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Sharing (12 cookies, 3 kids) and grouping (12 cookies, 3 each) are different problems. Students who see both never panic when the wording changes.
On a number line or in an area model, the remainder is a quantity students can reason about, not a surprise at the bottom of the algorithm.
The quotient interpretation, 12 ÷ 3 as "3 is one fourth of 12", is where fractions and proportional reasoning begin.
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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The Power of Division , the article, with the research and the classroom takeaways.
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DMT INSIGHT · The Power of DivisionWatch the lesson taught, models, questions, and the language, on tape.
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Open the free lesson →The people behind 40+ years of classroom research don't hand you a binder and disappear. They're in the portal, on the weekly calls, and, when you need it, building a plan for your students with you.
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