We’ve explored Parts Equal Total (PET), Repeated Equal Groups (REG), and how they sometimes overlap in my recent blog posts. This week, you’ll learn about the third and final Structure of Equality, Compare. With these 3 reading comprehension tools, your students will be ready to solve any elementary word problem type within the Common Core Standards.

SoE must-haves

There are 3 things all the structures have in common. These are what set SoE apart from other word problem strategies, and ensure student understanding.

They MUST:

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

When students can represent word problems using SoE with these elements, we know they have comprehension. You’ll have a chance to see this in action below.

Introducing the Compare SoE

The Compare SoE is used when a math story describes a situation where quantities are being compared. These types of number stories can be very confusing for students, especially if they’ve been taught to look for keywords. This is because the word “more” is often used in this problem type. Students who go through a rote series of steps, such as CUBES, usually choose to add quantities when they should be looking for a difference.

Let’s consider the example above:

If a student used CUBES, they would circle 5 and 3, box in “more”, and then use this information to solve. They would come up with 8 cars, and have no way to understand why the answer doesn’t make sense.

So what does it look like when students use this structure?

For the problem above:

a student explaining how the structure they drew represents the math story

Conclusion

The Compare structure takes the guesswork out of solving problems that involve a difference. The line of equality, the point up to which both quantities have the same value, helps students visualize the “more” or what’s leftover. Instead of confusing operations, they can clearly see they are looking for the extra. Providing students with this structure allows them to make sense of the mathematics and persevere in problem solving.

Don’t just take my word for it…

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

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