Updated 8.13.2025

We’ve explored Parts Equal Total (PET), Repeated Equal Groups (REG), and how they sometimes overlap in recent blog posts. This week, you’ll learn about the third and final Structure of Equality, Compare. With these 3 reading comprehension frameworks, your students will have the tools to comprehend any elementary word problem type within the Common Core Standards.

SoE must-haves

There are 3 things all the structures have in common. These are what set SoE apart from other word problem strategies, and ensure student understanding.

They MUST have:

• values (numbers)
• labels (units of measure, the things you are counting…)
• a representation of equality

When students can model word problems using SoE with these elements, we know they have comprehension.

Introducing the Compare SoE

The Compare SoE is used when a math story describes a situation where two distinct sets or quantities are being compared. These types of number stories can be very confusing for students, especially if they’ve been taught to look for keywords. . Students who use keywords and/or go through a rote series of steps usually choose to add quantities when they should be looking for a difference.This is because the word “more” is often used when there’s a comparison relationship in a word problem in this problem type

Let’s consider an example similar to the types of problems students often encounter:

There are 5 blue cars and 4 white cards in the parking lot. How many more blue cars are there than white cars in the parking lot?

If a student used CUBES, or other step-by-step procedure, they would likely:

• Circle the numbers 5 and 4.
• Underline the word “more”
• Box in the question.

They would then add 5 and 4 for a total of 9 cars, and have no way to understand why the answer doesn’t make sense.

A student who models this with a Compare SoE can visually see the difference. In order to draw this representation, they’d have to understand the relationship between the values.
This representation clearly shows that 5 cars is more than 4 cars. There is a point up to which they are equal, as shown by the line of equality, and then there is some left over. This ‘left over’ amount is the more.

It is impossible to create this drawing without comprehension of what’s happening in the story.

Conclusion

The Compare structure takes the guesswork out of solving problems that involve a difference. The line of equality, the point up to which both quantities have the same value, helps students visualize the “more” or what’s leftover. Instead of confusing operations, they can clearly see they are looking for the extra. Providing students with this structure allows them to make sense of the mathematics and persevere in problem solving.

Don’t just take my word for it…

“Julie Russo researched how to teach children mathematics and adapted some of the best ideas into the Structures of Equality (c). You have heard of Singapore Bar Models, tape diagrams, and graphic organizers. These are all great tools. But what Julie does is connect reading to mathematics in a way that is clear, effective and achievable in any classroom. In particular, “The Line of Equality,” engages students in conversations that develop both reading comprehension and number sense.” – Valerie Faulkner, PhD. Mathematics Consultant and Subject Matter Expert