# Alexandra O Fradkin: Playing Math Detectives: First Week of Second Grade Math

[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom]

The first week in our second grade class we did lots of time traveling. We played the role of math detectives and helped people from different time periods solve problems. We also learned about some ancient number systems.

On the first day we went back to several million years ago. (The idea for our scenario was taken from the wonderful book by Julia Brodsky, Bright, Brave, Open Minds: Engaging Young Children in Math Inquiry.) During this time period, there lived ferocious saber-toothed tigers with sharp teeth, crocodiles with awful jaws, and the first cave people, who had no strong jaws, long teeth, or sharp claws. How could we help those early people survive in their unfriendly world of dangers? The kids came up with making weapons out of sticks and stones, building fires, hiding in caves, running away, and climbing trees. I think they would have had a good chance of survival!

On the second day, we went back just 10-20-30 thousand years, to a time before numbers were invented but people had a need for keeping track. The kids’ task was to help a farmer determine whether his shepherd was bringing back all of his sheep at the end of day or whether he was stealing or losing some along the way.

The kids were split up into groups and each group got a bag of coins (which stood for sheep). They were told that when they were ready, I would take the “sheep” on a walk and bring them back. They would have to determine whether any were missing. The main rule was that they were not allowed to count in any way!

Here is their solution:

They made holes/homes for each of the coins/sheep, and when I brought back two fewer coins than they gave me, they were easily able to detect that because they had two empty holes. I was very impressed with their inventiveness. We then discussed and looked at pictures of how people actually did use dots, tally marks, stones, and knots to keep track of animals, money, and anything else they needed to.

Finally, on the third day we went back only several thousand years, to several locations around the globe. We visited the Babylonians, the Mayans, and the Romans, and learned how they wrote the numerals 1 through 10 in their number systems. The detective work consisted of helping them decide how they should write 11.

The kids examined the patterns closely, made suggestions, and discussed the merits of each one. In the end, they came up with versions that I think the ancient people would have been happy with.

Here is a picture of what it looked like (the Babylonian version did later get modified to be a horizontal wedge followed by a vertical one).

Next week we will begin our in-depth exploration of the Hindu-Arabic number system. More specifically, we’ll focus on the usefulness and meaning of place value and the importance of zero!

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