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drink mixes

Here are two ways to make grape drink using powder mix:

Mix  cups grape powder mix with  cups water

Mix cup grape powder mix with  cups water

Max thinks that the mixtures will taste the same because you add the one-cup of grape powder mix and one cup of water to the first mixture to get the second. Tuesday says that the mixtures will taste the same because in both mixtures there is  cups more water than grape powder mix.

1. Use a drawing (table, picture, etc.) to explain if Max’s reasoning is correct? If it isn't correct, why not?
2. Use a drawing (table, picture, etc.) to explain if Tuesday’s reasoning is correct? If it isn't, why not?
3. Should the two grape drinks taste the same? If not, which one should be grapier? Try to find several different ways of reasoning to answer these questions.

(Source: Adapted from Mathematics for Elementary Teachers, Sybilla Beckman, 2nd ed., 2008)

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