I hope this unit is clicking for you and your students. With dividing fractions, it's so easy to give kids a mnemonic or a shortcut that gets them correct answers but leaves them with the impression that math is mostly shortcuts to memorize.
That's why you've seen me encouraging you over and over again to start with their senses.
With this division problem, instead of starting with shortcuts or even operations, start with their spatial sense of the two bars. Consider asking, "About how much will the answer be?"
Students may tell you the answer will be greater than 1, which would be true if we swapped the divisor and dividend. Students may tell you the answer will be less than 1 and you can follow up by asking them what they think the fraction will roughly be about.
You can write those estimates down and point to them when students get an answer of ΒΌ on later screens. Their estimations may line up nicely with their calculations, connecting, and strengthening both.
Dan & the Desmos Classroom Team
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