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
• bar models and SoE are similar and different

You were introduced to the 3 types of SoEs:

• Parts Equal Total
• Repeated Equal Groups
• 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 explore one SoE in depth.

Parts Equal Total

It’s pretty exciting to think you only need to teach your students 3 structures to successfully solve 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.

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. Adults often see this as a subtraction problem. 

When young learners begin to use SoE, they’re not required 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 this example, you’ll see how a structure matches a math story that has two known parts.
In my second example, watch how a 2nd grader explains the structure he drew to match the story problem. Watch and look for:

• The values being represented
• The line of equality and what is represents
• The labels

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. SoE make solving story problems accessible to everyone.

Next week, we’ll explore another structure. Don’t want to miss it? Subscribe here for weekly tips on how to successfully implement SoE.