Updated February 16th, 2026

Teachers ask me all the time: “How do you get kids to understand multiplication and division word problems?” Today I’ll help answer that as we dive into the  Repeated Equal Groups (REG) structure.

Start with context, not computation

Before you use any structure to visually represent a number story, it’s important to build the context for the problems through questioning and discussion.

Here are a few of my go-to story element questions:

• What do you notice?
• What’s happening in the story?
• What’s the setting?
• Who are the characters?
• What’s the action? (What’s the verb?)
• What’s the math main idea?
• What’s the thing we’re counting?
• Close your eyes and visualize the story. Have you ever had (item)?
• What’s a (item)?

Once students have an understanding of the context, you’re ready to think about how to represent it with a structure.

Modeling problems with REG

This SoE is helpful if a math story describes putting equal groups together (compose) or taking equal groups apart (decompose). Some number stories could be represented with this model or a Parts Equal Total (PET) structure; context matters.

In a previous blog, I walked you through what an example problem could look like in the classroom. Today, let’s start with a story that describes a multiplicative relationship (sometimes referred to as a multiplication problem). I’ll show you how to represent it with a PET first, then with REG.

📹 boxes of markers 

The second video shows a math story that describes decomposing a total into equal parts. Solve it on your own first, then watch the video. This will help you anticipate misconceptions that might occur while students are first working with REG. (A teacher I interviewed recently said this was one of her best tips: work out the problems before doing them with students.)

Max the Monkey loves bananas. His trainer, Molly, has 24 bananas. If she gives Max 4 bananas each day, how many days will the bananas last?

In general, the structures help us visualize and contextualize the stories. In this case, we actually find a solution too. When stories describe decomposing a total into equal groups and we’re given the size of each group, drawing it out means we now see how many groups there are too.

📹 Max the Monkey

How REG relates to Cognitively Guided Instruction (CGI) 

There are 3 CGI problem types that can be represented with a single structure, 

REG. This allows students to focus on the relationships and create a visual representation before they worry about symbolic representations.

REG and 3rd-grade word problems

In order for students to understand what is happening in a number story, they have to understand what the values within the problem mean. Since all SoE require students to use labels, they must understand the context in order to accurately represent it with a REG structure. 

Here’s what makes this tricky:as students move from additive to multiplicative thinking, the units and labels become harder to grapple with. Instead of composing or decomposing like units, each value represents something different (groups, number in each group, or the total).

The REG structure also makes the connection between arrays and the representation explicit, scaffolding the learning for students. 

All 6 situations shown below can be represented with this one structure.

REG and 4th-grade word problems

In 4th-grade, the complexity increases. Students work with number stories “in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b.”)… Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.” (NC DPI Unpacking Grade 4, June 2022)

You can represent this relationship using a bar model. However, even when represented correctly, it’s impossible to tell if the students understand what the model represents if values, labels and equality are not included in the representation. With a REG, they’re required to interpret the value.

Conclusion

The REG structure sets students up to successfully comprehend and solve multiplication and division word problems. When you use it consistently, there’s no need for tips, tricks, or keywords. Students are able to represent and interpret these word problems accurately. Once a math story is mapped out using a SoE, their working memory is freed up to work on computation.

Yes, this structure is a bit complicated at first. But it’s a reading comprehension tool that eventually allows all students to access story problems with ease.

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Resources:

NC Department of Public Education. (2022, June). 3rd Grade Mathematics Unpacked Content.https://www.dpi.nc.gov/nc-3rd-grade-math-unpacking-rev-june-2022/open

NC Department of Public Education. (2022, June). 4th Grade Mathematics Unpacked Content https://www.dpi.nc.gov/nc-4th-grade-math-unpacking-rev-june-2022/open