You survived the wait! I’ve been teasing for the last 3 weeks, building up to the unveiling of Structures of Equality. Last week, you got a sneak peek. Today, you get a full introduction.

A Quick Recap

I created Structures of Equality when I became frustrated with common word problem solving approaches. In my blog 2 weeks ago, we delved into 4 strategies, their advantages, and disadvantages. 

One of the most effective strategies discussed was bar models. But even they have limitations. It’s possible a student can create a bar model and not fully grasp the context of a story problem. I knew the missing piece was a reading comprehension tool that would address this issue.

The Creation of Structure of Equality (SoE)

In addition to bar models, another approach with many merits is Cognitively Guided Instruction (CGI). The barrier for me was that there were so many problem types, I sometimes found it confusing to pick a model. 

So I took the best of both, along with a few other elements, and created Structures of Equality. I don’t often call things groundbreaking, but I truly think they are.

“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.” – Dr. Valerie Faulkner, Mathematics Consultant, Author, and Subject Matter Expert

So…what are the structures and what makes them so special?

Structures of Equality (SoE) are graphic organizers that help students map out a math story. The 3 different SoEs are:

• Parts Equal Total
• Compare
• Repeated Equal Groups

A SoE is made of three crucial elements. They MUST:

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

When a student includes all three, it indicates comprehension.

These are the only models you need to diagram any problem type in the elementary Common Core standards.

Can my students do these independently?

Yes! After explicit instruction and consistent use, students will internalize the structures. They will have a reading comprehension tool to confidently work through any word problem.

If they cannot decode, you will still need to provide support and read the problem to them.

How do I get started?

You’ll want to approach teaching the structures systematically. Initially, your students will need support to feel comfortable. Over time, instead of frustration, they will be excited to solve problems that previously challenged them. 

Over the next few weeks, we’ll dive deep into each of the structures, additional examples, and how to teach them to your students.

Don’t want to wait? Join my email list. You’ll get access to resources before they hit my website and learn about professional development opportunities.

Conclusion

By combining bar models and Cognitively Guided Instruction (CGI), I’ve cooked up something truly revolutionary. With these graphic organizers – Parts Equal Total, Compare, and Repeated Equal Groups – your students will have the tools and confidence to work their way through any word problem.