant will look like in each case.



Counting the number of negative signs under the radical in the Quadratic Formula helps cut down on sign errors when evaluating the discriminant


SIX SEVEN! Real Number System Math Sorting Activity


If you're a middle school teacher, I'm sure you've been hearing "Six Seven!" nonstop this year!  


We hadn't heard it in our algebra 2 class until about a month ago, when the 67 floodgates finally opened and now "67!" is an almost daily occurrence. It came up recently when solving x^2 - x = 42 (though this was on purpose).


As math teacher Ms. Campbell wrote, "Truth be told, it's the least offensive tiktok trend in years (at least for me!) And math teachers sure can have fun with it." Very true. And it's nice that math finally made it into a trend!



Six Seven Number Sort


This SIX SEVEN real number system sorting activity has students sorting numbers made of up of sixes and sevens into whole numbers, integers, rational numbers and irrational numbers categories. The activity includes the sorting mat, 18 numbers to sort, and a key.



Free Perfect Squares and imaginary numbers sheet


 

This past week, we started learning about imaginary numbers in algebra 2, which will lead into solving with the Quadratic Formula. I made this simple cheat sheet for the students so they can quickly check if a number is a perfect square and be reminded of how imaginary numbers work when simplifying and multiplying.