You’ve likely heard the saying nothing good comes without hard work. Last week, you were privy to a conversation with a 4th grade teacher who recently started implementing Structures of Equality (SoE) in her classroom. There was a point where she wanted to give up.

But she continued to explicitly and systematically introduce the structures to her students. And right when she began to question whether she should continue, it started to click. It wasn’t easy, but SoE have simplified math stories for her students. They now have a reading comprehension tool to support their understanding of word problems.

So how do you begin? One structure at a time. Let’s start with Parts Equal Total (PET). If you’d like a PET refresher before we dive in, you can learn more here.

To create Structures of Equality (SoE), I took the many CGI problem types and realized there were a few common relationships occurring within all of them, which can be represented by the 3 SoE. I grouped the situations by the common relationships occurring in each story, and then sorted them by the 3 SoE that could be used to model these situations. Paired with bar model diagrams, I added 3 essential elements that are critical for comprehension: values, labels, and equality.

Today, we’ll look at the different math stories that can be represented with a Parts Equal Total structure. You’ll notice that the 8 problem solving situations outlined in CGI can be modeled with 1 structure.

A student can use a Parts Equal Total SoE when a math story describes composing 2 or more parts to form a total or when a math story describes decomposing a total into 2 or more parts. Drawing a PeT SoE helps students understand the relationship between the parts and the total.

As you watch the videos, notice that we are only paying attention to the story. There are no questions posed. This is how you can begin implementing the structures successfully in your room. Focus on what is happening in the story and how the situation can be represented, not on finding a solution.

📹 Problem 1: There are 9 blue marbles and 6 red marbles in a bag. Maria put in 8 more marbles.

📹 Problem 2: Some students are in the cafeteria. 24 more students came in. Now there are 60 students in the cafeteria.

📹 Problem 3: There are 29 students on the playground. Some more students show up. There are now 47 students.

When you teach students that math stories are like other stories we read, they can focus on the comprehension aspect and will seek to understand what is happening. The focus is on the relationships within the problem, not on solving the problem.

Some questions to pose with your students:

- Who are the characters in the story?
- What’s the setting? Where is this story taking place?
- What happened at the beginning? the middle? the end?
- What’s the problem in this story?

Structures are tools for reading comprehension. Instead of focusing on what we know and what we don’t, or key words or numbers, we teach students to find the meaning within the story. They can then model the relationships using a SoE, allowing them the ability to use a variety of previously taught strategies to solve for their unknown values.

SoE give students a structure to comprehend word problems. By gradually introducing them and relating them to what they already know about reading, you can equip your students with the tools they need to tackle math stories.

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