Teaching Equations Without the Struggle: How Bar Models Can Deepen Student Understanding

It was 2018, and I was staring at the state assessment results with a knot in my stomach. The emphasis on rational numbers outlined in our standards had intensified and my colleagues and I were in a panic. Across our division we saw 56% mastery with sixth graders solving one-step equations with integers. Not great, but manageable. But with the increased rigor that called for adding fraction coefficients to those same types of equations, we saw that mastery plummeted to 9% in just two years.

Nine percent.

That's when I knew I had to find a visual solution that wouldn't force teachers to over-rely on teaching algorithms. I started introducing bar models as a core instructional strategy for teaching equations. Not as an occasional supplement, but as a systematic approach to developing algebraic reasoning. Within three years, mastery climbed to 72%, exceeding where we started. Fast forward to today and bar models are my go-to instructional strategy for developing algebraic reasoning in grades 6-8.

The Problem We Don't Talk About Enough

You know that sinking feeling when you've taught solving equations with whole numbers for multiple days, and your students freeze the second you introduce a fraction? This isn't a student problem, it's an instructional one. For years, we've asked middle schoolers to make a massive cognitive leap from using concrete tools like algebra tiles to the abstract thinking required to solve equations with rational numbers. We expected them to "just get" that modeling simple equations like 4x = 8 with algebra tiles means something fundamentally different from ¼x = 8, even though both involve the same operation.

And when they don't "get it"? We assume they need more practice, they're below grade-level, or worse, that they lack the ability altogether. So we continue with more repetition of the same instructional approach that students didn't understand the first time. But bar models offer something that algebra tiles alone cannot: they make operations with all rational numbers concrete. With bar models, students can gain clarity by illustrating the differences between the two equations mentioned above.

By representing that a number, x, has been divided into 4 groups, and 1 of those groups equals 8, the path to finding the whole becomes intuitive, not procedural. This type of modeling promotes reasoning and makes student thinking visible.

What Makes This Approach Different

Unlike traditional methods that prioritize memorizing inverse operations, bar models:

• Bridge arithmetic and algebra so students see algebra as an extension of concepts they already know, not a new set of disconnected rules.

• Encourage flexible thinking where students evaluate their own solutions and check for reasonableness.

• Provide consistency across problem types because the same visual approach works for any type of problem that involves equivalency

• Make mathematical properties visible so students see how the distributive property and the inverse properties actually work in context

This level of understanding aligns with the rigorous learning expectations outlined in most state standards for middle school mathematics. It's not about tricks or shortcuts, it's about developing algebraic reasoning.

What Teachers Say About the Shift:

"I was skeptical at first because I thought bar models were just for elementary students. But watching my 8th graders use them to solve multi-step equations with fraction coefficients and actually understand what they were doing changed my whole approach."

"My students used to panic when they saw a fraction. Now they ask, 'Can I draw this out first?' They've learned to trust their thinking."

"The best part about this approach is I'm not re-teaching the same concepts over and over. Students retain this because they understand it."

Ready to Transform Your Equation Instruction?

If you're ready to move beyond procedural teaching and help your students develop true algebraic reasoning, I've created a comprehensive system that makes implementation straightforward and sustainable.

Enroll in My Grassroots Online Workshop:
How to Use Bar Models to Develop Algebraic Reasoning in Grades 6-8.

What's Included in the Workshop:

✅ 7 in-depth video lessons walking you through the why, what, and how of bar models

✅ A complete workbook with reflection activities, practice problems, and planning tools

✅ The Concrete-Representational-Abstract framework specifically adapted for middle school algebra

✅ Classroom management protocols for student-centered bar model instruction

✅ Student work analysis so you know exactly what to look for and how to respond

✅ Ready-to-use activities including cut-and-sort tasks, tic-tac-toe games, and verbal-algebraic-visual equation sets

Regular price: $49

→ Enroll before December 1st and save 15% with code SAMS15

This isn't just another PD that you'll watch once and forget. This is a systematic approach you'll return to throughout the year as you teach equations, proportions, percentages, and any topic requiring algebraic reasoning. The workshop is self-paced, so you can start immediately and work through it on your schedule.

Questions? Let me know because I'm here to support you.