Updated July 16, 2025

There are so many word problem strategies to choose from. It can be confusing to figure out which ones to use or not use, and how to teach so students understand them. When I was in the classroom, I came across tons of tips and tricks, but they seemed to confuse my students more. Teaching story problems became frustrating to me, and my students got increasingly discouraged.

I knew there had to be a better way to tackle the struggles my students were facing.

A Quick Recap

In my last blog post, you got an overview of Structures of Equality (SoE). I talked about how:

• they support reading comprehension
• were derived from Singapore bar models but…
• are superior to typical bar models

You were introduced to the 3 types of SoEs:

• Parts Equal Total (PET)
• Repeated Equal Groups (REG)
• Compare

You also learned the 3 crucial elements that make up the structures. When a student includes all three, it indicates comprehension. They MUST:

• Contain values (numbers)
• Have labels (units of measure, the things you are counting…)
• Represent equality

Today, we’re going to begin to explore PET.

Parts Equal Total

It’s pretty exciting to think you only need to teach your students 3 structures to successfully comprehend all the problem types in the K-5 Common Core standards. Instead of tips and tricks, they become intimately acquainted with a reading comprehension tool that supports their understanding and builds their confidence. 

The first structure we’ll talk about is Parts Equal Total. 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. It helps students understand the relationship between the parts and the total.

Let’s consider this example:

This math story describes a situation where two parts are being composed to form a total. In this case, the unknown we are solving for is one of the parts. Students may see this as two parts being composed with one of the parts as an unknown.  It’s important that we don’t say to students,”This is a subtraction problem.

When young learners begin to use SoE, they’re not required  (or even encouraged) to define an operation. They use a visual representation to determine the relationship between the numbers. They can then use any strategy to solve for the unknown. Eventually, we connect these strategies to equations and operations.

How to teach Parts Equal Total: see it in action

When teaching SoE, we focus on the structure first. This is what helps students visualize the story.

📹 In the first video, I walk you through 2 number stories and show you how to represent them with a PET structure.

📹  In the second video, I show you exactly how to teach this to your students, from manipulatives to model.

If you’d like to see more, check out the PET playlist on my YouTube channel.

When you focus on the structure of the story, you’ll notice how students can determine the context of what’s happening, avoiding the ‘plug and chug’ strategy. Students can make sense of word problems instead of randomly choosing operations.

Conclusion

The Parts Equal Total SoE simplifies word problem solving when a story includes composing or decomposing parts or a total. It fosters understanding of what is happening so students can internalize the problem. After systematic, explicit instruction, students will have a tool they can use to comprehend math stories independently.

Next week, we’ll explore the Repeated Equal Groups structure.