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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