During a recent professional development, an important issue came up:

“Students can identify the math main idea. They can draw the structure. They include labels and values. But when it’s time to write an equation, they get stuck.”

At first, this feels like an equation problem. But when we look more closely, something else is usually happening.

What Structures of Equality Focus On (and What They Don’t)

Structures of Equality (SoE) is grounded in understanding the story and representing relationships, in making sense of quantities and how they relate.

Writing an equation is not the goal of the framework. 

At the same time, we know there are moments when students are expected to write an equation from a word problem. Some standards call for it and some assessments require it, so it’s worth asking:

If students already have a strong model, how do we help them record that thinking as an equation?

A Note About Equations

Students don’t need to write an equation to solve every problem. Many students can find solutions through models and reasoning alone.

When an equation is required, it should come from the structure and reflect the relationships students already understand.

Before Students Can Write an Equation

Before we ask students to write an equation that represents the math story, they need to be able to:

• Identify the math main idea of the story
• Choose a structure that represents that idea
• Draw the structure with:
  • labels and descriptors
  • values
  • a clear representation of equality

If those pieces are in place, writing an equation shouldn’t feel like a new or disconnected task. It should feel like continuing the same thinking in a different form.

So when students struggle here, it points us to something deeper.

Why Students Struggle to Write Equations from Models

Two patterns tend to show up:

▶️ Students aren’t consistently connecting the model back to the story.

Students may be able to draw the structure, but they’re not explaining what each part represents or how it connects to the context.

Each time students create a new representation (whether that’s with snap cubes, sentence strips, or drawings), they need to reconnect it to the story.  

▶️ Equality has not been made explicit.

If students can draw the model but can’t explain what is equal or why, that’s a signal that equality hasn’t been fully developed.

If they’re not talking about it in the model, it becomes much harder to express that relationship in an equation.

Start With Equality in the Model

Before writing an equation, pause and ask: Where’s the equality in this model?

You might ask:

• “What in this model has the same value?”
• “How do we know these are equal?”

This isn’t something we can assume students see.

In a Parts Equal Total (PET) structure, the total bar and the combined parts have the same length. That visual is important, but it is not enough on its own.

Students need language for what that means.

Equal means “has the same value as.”

The model shows equality visually, but understanding equality requires explicit conversation.

We need to point this out, and consistently hold students accountable for recognizing the representation of equality. 

A PET Model

17 kids were playing soccer at recess. Then 9 more joined them. How many kids are playing soccer now?

The math main idea of this story describes two groups being composed to form a total. Specifically, a group of 17 students is being combined with a group of 9 students to find out how many there are altogether.

We can represent this with PET.

How to Move From a Model to an Equation

Once students understand the model, the equation comes directly from it. We can take each part directly from the structure and record it.

Start with units to keep the meaning clear. It might sound like this:

• We know this group has 17 students, so I’m going to write that below

17 students

• This group is being joined by another group of students. So now there’s 17 students and some more. 

17 students and

• The other group has 9 students in it. 

17 students and 9 students

• Now, this is really important. Because the total bar and the parts bars are the same length, I know they have an equal value. 

17 students and 9 students equals

• We don’t know how many students the total is yet so we’ll show that with the label “? students”.

          17 students and 9 students equals ? students

• This sentence represents the story. If we want to write it as an equation, we can replace some of the words with symbols. I can use a plus sign to show “and”, or the groups joining, and an equal sign for the word “equals”.

17 students + 9 students = ? students

This sentence describes the relationship shown in the model. The equal sign shows that the quantities on both sides have the same value.

Once students consistently connect the equation to the story, the units can be removed. 

17 + 9 = ?  or   ? = 17 + 9

Each version communicates the same relationship. The order doesn’t change the value on either side of the equal sign. 

When students see these representations used interchangeably, we ensure they won’t internalize the misconception that the equal sign means ‘there’s an answer coming’. Rather, they’ll understand that the equal sign means that whatever is on one side has the same value as whatever is on the other side.

A Common Mistake: Focusing on Operations Instead of Relationships

It can be tempting to attach operations directly to structures.

• Seeing parts and thinking “add”
• Seeing comparison and thinking “subtract”

Notice that we didn’t call this an addition or a subtraction story.  Instead, the focus stays on the story and the relationships within it. The operation emerges from that understanding.

What to Try in Your Classroom Next

If your students are able to draw the structure and include all the key components, consider asking:

• Can they explain what each part represents in the story?
• Can they describe how the quantities are related?
• Can they identify where the equality is shown?

Those questions often reveal what students understand and what still needs attention.

When that understanding is in place, writing the equation becomes a natural extension of their thinking.