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The three ideas that do the heavy lifting. The full article goes deeper , free, no gate.
Most programs stop at "3 out of 4 slices." The other four interpretations are where fraction reasoning actually lives.
A fraction as a quantity you locate, the #1 predictor of later fraction success, only appears when students locate fractions as quantities on the number line, not count parts of a whole.
With the area model and ratio table, "3/4 of 12" and "3:4" stop being new topics and become the same understanding, applied.
Teachers who watched understanding arrive, and said so.
“I saw light bulbs turn on and thinking turn on that I had never seen with math.”
“This is it. This is how to teach math.”
“These kids aren't just saying math words anymore. They can explain them and show models to back it up.” (Rosie Ashcraft · and Ms. Hochstrasser's 4th graders made dramatic gains, the kind you can point to on the assessments and see in how students talk about the math.
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Five Interpretations of a Fraction , the article, with the research and the classroom takeaways.
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DMT INSIGHT · Five Interpretations of a FractionWatch the lesson taught, models, questions, and the language, on tape.
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