Teaching Solving Algebraic Equations with Bar Models

Solving algebraic equations can feel overwhelming for many middle school students, especially when instruction focuses only on steps and procedures. Bar models offer a simple way to make equations more visual and meaningful.

Instead of asking students to memorize what to do, bar models help them understand what the equation represents.

Why Use Bar Models in Algebra?

Bar models allow students to see the structure of an equation before solving it. This helps students:

• Identify what is known and unknown
• Understand relationships between quantities
• Feel more confident when solving equations

When students can visualize an equation, the math often starts to make sense.

Start with One-Step Equations

For an equation like
x + 7 = 19

Have students draw one bar to represent 19 and split it into two parts. One part is 7 and the other part is x. Students can easily see that x is the missing piece.

This approach reinforces that solving equations is about finding a missing value, not following rules.

Use Bar Models for  Multiplication and Division

Bar models also work well for equations such as 3x = 42 

Students draw a bar divided into three equal parts that total 42. Each part represents x. From the model, students can see why dividing by 3 makes sense.

This visual support is especially helpful for students who struggle with abstract reasoning.

Connect the Model to the Equation

After drawing a bar model, ask students:

• What does each part represent?
• Which part is unknown?
• How could this be written as an equation?

This helps students connect the visual model to algebraic notation.

Visual Supports Make a Difference

Consistent visuals help students remember strategies and build independence. Anchor charts and posters give students something to refer back to as they solve equations.

I created a set of Solving Equations with Bar Models Anchor Charts and Posters to support this exact work. The charts show how to model and solve addition, subtraction, multiplication, and division equations using bar models.

👉You can find the resource HERE

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Final Thoughts

Bar models help students slow down, think, and understand what an equation means. When students understand the structure, solving becomes less intimidating and more successful.

If you are looking for a simple way to strengthen algebra instruction, bar models are a strategy worth adding to your classroom.

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Michelle Sigaran

Why Math Mindset Matters

A strong math mindset is one of the most powerful tools we can give our students. When students believe they can grow, learn, and improve in math, everything changes—how they participate, how they respond to challenges, and how they see themselves as learners.

Instead of shutting down when something feels hard, they begin to see struggle as part of the process. 

A math mindset creates confident problem solvers, reduces anxiety, and opens the door for deeper, more meaningful learning. And the best part? It’s something we can intentionally nurture every single day.

What Math Mindset Really Looks Like

A growth-based math classroom doesn’t just praise effort. It normalizes:

• Making and analyzing mistakes

• Trying more than one strategy

• Taking time to understand, not just finish

• Explaining thinking, even when unsure

Students need to see these ideas often enough that they start repeating them internally.

Make Mindset Visible

You can talk about productive struggle all year long, but without visual reminders, students forget.

That’s why I created my Math Mindset Anchor Chart Posters — short, powerful messages paired with math-specific subtitles, written so middle school students actually connect with them.

These posters aren’t decor. They quietly coach students every day while they work.

Easy Ways to Use Them

Here are simple ways teachers are using the posters: 

• Create a dedicated “Math Mindset Wall”

• Ask students after a lesson: “Which poster matched your experience today?”

• Print mini versions for student notebooks or desktops

• Use posters as math journal prompts

• Tell groups they must apply at least one poster while solving a problem

• Use as an exit ticket question: “Which mindset helped you today?”

When used intentionally, students don’t just see the mindset — they begin to live it.

Want them Ready to Go?

If you want mindset to be embedded in your classroom without creating everything yourself, you can grab the full Math Mindset Poster Set HERE

They include:

• 20 mindset statements with matching subtitles

• Colored and black & white version

• Clean, modern layouts that fit any classroom decor

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Michelle Sigaran

What to Do with Early Finishers in Middle School Math: Easy Ways to Challenge Advanced Students

Every math teacher knows the moment: a student finishes early, looks around the room, and… zones out.

Not because they’re confused.
Not because they’re frustrated.
But because they’re done—and they have nothing else to do.

These students are capable, curious, and hungry for more. However, they easily get overlooked as you are busy trying to meet the needs of those who are behind. 

The good news? Challenging your advanced learners doesn’t require creating a whole second lesson plan or spending hours prepping enrichment work. With a few simple shifts, you can stretch their thinking, deepen understanding, and keep them meaningfully engaged.

Below are some easy, high-impact strategies you can start using tomorrow.

Ask for Multiple Strategies

When an advanced learner finishes ahead of the class, push their thinking by asking for another way.

• Can you solve this using a model instead of an equation?

• Can you show a visual strategy?

• What’s a second way to justify your answer?

When students compare and evaluate different strategies, they build flexibility and true conceptual understanding—not just speed.

Flip the Task

One of the simplest ways to deepen thinking is to reverse the direction of the work.

Instead of giving them a problem to solve, try:

• “Here’s the answer. What could the question be?”

• “Create a real-world situation that matches this equation.”

• “Write a story problem that results in a slope of –3.”

This approach moves students from answer-finding to problem-formulating, which is a much higher level of reasoning.

Add Constraints

Constraints force creativity.

You might ask:

• “Solve this using only fractions.”

• “Create an equation with a negative slope.”

• “Represent this relationship without using a graph.”

These limitations nudge students to think more intentionally and flexibly about how math works.

Invite Justification and Critique

Advanced students thrive when they’re asked to evaluate thinking—not just produce answers.

Try:

• Asking whether a student’s reasoning is valid

• Having them explain why a misconception is incorrect

This pushes them into mathematical communication, precision, and argumentation—all essential skills for deeper understanding.

Looking for Ready-Made Enrichment? Try What’s the Question?

If flipping the task sounds powerful, but you’d love a ready-to-use option, I have something perfect for you.

What’s the Question? activities start with an answer and challenge students to generate a possible question that leads to it.

It’s ideal for:

• Early finishers

• Enrichment

• Math centers

• Exit tickets

• Whole-class discussions that promote higher-order thinking

Teachers love it because students think creatively and deeply… while you don’t have to prep something extra.

👉 Explore What’s the Question? Activities

You’ll be amazed at the reasoning and originality students show when they work backward through a problem.

Challenging your advanced learners doesn’t need to be complicated. With a few small tweaks, you can keep every student thinking—without adding to your workload.

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Michelle Sigaran

How to Keep Students Engaged in Math During Halloween Week

Halloween week in middle school can be one of the toughest times to keep students focused. The excitement is high, energy levels spike, and attention spans drop fast. But instead of fighting the Halloween hype, you can use it to your advantage. With the right mix of structure and creativity, your students can stay engaged, learn, and even have fun while doing math.

Channel the Halloween Energy

Trying to power through your normal lessons rarely works this week. The key is to lean into the energy and give it a productive direction. Themed math lessons turn distractions into motivation—students are more likely to participate when lessons feel festive and relevant.

Keep Routines Steady

Consistency is your best friend. Start class the same way you always do—with bell ringers, clear expectations, and familiar transitions. Routine provides a sense of stability even during the most exciting weeks of the school year.

Use Short, High-Energy Activities

Avoid long lectures or extended worksheets. Instead, try math stations, task card games, or partner challenges. Short, varied activities give students chances to move and reset their focus. They’ll stay engaged longer, and you’ll get quick formative feedback on who’s mastering the content.

Add a Light Halloween Twist

You don’t need to decorate the entire classroom or plan an elaborate party. Simply changing the context can make math more fun. Try problems involving:

• Candy ratios and percentages

• Pumpkin prices and proportions

• Graphing ghosts or bats on the coordinate plane

These quick tweaks make ordinary review feel exciting and new.

Encourage Reflection

Build in moments for students to connect math to real life. Have them write short reflections like:

“How did you use math in your Halloween prep?”
They might talk about estimating candy bags, dividing treats with friends, or calculating decoration costs. Writing helps strengthen mathematical reasoning and reflection—without adding extra grading.

 

Ready-to-Use Halloween Math Activities

If you’re short on prep time (because, let’s face it, October gets busy!), I’ve created a few classroom-tested resources that make Halloween math both engaging and effective:

🎃 Halloween Activities for Grades 6–8 (Differentiable)
🧡 Halloween Adding and Subtracting Integers Coloring Activity
👻 Halloween Scientific Notation Conversions Coloring Activity
🕸️ Halloween Graphing Linear Equations Mystery Picture

Each activity reinforces key middle school math standards, looks festive, and keeps students learning even when they’re full of Halloween energy.

Final Thoughts

Halloween week doesn’t have to be chaotic—it can be an opportunity to create memorable, meaningful math experiences. With a little planning, a solid routine, and a sprinkle of creativity, you can keep students engaged and excited about math all week long.

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Michelle Sigaran