Constructing Scientific Understandings 4.5 Torres_04

Their first task was to see if their bags were the same as the one sitting on the demonstration table. After careful examination, all the groups decided that the bags were identical, as far as they could tell.

For their next task, they opened their bags and looked at the contents. They were not allowed to share this knowledge with other groups until they were told to do so. They were asked to discuss in their groups how this knowledge would help them figure out the contents of the bag found a million miles away.

After about 20 minutes of lively debate within the class, Mr. Hansen drew a chart on the whiteboard. The students, for the first time, realized that all the bags held differing amounts of pennies. The students were then asked to use this data to once again determine what was in the bag located a million miles away.

As the students looked over the problem, the chart revealed that the total number of pennies in the bags were all prime numbers.

“So, class. We now have data to help us develop our theory (prediction) as to what is in the bag found a million miles away. Will someone please share their theory with the class?” asked Mr. Hansen.

Without hesitation, Dottie shared her theory. “OH! OH! The bag a million miles away holds pennies just like the other bags! And the total number of pennies in the bag equal a prime number.”

“Excellent!” Mr. Hansen replied. “You shared a prediction. ‘That explains why you made your claim. But how can we be sure you are correct?”

The class went silent.

“Let me pose this question then,” Mr. Hansen added. “What if we had a million paper bags and they all held pennies totaling up to a prime number? Would we be any closer to knowing what was in the bag a million miles away?”

Shyly, a student answered, “We would be more comfortable with the theory. But still, we would not be sure.”

“So, it could still be a million dollars,” chanted John hopefully.