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.

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Domain & Range Finder Tools

2 free factoring quadratic trinomial cheat sheets

What's your favorite method for factoring quadratic trinomials? For me, it's the AC method with grouping because there's no guess and check, which frustrated me as a high school student. I remember endlessly erasing my work, and settling with "close enough" on some problems. The box, or area, method has grown on me over the years, especially how it links back to multiplying polynomials.

The structure of the AC method works for me, and is the method I have used most when teaching students to factor. I don't know when I learned it, but I remember thinking that it would have been a helpful tool for me in high school. If making the list of factors is difficult, students can divide AC with 2, 3, 4, ... with a calculator and write down any quotients without decimals, checking which factor pair adds to B.

I made a couple factoring quadratics cheat sheets and posted them on Facebook this week.

We're getting to factoring in a few weeks after imaginary number operations, Quadratic Formula and solving with square roots and we're going to teach the kids the box (area) method, which they may have seen in algebra 1. AC with grouping will be the backup plan for students who aren't clicking with the box method. Multiplication charts will also be available to students who need them.

Box method factoring

AC method with grouping

If you are teaching factoring this year, I wanted to share the two cheat sheets above in case you find them helpful. I also wanted to mention that the cheat sheets I share are never intended to be standalone teaching tools. They always go along with lessons as a way to help students through independent work. This was something that came up this week, too. 

> Browse all Quadratics activities

You can download the two factoring cheat sheets here from my Google Drive.

free math resource library

 

Function Composition Cheat Sheet

We've been working on composition of functions in algebra 2 the last couple weeks, and some students are still having a hard time with composing functions shown in graphs and equations. We're also seeing a few students looking at the y column in tables when evaluating functions shown in tables.

There are a bunch of free math cheat sheets on my blog here, and I wanted to add another one for composing functions.

How to Make Any Math Word Problem Solvable for Students

Solving math word problems is tricky for students whether they are in 3rd grade using multiplication, in middle school solving ratios, or in high school working through quadratic word problems. If you're looking to support students through solving word problems, this math bulletin board set is a guide to solving any math word problem students will see throughout school.

The bulletin board posters are written in simple language so that all students can access the information and outline five steps in the solving process. 

1: UNDERSTANDING 

This step asks students if they understand what is being asked of them to solve and if they understand all of the vocabulary in the word problem. 

2: PROCESSING 

This step asks students if they are able to restate the problem in their own words, if they can draw a picture, if they can make an easier example, and if it's possible to add their own name into the word problem. This always seems to make word problems easier! 

3: PLANNING 

In this step, students make a plan to solve their word problem. Strategies include writing an equation, using reasoning, making a list, finding a pattern, etc. 

4: SOLVING 

Students always want to jump to solving, so they'll begin to see that solving can only come after a plan has been put in place. This step asks students to go ahead with their plan, and if their plan fails to try a new plan. Most important is staying persistent. 

5: LOOKING AHEAD 

This final step asks students to think ahead to when they might see a similar problem and to consider what approach might be best then. 

You can find this math word problems bulletin board set here.

Math Word Problems Bulletin Board

> Browse word problem activities.

More posts:

Math Classroom Decoration Ideas

Math Word Walls

Consumer Math Curriculum Warm-Ups 18 Units of Financial Literacy Bell Ringers

Do you start math class with a warm-up or a bell ringer? My classes started going more smoothly once I got my warm-up routine down. 

Our classroom routine: 

Students enter our classroom and grab a warm-up out of the basket at the front of the classroom. The warm-ups were either a 1/2-sheet or 1/4-sheet of paper and would get glued into their interactive notebooks or on binder paper. Students get time to work on their warm-up independently before we go over the answers together to make sure we were all on the same page.

Sometimes if students weren't focused, I'd switch gears and collect the warm-ups for points. This kept students on their toes. I'd only ever do this when the warm-up was a spiral review of material students had recently learned. This was usually the case with our warm-ups-- they'd be a short review of previous material before moving on to learn new math concepts.

I put together an 18-unit pack of consumer math warm-ups to get students thinking about real-world math as soon as they sit down for class. There are at least 6 warm-ups included for each curriculum unit listed below, along with answer keys:

18 units of consumer math warm-ups: 

• Wants vs. needs 
• Checks and registers 
• Wages and salary 
• Bank accounts 
• Budgets 
• Electronic banking and credit cards 
• Credit score 
• Discounts and coupons 
• Sales tax and tip 
• Percent change 
• Unit price 
• Income taxes 
• Car loans 
• Mortgages 
• Student loans 
• Investing 
• Car insurance 
• Health insurance

The warm-ups are all sized to be cut and pasted into an interactive math notebook. Students answer their warm-ups on their notebook paper, discuss with each other and report out on their answers to create a classroom discussion. These are the same warm-ups included in the Scaffolded Consumer Math Curriculum.

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First Week of School in the Math Classroom

Do you have any math activities planned for the first day of school? In this post are a few back to school math activity ideas and classroom resources to help students ease into the new school year.

Editable Back to School Desk Plate

Students get to know each other through numbers with this back to school math desk plate activity. Students answer 10 questions about themselves that are all answered with numbers. The questions are ell editable, so you can change them to match what you'd like to know about students at the beginning of the school year.

Golden Spiral Back to School Math Pennant

Students color the different sections of their back to school math pennants based on their answers to questions like "favorite class?" and "birth month?" When all colored in, the final pennants make colorful math classroom décor that can be displayed for back to school night.

Back to School Picture Puzzles Escape Room

Braking free from this math picture puzzles escape room is a fun way for students to get to know each other while working together on the first day of school. To move to each next puzzle, students have to solve for the values of school-themes pictures and type the correct 4-letter code.

Back to School Picture Puzzles Escape Room

Graphing algebraic function transformations with cut paper videos

In this post are a bunch of function transformations videos showing how vertex form functions all transform using the same pattern. The way that functions transform in the coordinate plane can feel pretty abstract to algebra 2 students just learning about nonlinear functions. But every algebraic function in vertex form transforms the exact same way.

Functions can translate vertically and horizontally, and even reflect over the x and y axes just like geometric shapes. The one quirk is that horizontal transformations feel opposite from expected. 

Why are horizontal transformations opposite? It feels backwards for the vertex of y = |x - 3| to translate right 3 units. With all horizontal shifts, we're looking for the value of x that will "zero out" the inside expression. For x - 3 = 0, x would need to be 3. With x gone, we can find the function's lowest or highest y value, i.e. the vertex's y value.

Here is how we can find the horizontal transformation of a quadratic function in vertex form and why the inside shift is opposite. 

function transformations cheat sheet

This function transformations cheat sheet in my Google Drive has graphics from an algebra 2 word wall for absolute value, quadratic and square root graphs. There's also a free set of dancing skeleton functions posters here.

Below are a bunch of function transformation video shorts using cut paper. In each video you'll see familiar nonlinear algebraic functions transformed in the coordinate plane. 

9 Math Classroom Setup Ideas and Must-Haves

What are your absolute must-haves in your math classroom? This past year, I worked at my former high school as an MCAS tutor to help kids graduate. The MCAS is the Massachusetts state test that students needed to pass in order to receive a high school diploma. The requirement was in place for around 20 years, and was finally eliminated in November 2024.

No one really believed we'd finally end this mandate, so when it was voted out we were all surprised. Since my students would now be receiving their diplomas (if they pass all of their required classes), I finished out the year as a support teacher.

Next year, I'll be back at the same school co-teaching algebra 2 as the special educator. I love teaching algebra 2, which I've written a lot about here. There's something really special about the amount of growth kids make in this course.

End of the Year Math Activities

It's hard to believe it's almost the end of the school year! In this post, I want to share a few end of the year math activities to keep students engaged in these last days of school (and also having some fun). 

The first is a new end of the year math escape room that comes in both digital and print form. Students use their logic to solve for the values of summer-themed pictures in equations while celebrating making it to summer break.

End of the School Year Math Escape Room

Free Slope Word Cloud Classroom Poster

There are so many different ways to express slope. From constant of proportionality to rate of change to unit rate. I wanted to make a poster to help students make connections between all of the different ways they will see slope described as they move from middle school to high school.

The poster includes the math vocabulary:

• Slope
• Rise/run
• Rate of change
• Gradient
• Delta Y over delta X
• Constant of proportionality
• Speed
• Unit rate
• m=
• k=

There's a color version (shown above), and also a black and white version, if you'd rather your own color scheme. 

The poster is a free download here in my TPT: Slope Word Cloud Poster

If you'd like to enlarge it or any other PDF on your home or school printer, there are simple directions for enlarging any PDF here.

Fun Slope Activity Ideas

Inverse Operations Classroom Poster

Here's a super simple poster to help students remember inverse operations when solving equations in algebra. There are 4 variations of the poster so that you can use the one that matches your curriculum's notation.

Spring Logic Picture Puzzles Digital Math Escape Room

I just finished working on a new spring math picture puzzles escape room that comes as a no-prep, self-checking Google Form and as a printable PDF. 

This math escape room is a perfect spring-themed math activity that requires no prep and no grading. Students can't move to the next puzzle until successfully entering a puzzle's 4-letter code, so you will know who did -- and who didn't -- break out!

Students add, subtract, multiply and divide to figure out the values of spring pictures. It's a fun brain break, filler activity for after testing, PEMDAS review, or can be left with a sub on a day you won't be at school.

An answer sheet and graphic organizer are included to help students keep track of each picture's value. An answer key is also included. 

Spring Math Picture Puzzles Escape Room

You can find the spring math escape room here:  Spring math picture puzzles escape room 

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Katherine Johnson Color-By-Number Math Activity (free)

Mathematician Katherine Johnson was a trailblazing NASA scientist back in the 1950s and 60s. Her work was so important that after NASA started using computers in the late 1950s, astronaut John Glenn refused to fly on his 1962 orbit around the Earth until Johnson checked the computer's calculations by hand. She was invaluable to NASA and to the US space program for 33 years.

To give students a way to learn learn more about Katherine Johnson's life, I put together a 2-step equations color-by-number activity. The activity is editable if you would like to change any of the equations or facts for your students. You can access the activity for free here.

"We needed to be assertive as women in that days – assertive and aggressive – and the degree to which we had to be that way depended on where you were. I had to be. In the early days of NASA women were not allowed to put their names on the reports – no woman in my division had had her name on a report. I was working with Ted Skopinski and he wanted to leave and go to Houston, but Henry Pearson, our supervisor – he was not a fan of women – kept pushing him to finish the report we were working on. Finally, Ted told him, "Katherine should finish the report, she's done most of the work anyway." So Ted left Pearson with no choice; I finished the report and my name went on it, and that was the first time a woman in our division had her name on something." 

- Katherine Johnson, Black Women Scientists in the United States, Indiana University Press, 1999

Pi Day Math Worksheets

It was February break here this past week, so I rested a lot and worked on a pack of 16 math worksheets for Pi Day. The worksheets include:

• Pi Day word search (2 levels) 
• Puzzle sheet #1 (2 levels) - number puzzles and maze 
• Puzzle sheet #2 - number puzzles and maze 
• Puzzle sheet #3 - number puzzles and maze 
• Order of operations sheet to solve for missing digits of pi 
• 2-step equations sheet to learn about Albert Einstein 
• Circles sheet for area and circumference (2 versions - 3.14 and pi button)
• Cylinders sheet for volume (2 versions - 3.14 and pi button) 
• Cones sheet for volume (2 versions - 3.14 and pi button) 
• Spheres sheet to solve for radius given volume or surface area 
• Pi Day coloring sheet with Albert Einstein

Details:

The circle, cylinder and cone sheets come in 2 versions-- one for using 3.14 and one for using the calculator's pi button. 

There are 2 versions of the word search, both with 15 Pi Day themed words to find. One word search has a 20x20 letter grid, and the other has a 15x15 letter grid. The words are the same between the two versions.

The puzzle sheets include number puzzles, picture puzzles and mazes. The number puzzles ask students to use the order of operations, arrange given numbers into a grid to make sums, arrange operations around four 4s to make given numbers, and figure out missing numbers in crossword-like puzzles.

Students simplify expressions with addition, subtraction, multiplication, division and groupings on the order of operations sheet. Answers fill in missing digits of pi to the 35th digit. 

The 2-step equations sheet asks students to solve equations to figure out the missing numbers in facts about Albert Einstein's life.,

The last page is a Pi Day coloring sheet for all ages featuring Albert Einstein.

You can see all of the worksheets included here:

Pi Day math worksheets

Encyclopedia of Integer Sequences OEIS Finally Found!

Thanks to teacher John Holmlund from the Building Thinking Classrooms Facebook group, a multi-year math mystery has finally been solved! 

Back in graduate school, we learned about a website that takes any string of integers and returns all possible number sequences. Since then, I had forgotten the web address and kept failing miserably searching Google and describing the website to Chat. Enter John in the BTC group...

So finally the mystery has been solved. Thank you, John! And I am parking the website here to never forget again!

oeis.org

Holiday Math Logic Picture Puzzle Escape Room Games

This bundle of picture puzzle escape rooms will engage your math students around the holidays throughout the year while being a breeze to assign.

Fall logic picture puzzles escape room

Most digital math escape rooms are standards based, but I've also been making some fun logic puzzle escape rooms with holiday themes. 

Valentine's Day picture puzzles escape room

Each picture puzzle escape room comes as a self-checking Google Form that eliminates your need to grade, and as a printable black & white PDF. 

Valentine's Day printable math escape room

Each escape room has 20 questions broken into 5 puzzles. Students solve four problems in each puzzle, then type the correct 4-letter code to move to the next puzzle. 

There are 3,024 possible 4-letter codes for each puzzle, so the chance of guessing correctly is pretty low!

Football Game Day picture puzzle escape room

There are 2 types of escape rooms in this bundle: 

In the logic picture puzzle escape rooms, students solve for the values of holiday-themed pictures in equations. 

Christmas cookies picture puzzle escape room

Each picture puzzle escape room comes with a graphic organizer to help students keep track of the values of the different pictures.

Each also comes with an answer sheet where students working on the printable escape rooms can write down their codes. 

Halloween picture puzzle escape room

There are also 2 escape rooms especially for Pi Day where students solve for variables in the circle and volume formulas. 

Pi Day escape room - middle school

One Pi Day escape room is geared towards middle school students, while the other can be completed by students in 8th grade and up. 

Pi Day escape room - 8th and up

Each escape room includes a link to its digital version in Google Forms, a printable black & white version, a printable student answer sheet and an answer key. The picture puzzle logic escape rooms also include a printable graphic organizer to help students keep track of each pictures' value.

To add the digital escape rooms to your Google Drive: please open its PDF and click the button on page 3. Each escape room also comes with a printable, black & white PDF version for days you'd rather work on paper.

Inside this bundle are digital math escape rooms for Back to school, fall, Halloween, Thanksgiving, Christmas, winter, Super Bowl, Valentine's Day, spring, Pi Day and End of the school year. And the bundle is still growing! All future additions are free to download. What other holidays would you like to see?

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