How to Teach the Pythagorean Theorem Conceptually (Before the Formula)

If you teach 8th grade math, Algebra, or Geometry, you already know that students can memorize a² + b² = c², but that does not mean they understand it.

If you start with the formula, many students just plug and chug. Then they forget it, mix it up, or don't know when to use it.

The fix is simple: start with understanding first. 

Here's how to teach the Pythagorean Theorem conceptually so it actually sticks.

Start with the Big Idea (No Formula Yet)

Before you show a² + b² = c², students need to see what is
actually happening.

The core idea:

• You are comparing areas of squares
• The two smaller square combine to equal the largest square

Say it simply:

The area on the two shorter sides equals the area on the longest side. 

That's it. Keep the language simple.

Use Visual Models First

This is where the understanding happens. 

• Draw a right triangle
• Build a square on each side
• Shade or label the areas

Tell your students that you are going to explore the relationship between the areas of these triangles.

Ways to do this:

• Cut and rearrange paper squares
• Use grid paper and count squares
• Drag pieces digitally if you're using slides.

Let Students Discover the Pattern

Analyze a few triangles without telling them the connection

• Triangle with sides 3, 4, 5
• Triangle with sides 6, 8, 10 (even though this is a multiple it will give them more data.)
• Triangle with sides 5, 12, 13

Ask: 

• What do you notice about the areas?
• What stays true about the relationship between the areas every time?

Let them say it before you do.

Then Connect It to the Formula

Now bring in a² + b² = c²

But connect it directly to area:

• a² = area of one square
• b² = area of of the other square
• c² = area of largest square

So now the formula actually has meaning.

Use Real World Context (But Keep It Simple)

Once they understand the idea, connect it to real situations.

Examples:

• Finding the diagonal of a rectangle
• Distance between two points on a grid
• Shortest path across a field 

Don't overload it. Just enough to show it matters.

Common Mistake to Avoid

Starting with, "Here's the fomula, now plug in numbers." This leads to:

• Confusion about when to use it
• Mixing up sides
• Forgetting quickly

Teaching conceptually first will help with these mistakes. 

Final Thought

If students only see the formula, everything feels harder. Start with the picture, then build to the math. 

Check out these Pythagorean Theorem anchor charts that focus on both conceputal teaching and the formula.

Read more »

Michelle Sigaran

 How to Use Math Talk in Middle School Math (Simple and Effective)

If your students can solve a problem but can’t explain why it works… they don’t really understand it.

That’s where math talk comes in.

Math talk is one of the simplest ways to help students build understanding, confidence, and problem solving skills—without adding more to your plate.

And the best part?

You don’t need to change your entire lesson to use it.

What is Math Talk?

Math talk is just giving students opportunities to talk about their thinking.

Instead of:

• just writing answers
• or following steps

Students:

• explain their reasoning
• compare strategies
• ask questions

This kind of discussion helps students clarify their thinking and make connections, which leads to deeper understanding.

Why Math Talk Works

When students talk about math, something powerful happens.

They:

• understand concepts more deeply
• learn from other students
• build confidence in their thinking
• develop math vocabulary

Research shows that discussing math helps students make connections and strengthen understanding, not just memorize steps.

It also helps you as the teacher.

You can:

• see how students are thinking
• catch misconceptions quickly
• adjust instruction in real time

Simple Ways to Use Math Talk (Without Adding More Work)

You do NOT need a full “math talk lesson.”

Start small.

1. Turn and Talk

After giving a problem, have student turn to a partner and explain their thinking.

This is low pressure and gets more students involved, especially those who don’t want to share with the whole class. 

2. Ask One Simple Question

Instead of:

“What’s the answer?”

Ask:

• How did you get that?
• Why does that work?
• What did you notice?

One question can completely change the depth of the lesson

3. Show Different Strategies

Have students share multiple ways to solve a problem.

This helps students:

• see that math isn’t just one method
• compare ideas
• build flexibility

4. Normalize Mistakes

Math talk works best when students feel safe to share.

Make it normal to say:

• “I’m not sure…”
• “I tried this…”

This is where real learning happens

A Simple Way to Get Started

I created a free set of 20 math talk prompts you can use in your classroom to get students explaining their thinking and sharing ideas.

👉 Math Talk Free Prompts

They’re simple to use and an easy way to start building more discussion into your lessons.

Final Thoughts

Math talk doesn’t have to be complicated.

You don’t need a new curriculum or a full lesson overhaul.

Just small shifts like:

• asking better questions
• giving students time to explain
• letting students share ideas

can make a big difference.

When students start talking about math, they start understanding math.

Want more middle school math ideas sent straight to your inbox?
⭐⭐ Join thousands of  teachers who get weekly tips, freebies, and inspiration. JOIN BELOW 👇

Read more »

Michelle Sigaran

Why Your Middle School Math Students Are Losing Motivation (and What to Do About It)

If your students seem less engaged lately, you’re not imagining it.

The participation drops.
The effort fades.
And suddenly, even your strongest students seem checked out.

This is one of the most common challenges in middle school math this time of year, and it has very little to do with laziness.

Let’s break down what’s really going on and what you can do to turn things around.

Why Student Motivation Drops in Math at the End of the School Year

1. They’re Feeling Overwhelmed

By spring, students have covered months of content:

• Integers

• Fractions and ratios

• Equations

• Geometry

For many students, those concepts aren’t fully solid.

Instead of asking for help, they think: 

• "I don't get this... so what's the point?"

 

2. Small Gaps Have Turned Into Big Problems

A student who didn’t fully understand integer operations is now trying to:

• Solve equations

• Work with slope

• Apply multiple skills at once

That gap grows—and so does frustration.

3. They’ve Lost Confidence

Middle school students are quick to label themselves:

• “I’m bad at math”

• “I just don’t get it”

Once that belief sets in, effort drops fast.

4. The Format Feels Repetitive

By this point in the year, many students feel like:

• “It’s just more worksheets”

• “We’re doing the same thing again”

Even if the content is different, the experience feels the same.

What Actually Helps Re-Engage Students

You don’t need to completely change everything.

Small, intentional shifts can make a big difference.

 1. Focus on Small Wins

Instead of reviewing everything, narrow it down.

• One skill

• One concept

• One focused activity

When students feel successful—even briefly—it builds momentum.

2. Change the Format (Not Just the Content)

Sometimes the issue isn’t what you’re teaching—it’s how it feels.

Try:

• Foldables or flip books

• Task cards

• Partner activities

• Short challenges

A new format can make familiar content feel manageable again.

 3. Make Review Feel Doable

Avoid overwhelming students with large review packets.

Instead:

• Break review into smaller chunks

• Use structured, guided formats

• Keep directions simple

When students feel like they can start, they’re more likely to engage.

4. Build in Confidence

Look for ways to help students experience success:

• Start with easier problems

• Include visual supports

• Provide clear steps

Confidence is one of the biggest drivers of motivation.

5. Lower the Barrier to Participation

Right now, students don’t need more pressure—they need an easier entry point.

• Quick warm-ups

• Low-risk practice

• Opportunities to try without fear of being wrong

A Simple Way to Re-Engage Students in Math

One strategy that works especially well this time of year is using structured, interactive review.

Instead of overwhelming students with everything at once, it:

• Breaks concepts into smaller pieces

• Feels different than a worksheet

• Helps students focus on one idea at a time

If you’re looking for something easy to implement, you can check out these here:

👉 6th Grade Math Review

👉 7th Grade Math Review

👉 8th Grade Math Review

They’re designed to be:

• Low prep

• Focused on key skills

• Simple for students to follow

Most importantly, they help students rebuild confidence while reviewing.

Final Thoughts

If your students seem unmotivated right now, it’s not because they don’t care.

It’s usually because they feel:

• Overwhelmed

• Behind

• Unsure where to start

Your goal isn’t to fix everything at once.

It’s to:

• Create small wins

• Make learning feel manageable

• Help students believe they can do it again

And that’s what brings motivation back.

Save for Later

Read more »

Michelle Sigaran

7th Grade Math Review Notes for Spiral Review and Test Prep

Stop the “I forgot how to do this” problem in 7th grade math

By the middle of the year, students have learned a lot of math, but they often struggle to keep it all organized. They mix up formulas, forget steps, and lose confidence.
A simple system of review notes helps students keep track of what they’ve learned so they can review, apply, and retain skills all year long.

Why Review Notes work

When students have clear, organized notes, they can:

Quickly review key concepts
See step-by-step examples
Remember formulas and vocabulary
Work more independently
Prepare more effectively for tests
Instead of re-teaching constantly, students have a tool they can use on their own.

7th grade math Review Notes Bundle 

This bundle gives you a done-for-you system of clear, student-friendly notes that cover the major 7th grade math standards. It is designed to support daily instruction, spiral review, and test prep throughout the year.
It pairs perfectly with a math reference folder or binder so students can revisit concepts anytime they need them.

Easy Ways to Use It In Your Classroom

Give each sheet at the start of a unit as guided notes
Keep all sheets in a math reference folder
Use them for quick spiral review warm-ups
Use them as study guides before assessments
Provide them as support for struggling learners

A Simple Ways to Help Students Retain Math

Clear, consistent reference notes help students remember what they’ve learned, build confidence, and become more independent problem solvers.

If you want your students to stop saying “I forgot,” this system makes a big difference.

Check out the no-prep 7th Grade Math Review Notes. 

Read more »

Michelle Sigaran