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The visuals were so powerful, especially with the multiplication and division of fractions. I appreciated Kyle’s advice to hold off on the algorithms and the symbolic use of numerators and denominators. It is so important for students to see the unit fractions inside of other fractions. This idea is something they have explored as young learners when they thought about what is inside the whole number 5 or 10. Composing and decomposing — it comes up again! But not when we rush to teach by algorithms and rules (that expire).
Quotitive vs. partitive — very important as well. I still have to cheat and look at my notes when I am teaching this!!! Drawing the models are so important because the representations you end us creating look different based on whether quotitive or partitive.