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Hello! I am working with colleagues this summer in trying to design some performance tasks related to the standards. We started by examining the sample performance tasks that came with our textbook series, but are also trying to branch out to make sure what we put together matches CCSS as closely as possible.
I was hoping to get some guidance regarding 7.SP.8 (shown below):
7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
c. Design and use a simulation to generate frequencies for compound events.
The standard seems to stop short of introducing a formalized algorithm for finding the probability of compound events via multiplication… here is my example: You roll a six sided die and flip a coin, what is the probability that you will role a 4 and land on tails? The standard seems to suggest that we would solve this problem by creating a sample space and deriving our probability from that. The textbook materials we use have the students create a sample space, but also take students to the next level of having them calculate P(A and B) = P(A) * P(B) in a later section…
I also took a look through the progressions document, and while it does reference teaching the counting principle, it doesn’t reference this probability rule at seventh grade.
My question is this – is teaching the use of multiplication to find the probability on compound events in this case part of the standard? If so… can I get a little help in dissecting the standard so I can understand the phrasing? If not… can I ask at what level it would be appropriate to teach this “rule” to the students? My colleagues and I were baffled by this one!
I apologize for my imprecise vocabulary! I have a spent the past two years as a technology curriculum integration specialist, and am looking forward to getting back into the classroom next year as a seventh grade math teacher.
The formal probability rules are in the high school standards, and in that case it is the general rule that does not assume the events are independent: P(A and B) = P(A)*P(B|A) = P(B)*P(A|B). The Grade 8 standards are really focused on understanding the underlying concepts of sample space, event, and probability model in concrete terms, without getting into the formal calculus of probability. So I would say that it goes beyond the standards to introduce the multiplication rule at this stage. Of course, if it arises naturally in an example there is no harm in pointing out that the probability of the compound event is the product of the individual probabilities, but that is not quite the same as introducing a formal rule. And it would be important to point out that this simplified multiplication rule does not always apply.
Thank you for the perspective! I like your suggestion of pointing it out in the context of an example problem while also addressing that this method doesn’t always apply. Teaching the rule “formally” at the middle school level could definitely lead to misconceptions if not tempered with appropriate explanations.
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