standard_description: Explain a proof of the Pythagorean Theorem and its converse.
problem_activity: Task
Lucy has measuring cups of sizes 1 cup, $\frac{1}{2}$ cup, $\frac{1}{3}$ cup, and $\frac{1}{4}$ cup. She is trying to measure out $\frac{1}{6}$ of a cup of water and says, ''If I fill up the the $\frac{1}{2}$ cup and then pour that into the $\frac{1}{3}$ cup until it is full, there will be $\frac{1}{6}$ of a cup of water left.''
Is Lucy's method to measure $\frac{1}{6}$ of a cup of water correct? Explain.
Lucy wonders what other amounts she can measure. Is it possible for her to measure out $\frac{1}{12}$ of a cup? Explain.
What other amounts of water can Lucy measure?


aligns: no