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.
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.
Algebra 2 is a big jump from algebra 1, and 11th graders can still benefit from extra supports. The cheat sheet covers composing function graphs and equations on the front, and graphs and tables on the back.
The graphics on the back are from my algebra 2 word wall. The table got an update, so if you have this word wall, please re-download the file from TPT or my website to get the updated version.
Students worked on this composition of functions matching worksheet that's also in the cheat sheet file. There are also 4 expressions on the back for students to evaluate.
This function composition escape room is self-checking, eliminating your need to grade. Students compose functions shown in tables, graphs and equations, then type their 4-letter code to move to the next puzzle.
Students can't move on until typing the correct code. You can then see who successfully broke out in the Google Form's responses tab. A paper version of the escape room is also included.
Download the free function composition cheat sheet here.
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.
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.
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.
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.
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.
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.
This math picture puzzles escape room also comes as a printable PDF version, if students don't yet have access to their devices or you'd rather they work on paper.
These math bulletin board borders add a little math to the edges of your classroom bulletin board. Wavy and straight edged borders are included in a few different styles.
Ms. Mundy sent a photo of her classroom where she hung the straight-edged borders around her math bulletin board. I love getting photos from teachers of my resources in action in your classrooms.
Students love seeing their work displayed. These student work toppers make it easy to create a confidence-boosting bulletin board display that showcases student work for Back to School Night. There are a few different styles that fit both horizontally and vertically-orientated worksheets.
My math word wall completely changed my teaching and how my students accessed our curriculum. Some teachers choose to hang their entire math word wall at the start of the school year, and others, because of space or personal preference, build their word wall throughout the year.
There are math word walls available for financial literacy, area, volume, elementary grades 2 through 5, middle school grades 6 through 8, and high school algebra, geometry, algebra 2 and the unit circle.
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.
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.
This function transformations cheat sheet 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 parent 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.
We started our function graphs unit every year by transforming absolute value graphs. There's an absolute value cheat sheet for graphing linked in this post. First we find and plot the vertex, then choose x values on either side of the vertex's x, then calculate all y values by evaluating the equation at our x values.
Next up was graphing quadratic functions in vertex form. Just like absolute value, we created tables centered on the vertex to plot all points.
Graphing quadratics in factored form always came a little later, but I thought it would be fun to include a video for this, too. When we get to factored form quadratics, the "horizontal shifts are opposite" starts to make sense.
What x values would make (x - 5)(x + 7) = 0 true? +5 and -7. All horizontal function shifts are just like this. We're looking for x values that will zero out the parenthesis, which is why "inside is opposite".
After quadratics, we'd move on to radicals. By now, function transformations are really clicking with students, and they are able to move a graph all around the coordinate plane. Most of my years teaching algebra 2 have been spent in the special education setting. It's cool seeing students who can be unsure of their math abilities confidently shifting radical functions by the time we get to this unit! There's a free graphing radicals cheat sheet linked in this post.
Cubic functions in vertex form are fun to graph. Just a little squiggle through the point.
Towards the spring, we'd learn how to sketch polynomial functions. This was another unit in algebra 2 where students showed a lot of growth. At first, graphing a polynomial seems completely abstract, but soon enough students are crossing and bouncing their graphs on the x axis and sketching in their graphs! There's a free sketching polynomials cheat sheet, along with a couple activities in this polynomials post.
After polynomials, we'd move on to graphing exponential functions. There's a free graphing exponential functions cheat sheet linked at the bottom of this post.
We'd get to graphing logarithms towards the end of the year in our inclusion class. There's a free graphing logs cheat sheet linked in this post.
At the very end of the year, our inclusion students would complete a conics project. It was so inspiring seeing what they created with their mathematical equations. If you've never done a conics project, there are examples and tutorial videos in this post.
Lastly there's sine, which isn’t an algebraic function but I wanted show how it shifts in the same way. My original graph looked like a cubic, and I rightfully heard about it from a couple people on Facebook. So I deleted the video, beat myself up for a couple days, remade the graph, and then remade the video.
I hope you enjoyed the videos! Is there another function you’d like to see?
