Category: Uncategorized

The Golden Nugget That Changed My Students’ Confidence in Math

We’ve all sat through them—guest presenters, workshops, webinars, professional development sessions. As teachers, we go in hoping to walk away with something we can actually use in our classrooms.

After more than twenty years of teaching, I’ll be honest: not every training leaves me with a fresh idea. But about 6 or 7 years ago, I picked up one small but powerful nugget that completely shifted the way my students engage with math—and the way they feel about themselves as learners.

The Golden Nugget: “Let’s See if We Need to Make an Edit”

During that training, the presenter suggested swapping out words like:

  • “Fix an error”
  • “You made a mistake”

…for the much friendlier phrase: “Let’s see if we need to make an edit.”

It’s such a simple change, but it’s magic. Why? Because students are already used to making edits in ELA—it’s an expected part of writing. No one panics when their paragraph needs revising. So why not bring that same mindset into math?

Now, I encourage my students to:

  • Try the problem
  • Review their work
  • See if it makes sense
  • Make edits if needed

It removes the sting of “being wrong” and reframes it as part of the process.

How I Use It in Class

This works beautifully when I’m teaching at the board. If I call on a student and their answer is incorrect, I write it down anyway and keep moving. Later, I step back and ask the class:

“Do we need to make an edit?”

Suddenly, I’m not the only one spotting errors. My students become the editors—the experts—finding and fixing the math themselves.

And here’s the thing: it’s empowering.

What This Shift Has Done for My Students

Changing my language from “mistakes” to “edits” has:

  • Boosted their confidence
  • Given them permission to experiment with math
  • Encouraged them to actually look for places to improve
  • Made “being wrong” less scary

A few years ago, I had a particularly large—and challenging—group of Algebra 1 students. Another teacher visited my room and said in surprise, “They’re all working.”

I smiled and said, “Well, yeah.”

These were students who often struggled academically, but they still tried. And I believe this small change in language played a big part in that.

Give It a Try

If you’ve never used this strategy, try replacing “fix the error” with “let’s see if we need to make an edit.”

It’s such a small shift, but the impact? Golden.

The Ultimate Math Resource Bundle 2024 is Here!

Math Teachers Get Ready – The Ultimate Math Resource Bundles Are BACK!

If you’re a math teacher looking to make your lessons more engaging, effective, and downright fun, we have fantastic news for you. The Ultimate Math Bundles are back for 2024! 🎉

For a limited time only, you can select the perfect bundle for your grade level of math resources valued at over $400, now available for the unbelievable price of just $35! Yes, you read that right—over $400 worth of top-notch math teaching materials, all for the price of a few fancy coffees! ☕✨

Ultimate Math Bundle 2024

Why You Need This Bundle:

  • 🧮 Comprehensive Coverage: From fractions to calculus, we’ve got every grade level covered! No more searching for the right resources.
  • 🎲 Engaging Activities: Keep your students hooked with interactive and exciting math games. Make learning math a joyous adventure!
  • 📚 Expertly Designed: These resources are created by experienced math teachers, ensuring quality and effectiveness in every lesson.
  • 💡 Stress-Free Planning: Save valuable time with ready-to-use lesson plans, worksheets, and more, allowing you to focus on teaching.

And that’s not all! We’ve also introduced the extra big MEGA BUNDLES. 📦 These colossal collections are packed with even more resources to make your math lessons shine.

Teaching Inverse Functions in Algebra

Teaching Inverse Functions

In elementary school, students learn how some mathematical operations are opposites of other operations. Addition is the opposite of subtraction. Multiplication is the opposite of division. As students get older, we introduce the word inverse. Inverse operations undo what has been done and are essential for solving equations. In algebra we expand the idea of inverses to functions. In geometry, the inverse of a conditional statement is when the hypothesis and conclusion are negated. In calculus students learn that integration is the inverse of taking the derivative.

Today we are going to delve into inverses with respect to the algebraic lens of functions, both analytically and with the geometric connection graphically.

Graphical Inverse

A function and its inverses are connected graphically by being the reflection over the line y=x.

When I start teaching inverses of functions, I often will start with points on the coordinate plane and have students switch the x and y coordinates to find the inverse. If you do this with several points and then ask students to graph the line y=x, they often will notice the connection of the reflection over the line y=x on their own. Here is a sample prompt to give your students.

We would discuss the domain and range of the function and its inverse as well as deciding if the inverse is still a function or just a relation.

Next, we look at a linear function, because this is the function that my students are most comfortable with and you do not need to restrict the domain for the inverse to be a function.
I may use a function similar to the graph shown in the first image above, f(x)=2x+4. Students will table the function and then switch the x and y coordinates to graph the inverse. They then would graph the line y=x and really see the connection that the function and its inverse are reflected over the line y=x. It would be good to note whether the inverse of the function is also a function at this point, as it will set up a future discussion when graphing parabolas.

After students start to get a feel for what an inverse looks like graphically, it is time to introduce the algorithm for finding the inverse.

Steps to Find the Inverse of a Function Algebraically

We will go over the steps and an example followed by some practice problems.

Restricted Domains

Finally, we will look at functions that need to have a restricted domain to make the function’s inverse also a function. It should be noted that if the inverse is not a function, then we would classify it simply as a relation.

The parent function for quadratics is a great function to start with when looking at restricted domains.

How do you teach inverse functions? Leave a comment below! If you are interested in my lesson or more teaching resources for inverse functions, visit my TPT store below!