Using bar models as the foundation, I created Structures of Equality (SoE) to help students and teachers make sense of math stories. But I understand that in addition to understanding what the problem is asking, your students need to solve them too. 

Explicit connections from conceptual to symbolic

Today, we’ll peek inside a 2nd-grade classroom as students connect the visual representations to the work they’ve done around composing and decomposing, subitizing, and base ten concepts.

If you’re not familiar with subitizing, you can learn more in my blog post explaining its importance. Valerie Faulkner, a leading mathematics educator, has done extensive work around subitizing and tells us more about how it helps kids in this video.

CRA (Concrete Representational Abstract) in action

In a moment, I’ll share a video created for students in Valerie Faulkner’s elementary mathematics college education program. (Please excuse the video quality as it was originally intended for classroom use only.) 

You’ll see her move students from conceptual subitizing to symbolic representations. She then connects solving number stories to a real-life situation before moving into a word problem.

Key points to observe:

• equality is shown by framing both sides of the bar model
• scaffolding is provided with trains of cubes
• explicit connections to decomposing around ten are made

We recently explored the CRA framework and how it can work in conjunction with SoE. In this video, you’ll see where the magic happens as she integrates all 3 phases into one lesson.

• Concrete: trains of cubes to represent composing, decomposing, and equality.
• Representational: use of bar model representation to connect the symbolic representation to the cube model
• Abstract: expression written on the board while students use what they know about breaking apart to make ten to solve

Notice how these are not used sequentially but as needed throughout the lesson to make connections.

Subitizing, Decomposing, Bar Models, & Word Problems: Part 1

As promised, you can view Dr. Faulkner’s instruction here. Note the ideas mentioned above as you watch. Then, we’ll wrap up with a few more key ideas related to SoE.

? Subitizing, Decomposing, Bar Models, & Word Problems: Part 1

Bar Models and SoE

In the video, Dr. Faulkner used a bar model similar to a Parts Equal Total model to bridge the gap from subitizing to solving. She discussed equality throughout, which is a key component of the structures.

Because SoE is a reading comprehension tool, the discussion piece around the context of what’s happening is essential. When she introduced the proto-word problem through the use of the cubes, she set students up to make connections between the discussion and number stories they would encounter in the future.

Conclusion

Number stories aren’t easy. That’s why teachers and students have struggled with them for as long as they’ve been around. Using the SoE structures changes that. 

After students have comprehension of the situation occurring in a number story, you can make explicit connections to the arithmetic and strategies they’ve been taught. Students will be able to understand what the problem is asking and then use what they know about mathematics to help them solve it.

Would you like more support with the implementation of the structures? That’s why I’ve created a Facebook community where I’ll personally respond to your questions and comments. Join us!

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