Standards, Standards, Everywhere (apparently)

• compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models (NCTM)
• Compute and compare the chances of various outcomes, including two-stage outcomes (CMP)
• (7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, 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.)
Initially, I made the mistake of matching the top two standards with the last standard. The following is my comparison:

The three standards converge on probability and its computation. However, they all vary on the breadth of strategies involved. The CMP standard is, by far, the most vague and seems to really only involve the computations themselves, with the added bonus of learning to “compare.” NCTM incorporates the task of reading/interpreting graphs and lists to the task of making those computations of probability. In contrast, 7.SP.8 is focused on data collection, observation, and predicting. Indeed, the computations/approximations for probability seem to be secondary to the other tasks and strategies in this particular standard (7.SP.8). the complexity of the tasks should be greater if they are able to meet that last standard—as it is intended to promote higher-order thinking skills (prediction) and practical skills (those that are applicable to life outside of the math classroom). Students whose teachers focus their curriculum around 7.SP.8 should be engaged in steps that are known as “scientific methods. The said standard, I argue, was written with specificity so that there was less of a chance of students spending all of their math class sitting at their desks, staring at books and copying numbers.

Surprisingly, just as I was about to post my thoughts for this week’s discussion, I noticed that I had failed to notice one standard—one that matches the first two more closely.
• 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Well, there you have it. The first standard (compute probability for simple compound events using lists, etc) and the above one (7.SP.8) really only differ on the event in question (be it the compound event or be it the oxymoron—a simple compound event?). The second standard (CMP) is a mix of the other two; it suggests computing probability for various outcomes, including two-stage outcomes—otherwise known as that compound event as seen in 7.SP.8—and simple compound events. Of course, this is not to say that they “blend harmoniously.” They just happen to all be the same thing, worded a bit differently every time. The good news? If you do some probability questions in your textbooks, you are bound to have met all three standards.