Reason Abstractly and Quantitatively


Imagine the information below as an entry in a student's math blog. Through the blog, the student could contextualize a problem by applying it to an authentic context and decontextualize it by creating an expression or using a mathematical process to represent the problem. A student can explain his/her reasoning through the blog, and the teacher or classmates can add comments to each post to provide feedback or question the student's thinking.

Problem:


When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Decontextualize:


2/6 = 1/3
600 x 1/3 = 200

Contextualize:


Using the online probability generator, my parnter and I rolled the dice 60 times and found out how many times we rolled a 3 or a 6. Then, we multiplied this probability by 10 to determine an approximate probability that a 3 or 6 would be rolled if we rolled the dice 600 times.

We rolled a 3 or 6 19 times out of 60.
19 x 10 = 190

http://www.subtangent.com/maths/flash/probsim.swf
http://www.spreadsheetconverter.com/calculate/html/entertainment/One_die/One_die.htm