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MemberDecember 1, 2020 at 1:53 pm
I can think of two that I have used.
One is something I adapted but don’t remember the original source. It is about three brothers and their growth patterns over one summer. You can see where this goes…when you ask Which brother grew the most? The older brother who grew 2 inches (let’s say) is the brother who grew the most if you are thinking additively. But, the youngest brother who grew 1.25 inches, actually grew the most because his amount of growth was a larger proportion his height in the spring. So if you are thinking multiplicatively, hew grew the most!
The other task I think is in Great Tasks from NCTM (The brown cover not the green one).
It is about sharing cookies with people. It starts with whole numbers. A serving a cookies is 2 cookies. I have 10 cookies. How many people can be served cookies?
It moves onto fractional amounts. I use foamy circular and rectangular fraction pieces to support teachers’ learning about this. It helps them to see that if I have one-half of a cookie and a serving size is three-fourths of a cookie, then I can’t make a whole serving, but what part of a serving do I have? I have two-thirds of a serving. (Hope I explained this well enough so you get the picture. It is about division of fractions and the “referent whole” which so many students and teachers find challenging.