The RULES Framework: Helping Geometry Students Build Critical Thinking Skills

Geometry isn’t hard.

Understanding geometry questions is.

With South Carolina’s new math standards, students now take geometry before Algebra 1, and this shift has revealed a major gap in many classrooms:

critical thinking and problem analysis skills.

I see it clearly with my students. My sophomores, who already completed Algebra 1, tend to perform much better on geometry problem-solving tasks. My freshmen, however, many of whom are English Language Learners (ELLs), struggle significantly.

And it’s not because they can’t do the math.

It’s because they can’t always figure out what the question is asking.

Why Geometry Is Especially Challenging for English Language Learners

Geometry requires students to do much more than calculate. Before they ever solve, they must:

• Interpret academic math vocabulary

• Analyze diagrams and visuals

• Connect new information to prior knowledge

• Determine what the question is actually asking

For multilingual learners, this cognitive load is even heavier. I often ask students to explain a geometry question in their own words, and many can’t, even when the math itself is within reach.

That’s when I realized something important:

👉 If students can’t analyze a question, they can’t solve it, no matter how strong their calculation skills are.

So I stopped focusing only on how students evaluate problems and started teaching them how to think through them.

Introducing the RULES Framework for Geometry Problem Solving

To help my students—especially ELLs—break down geometry questions, I created the RULES Framework.

This framework explicitly teaches students how to analyze math questions before doing any calculations.

RULES stands for:

• R – Read the question

• U – Understand the question

• L – Look for a strategy

• E – Evaluate

• S – Stop and check

Each step is intentional, structured, and designed to build critical thinking skills in the math classroom.

R & U: Read and Understand the Geometry Question

I teach read and understand together, because students naturally move back and forth between the two.

When students read a geometry question, I ask them to:

• Highlight or underline important math vocabulary

• Box or circle what they are being asked to find

• Identify keywords that signal meaning (such as bisect, congruent, or supplementary)

Example: Angle Bisector Questions

A typical question might say:

Ray BD bisects angle ABC. Solve for x and find the measure of angle ABC.

The word bisects is critical. Even if students don’t immediately recall the definition, we think through it together: Bisect means the angle is divided into two congruent parts.

To help students understand the question, we:

• Mark the diagram to show equal angles

• Write what we know directly on the image

• Create a blank for the final answer so students know their endpoint

We reread the question multiple times, asking:

• What is this asking me to find?

• What information is being given?

We do not move on until the question makes sense. For ELLs, simplifying the question helps to reduce the language barrier of the question without reducing the rigor.

L: Look for a Strategy Using Diagrams and Visual Clues

This step is especially important in geometry.

Many students skip over diagrams entirely, even though geometry questions often give more information visually than verbally.

When students look for a strategy, they analyze:

• What type of figure is shown?

• What kind of geometry question does this resemble?

• What relationships might exist here?

For example:

• Seeing angles signals angle relationships

• A split angle suggests bisectors or angle addition

• Multiple measurements indicate parts combining to form a whole

This step helps students connect the problem to similar questions they’ve solved before, without doing any math yet.

E: Evaluate (Now the Math Happens)

Only after students read the question, understand what it’s asking, AND identify a strategy can we begin to evaluate.

This is where students:

• Solve equations

• Substitute values

• Perform calculations

For many students, this is the most comfortable step. I still model heavily here, especially for students who struggle with algebraic reasoning, and I use frequent think-alouds.

But it’s important to note:👉 Three thinking steps come before evaluation.

S: Stop and Check Your Work (The Most Skipped Step)

Most students believe they’re finished once they solve for x.

In geometry, that’s rarely true.

In our angle bisector example, solving for x doesn’t fully answer the question. Students must:

• Substitute the value back into the expressions

• Find the measures of both angle parts

• Combine them to determine the measure of the full angle

When students skip the stop and check step, they often:

• Miss part of the question

• Provide incomplete answers

• End up with values that don’t make sense (like negative angle measures)

This final step forces students to:

• Reread the question

• Confirm they answered everything

• Check if their solution is reasonable

These habits matter.

Why the RULES Framework Builds Critical Thinking Skills

The RULES Framework intentionally shifts the focus from memorizing steps to analyzing problems.

This benefits all students, but it is especially powerful for English Language Learners.

We can’t always:

• Simplify academic language

• Provide step-by-step scaffolds

• Modify every assessment question

But we can give students tools to analyze questions independently.

By using the RULES Framework, students learn to:

• Break down complex math questions

• Interpret academic vocabulary

• Think before calculating

• Reflect before moving on

These are essential skills, not just for geometry, but for life beyond the classroom.

Final Thoughts: Teaching Students How to Think in Math

Critical thinking is not an innate skill. It must be explicitly taught, modeled, and practiced.

When we teach students how to analyze questions, rather than rushing them straight into calculations, we give them access to rigorous math content and long-term success.

And every student deserves that chance.

Want a Ready-to-Use Version of the RULES Framework?

If you’d like to implement the RULES Framework in your own classroom without building

everything from scratch, I’ve created a R.U.L.E.S. Framework Toolkit designed for struggling learners and English Language Learners.

It includes student checklists, posters, modeled examples, and teacher guidance to help students move from guessing to confidently analyzing and solving math questions—especially in geometry.

👉 Find the R.U.L.E.S. Framework Toolkit on Teachers Pay Teachers