## Exploding Dots

### 5.7 Wild Explorations

Here is a “big question” investigation you might want to explore, or just think about. Have fun!

 EXPLORATION: LEFT TO RIGHT? RIGHT TO LEFT? ANY ORDER? When asked to compute $$2552 \div 12$$ Kaleb drew this picture, which he got from identifying groups of twelve working right to left. He said the answer to $$2552 \div 12$$ is $$121$$ with a remainder of $$1100$$.   Mabel, on the other hand, identified groups of twelve from left to right in her diagram for the problem. She concluded that $$2552 \div 12$$ is $$211$$ with a remainder of $$20$$.   Both Kaleb and Mabel are mathematically correct, but their teacher pointed out that most people would expect an answer with smaller remainders: both $$1100$$ and $$20$$ would likely be considered strange remainders for a problem about division by twelve. She also showed Kaleb and Mabel the answer to the problem that is printed in the textbook. $$2552 \div 12 = 212 R 8$$ How could Kaleb and Mabel each continue work on their diagrams to have this textbook answer appear?

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