✨ The Ultimate Math Bundle 2026: Your Year of Stress‑Free Planning Starts Now

categories: Deals

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08
Jul
2026

Factoring Quadratic Trinomials a > 1: Helping Students See the Structure Through Grouping

categories: Algebra

I teach factoring by grouping with quadratics because it sets students up for success later in Algebra 2, where they’ll use the same strategy to factor higher‑degree polynomials. The earlier they see the structure, the easier those advanced skills become.

One of the biggest challenges students face is recognizing how many groups of a binomial they have. For example, in an expression like

$x (x + 2) + 5 (x + 2),$

students often struggle to “see” how many $(x + 2)$ ’s there are.

To help them make this connection, I take them back to something familiar, elementary‑style counting, before we layer in the algebra.

Start With Something Concrete

I begin with simple visuals:

$1 😀 + 1 😀 =___😀$
$3 😀 + 2 😀 =___😀$

Students immediately answer 2😀 and 5😀. No hesitation. No confusion. Just counting groups of the same thing.

Then we shift to algebraic “smileys”:

$x 😀 + x 😀 =___😀$

$x 😀 + 2 😀 =___😀$

Some students see it instantly: 2x😀 and (x + 2)😀. Others take a moment, but they all eventually realize we’re still just adding groups of the same object—only now the “object” is an algebraic expression.

This is where the ah‑ha moments start rolling in. There’s a ripple effect across the room as students understand that grouping is simply counting how many of the same binomial you have.

Then Replace the 😀 With Binomials

Once students are comfortable, we swap the smiley faces for actual binomials:

$x (x + 2) + 5 (x + 2)$

Suddenly, the structure becomes clear. They can see the common factor, understand why grouping works, and explain it to each other using the same “counting smileys” logic.

This approach makes factoring by grouping feel accessible, visual, and even fun. Students stop memorizing steps and start understanding the why behind the method.

Connecting This to Trinomials Where a > 1

Now that students understand grouping, we apply it to trinomials:

$a x^{2} + b x + c$

We find two numbers that multiply to $a \cdot c$ and add to $b$ , split the middle term, and group. Because students already understand grouping conceptually, this process feels far less intimidating.

The smiley‑face warm‑up gives them a mental model they can rely on.

Grouping Doesn’t Have to Be Scary

This strategy builds confidence, deepens understanding, and sets students up for success in future algebra courses.

Ready‑to‑Use Lesson for Factoring Trinomials a> 1

If you want a print‑and‑go lesson that teaches this exact method from start to finish, complete with guided notes, practice, an exit ticket, card sort and a student‑friendly structure, I’ve created a Factoring Trinomials (a > 1) Lesson. that walks students through the grouping process step by step.

It’s designed to make the “smiley‑face” insight stick, help students see the structure, and give them plenty of supported practice. I replaced the smiley faces with sea turtles in the lesson to make it even more engaging. The moment students see the turtles, the activity becomes instantly more memorable—and the grouping concept sticks. Counting “how many sea turtles” they have feels just as natural as the elementary examples, and the visual makes the transition to binomials smoother and more fun.. You can take a closer look at the full resource here: Factoring Trinomials a > 1 Lesson

Factoring trinomials with a > 1 is often the point where students start to doubt themselves—but it doesn’t have to be. When they understand grouping as “counting how many of the same binomial you have,” the entire process becomes more intuitive.

This strategy builds confidence, deepens understanding, and sets students up for success in future algebra courses.

08
Jul
2026

How to Teach Factoring Quadratic Trinomials with a = 1

categories: Algebra

Factoring quadratic trinomials is a foundational Algebra 1 skill that students need to master to feel confident moving into Algebra 2.

One of the biggest challenges students face when learning to factor is not knowing their multiplication facts well enough to identify number pairs quickly. To support them, I keep a stack of multiplication tables printed on cardstock at the front of my classroom. Students love having this resource available. They will grab one, tuck it into their binders, and use it whenever they need a little extra support. If you’d like a copy to print for your own classroom, you can download it as part of the Free Factoring Quadratics Actitivy Pack at the end of this post.

Why Start with a = 1?

When students first learn to factor quadratics, beginning with trinomials where a = 1 sets them up for success. The structure is predictable, the pattern is clear, and students can focus on the core idea without juggling extra coefficients.

A quadratic in the form x²+bx+c can be factored by finding two numbers that multiply to c and add to b. Once students identify the pair, the trinomial breaks apart cleanly into: (x+m)(x+n)

This is often the moment when students realize factoring isn’t magic. It’s like a game or puzzle.

Factoring becomes much more approachable when students can see how each part of the trinomial fits together, so I like to use a simple table to help them organize their thinking as they work through each step.

Once students get comfortable using this structure, the pattern behind factoring trinomials with a = 1 finally clicks, and they’re ready to tackle more challenging factoring types with confidence.

If you’re looking for a ready‑to‑use lesson that walks students through factoring trinomials when a = 1 step by step, I’ve created a resource that pairs perfectly with the method shown above. It includes guided notes, structured practice, and a maze activity that helps students build confidence through repetition and pattern recognition. Everything is print‑and‑go, so you can introduce the skill, model it with your class, and immediately give students meaningful practice. You can take a closer look at the full lesson here: Factoring Trinomials (a = 1) Lesson.

If you’ve already taught factoring quadratics and your students just need a little more practice, you can download my Free Factoring Quadratics Activity Pack. It includes a graphic organizer, a maze, a color‑by‑number, and an outing‑club‑themed mystery that gives students structured, engaging practice with trinomials where a = 1. Everything is print‑and‑go, so you can reinforce the skill without adding extra prep to your day.

Happy Mathing!

14
Sep
2025

How to teach X and Y Intercepts with a A Hands On, Visual Approach: Algebra Key Features of Functions,

categories: Free Resources, Key Features of Functions

X- and y-intercepts are one of those foundational concepts that pop up again and again in algebra, graphing, and real-world modeling. But for students, they can feel abstract—just another pair of coordinates to memorize. So how do we make intercepts click?

Here’s a step-by-step approach that blends visual learning, student agency, and collaborative thinking to help students not just find intercepts—but understand what they mean.

🧠 Step 1: Start with Noticing

Begin with a warm-up that invites curiosity. Show a couple of graphs and ask students:
“What do you notice?”
Let them pair-share, jot ideas on sticky notes, or do a silent chalk talk. This primes their brains to look for patterns and builds confidence before any formal instruction begins

🎨 Step 2: Color the Axes

Hand out colored pencils or highlighters and have students trace the x-axis one color and the y-axis another. This simple move helps anchor their spatial understanding and makes it easier to spot intercepts visually.

Then ask:

Where does the graph cross the x-axis?
Where does it cross the y-axis?

Let students circle those points and label them. You’re building intuitive understanding before introducing vocabulary.

📊 Step 3: Explore Tables and Graphs

Give students graphs and tables of functions. Ask them to find the intercepts in each format. Then flip the task: give them intercepts and ask them to sketch possible graphs. This back-and-forth builds flexibility and reinforces the idea that intercepts are where the function meets the axes—not just numbers to plug in.

🧩 Step 4: Define and Organize

Now that students have seen intercepts in action, introduce formal definitions. Use a graphic organizer to show:

How to find intercepts from a graph
How to find them from a table
How to find them from an equation

This organizer becomes a reference tool they can return to throughout the unit.

✏️ Step 5: Practice with Purpose

Use practice problems that ask students to:

Identify intercepts from different representations
Create graphs with given intercepts
Match equations to intercepts

For early finishers, offer an extension:
“Can you make a table for this graph?” or
“Can you graph this table?”
This keeps students engaged and deepens their understanding of how intercepts connect across formats.

📎 Want a Ready-to-Go Resource?

If you’d like a lesson that walks students through all of this—complete with warm-ups, notes, graphic organizers, and practice pages—I’ve got one ready for you. It’s available on my TpT store, and it’s designed to be flexible, visual, and student-friendly.

Grab this X and Y Intercept Graphic Organizer!

Get Your Free Copy Here!

Whether you’re introducing intercepts for the first time or revisiting them before diving into linear equations, this approach helps students build lasting understanding—one axis at a time.

Thanks for stopping by! I hope this lesson idea brings a little more clarity (and color!) to your classroom. And if you grabbed the free graphic organizer, keep an eye on your inbox—I’ve got more teaching inspiration headed your way soon.

15
Aug
2025

The Golden Nugget That Changed My Students’ Confidence in Math

categories: Uncategorized

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.

24
Jul
2024

The Ultimate Math Resource Bundle 2024 is Here!

categories: Uncategorized

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

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17
Jul
2024

Mastering Surface Area: Teaching Tips for Math Teachers

categories: Geometry

Teaching surface area can be one of the more challenging topics in geometry, but with the right strategies and tools, it can become an engaging and rewarding experience for both teachers and students. As a seasoned math teacher, I’ve developed several lessons to help students grasp the concept of surface area. In this blog post, I’ll share these strategies and introduce you to a valuable resource that will make your teaching even more effective: the Surface Area Formulas Graphic Organizer.

Why Starting with a Low Floor Warm Up is Important

Engaging students at the start of the lesson is crucial. If you lose their attention in the first few minutes, it can be difficult to get their attention back. One way I have found to engage all students at the start of a lesson is to incorporate an entry level warm up prompt. I really like using “What do you notice?” and “What do you wonder?” as entry level prompts. All level of students can be successful with this task and I am always surprised when they notice or wonder ideas I would never have thought of myself.

One entry level notice and wonder for surface area could be to show different types of nets and to ask students what they notice and wonder. You could then extend the discussion to ask them to think about which net would make a cone, rectangular prism, etc. You could find real life objects to represent these shapes, such as a cereal box for a rectangular prism, a ball for a sphere, a oatmeal container for a cylinder, etc.

Strategies for Teaching Surface Area

Nets: Start the unit with a hands on introduction lesson to help students better understand what surface area is all about. Exploring different nets is a great activity to help students understand surface area for different shapes.
Vocabulary: When introducing formulas for surface area, it is important to review each vocabulary term that is part of the formula. For example, if the surface area of a sphere has “r” for radius in the formula, then make sure that students know the difference between a diameter and a radius.
Review Basic Area formulas: When I taught surface area to my class, I found that some students needed a review of finding the area of basic 2 dimensional shapes. These shapes would be the bases of our 3 dimensional solids.
Real-Life Applications: Connect the topic to real-life situations. Have students calculate the surface area required to wrap a gift, the leather of a baseball, or the fabric of a tent. These practical applications make learning more relevant and interesting.
Practice, Practice, Practice: Provide ample opportunities for practice. Use a variety of problems so students can apply their knowledge in different contexts.

Need a Surface Area Graphic Organizer?

I’ve got you covered! To further support your teaching, I’ve created a Surface Area Formulas Graphic Organizer, a powerful tool designed to help students visually organize and remember the different surface area formulas. This organizer includes formulas for finding the surface area of the following solids:

Sphere
Cylinder
Prism
Pyramid
Cone

By using this graphic organizer, students can easily reference the formulas and understand the relationships between different shapes. It’s an excellent resource for in-class activities, homework assignments, and test preparation. And, I’ve included 2 pages of practice worksheets too. Grab your free copy below!

Interested in checking out my lessons? If so, visit my TPT shop linked here or click on an image below.

I hope these tips and resources help you in your classroom. Happy teaching!

28
Apr
2024

Surface Area of Spheres Investigation with Oranges

categories: Geometry

I love a good hands on activity that helps my students remember the math they are learning. A great activity to remember the surface area of a sphere formula is to investigate the surface area of an orange.

Make sure to use oranges instead of clementines as the clementines are not as spherical as oranges. Students trace the outline of an orange onto a piece of paper, keeping their pencil perpendicular to the paper as best they can. Then have students use a compass to copy the same size circle several more times on their paper. Ask students to make a conjecture about how many circles they believe the orange peel will cover once they have peeled the orange.

Once students have their circles and conjecture, it is time to peel the orange. Students peel the orange and then test out their conjectures by covering each circle, one at a time. Students should find that the orange peel is able to cover 4 circles. Then as a class, make the connection between the radius of a circle and the radius of a sphere, like an orange. Ask students to write a formula for the surface area of their orange.

If you would like to grab a free copy of my Surface Area Investigation Activity, here is the link:

Alternate Ways to Facilitate this Activity:

Each student completes the activity on their own(an orange for each student)
Students work in groups of 3 or 4 students (7-10 oranges)
Teacher has student volunteers go to the front of the room to model the activity for the class (1 orange)

01
Aug
2023

Teaching Increasing and Decreasing Functions

categories: Key Features of Functions, Mathberry Lane Resources on TPT

For some reason students tend to have difficulty with this concept. At first glance, it seems rather straightforward. If a graph is going up, then the function is increasing. If the graph is going down, then the function is decreasing. If the graph is a horizontal line, then the function is constant. This is the level of this key feature of functions taught in my algebra 2 class.

In calculus, we take it a step further and look at intervals where the first derivative is positive to see where the function is increasing. And likewise, intervals where the first derivative is negative tells us where the function is decreasing. If the first derivative equals zero, then the function is constant.

Next, are the intervals for increasing and decreasing open or closed? Different textbooks will have different notations. Some will use open intervals while others will use closed. I used to be in the open interval camp, but have switched over to closed. I discuss this with my students about how textbook publishers and even math teachers cannot agree on this topic. With that said, if a function is increasing as it goes to an asymptote or infinity, then an open interval would be used.

Let’s look at the definition for a function increasing or decreasing on an interval.

I start this topic with a what do you notice prompt for the graph shown above. It is an entry point into the lesson where each student can share what they see. We then get out some crayons or colored pencils to shade in different portions of the graph.

Next I ask students to try sketching their own examples of graphs that are increasing, decreasing or constant, followed by a graph that exhibits more than one of these behaviors.

Before we start creating intervals for increasing and decreasing, we first review interval notation. Click HERE if you are interested in my free graphic organizer for interval notation.

Finally, we analyze graphs to identify intervals of increasing, decreasing or constant. After students feel comfortable identifying these intervals, I give them intervals with specified criteria and ask them to create the graph that would meet these criteria.

If you are interested in my lesson, it is available in my TPT shop as part of my Key Features of Functions Unit. I have included 2 versions: closed interval notation and open interval notation. Cheers!

30
Jul
2023

Teaching Inverse Functions in Algebra

categories: Uncategorized

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!