
The CRA Model isn't a linear path. It's a Venn diagram. And when you hit the Sweet Spot, where concrete, representational, and abstract all overlap, that's when the magic happens.
In this episode, I'm revisiting one of my favorite topics and showing you why hands-on and visual learning matter MORE than ever for upper elementary students.
Two examples of the CRA Sweet Spot:
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Early elementary: 7 + 8 on a Rekenrek (concrete) → drawing it on a number path (representational) → writing the equation (abstract)
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Upper elementary: 3 × 1/4 with fraction tiles (concrete) → drawing rectangles or number lines (representational) → symbolic notation (abstract)
Why manipulatives aren't just for little kids: Upper elementary is when math gets MORE abstract. But if students don't have concrete and visual experiences to anchor their understanding, they end up memorizing procedures without knowing what they mean.
How to normalize manipulatives: Don't make them optional or "for struggling students only." Make them available for everyone. Model using them yourself. Show students that even YOU use tools to think through problems.
Tools that help:
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Brainingcamp (digital manipulatives) - All Virtual Math Summit registrants get 6 months FREE access
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Didax (physical manipulatives) - Celebrating 50 years! Giveaways during live summit sessions
The CRA Sweet Spot isn't just for younger kids. It's for upper elementary too. Don't skip the connections, that's what makes the learning stick!
Virtual Math Summit (Feb 28-Mar 1):
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34 FREE sessions
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Sessions from John SanGiovanni, Ryan Dougherty, Sara VanDerWerf & Nina Smith
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Brainingcamp 6 months free access for all registrants
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Didax giveaways during live sessions (must be present to win)
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10 Build Math Minds memberships given away during live sessions
Register at VirtualMathSummit.com to learn from experts to help you incorporate more of the CRA into the classrooms.
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