Same vs. Equivalent Story

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  • One day, Jess and Mikey went to their favorite ice cream shop. Jess ordered a medium cone, while Mikey ordered a large.
  • Great idea to get ice cream, Mikey!
  • Utterly Great Ice Cream
  • Thanks, Jess! Let's eat before it all melts!
  • After a few minutes of eating, Jess noticed that they both had one scoop of ice cream left. This made her think of something they had learned about fractions in math recently.
  • Hey! We both have one scoop of ice cream left. That means we have equivalent amounts left from what we started with!
  • Utterly Great Ice Cream
  • Well, we do both have one scoop left, but I think you are confused by the meanings of same and equivalent.
  • Luckily, Mikey was a whiz with fractions, and was able to help Jess out...
  • Really? What do you mean?
  • You were right in saying that we have the same amount of ice cream-- we both have one scoop. Those a equal amounts. BUT, we don't have equivalent portions left because I had more ice cream than you to begin with.
  • So you're saying same and equivalent aren't synonymous? What fraction of our ice cream do we each have left then?
  • Exactly. You have 1/2 of your ice cream left because you have eaten 1 scoop out of the 2 total scoops you started with. I have 1/3 of my ice cream left because I have eaten 2 out of 3 scoops of ice cream-- leaving me with 1 of 3 scoops total.
  • Now I get it! We both have one scoop left which means we have equal amounts of ice cream, but because we did not have the same wholes, we don't have equivalent portions of ice cream left!
  • The friends finished their ice cream and wondered what they would be learning tomorrow in math class.
  • Thanks for helping me, Mikey! Maybe tomorrow we will learn about multiplying fractions!
  • Utterly Great Ice Cream
  • Yeah, no problem! I'm glad I could help. I can't wait for tomorrow!
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