Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
INTERPRETATION OF OBJECTIVE - S.CP.A.1
This objective has a lot in it for such a short description. This objective lays out the basics of probability by building sample spaces and diagramming them. It then leads into the use of mutually exclusive, complement, intersection and union to describe and diagram certain relationships between those subsets.
(1) The student will be able to determine sample spaces and distinguish between uniform and non-uniform spaces.
(2) The student will be able to diagram and visualize sample spaces using set lists, tree diagrams, tables, and Venn diagrams.
(3) The student will be able to define an outcome as a subset of the sample space and diagram it using a Venn diagram.
(4) The student will be able to use mutually exclusive, complement, intersection and union to describe subsets of sample space and diagram them using a Venn diagram.
THE BIG IDEA
Probability is calculated by dividing an outcome (a subset) by the sample space (universal set) and to understand probability you need to understand how subsets work and how they interact with each other. Knowing what mutually exclusive, complement, intersection and union mean will greatly help you visualize and understand many of the probability relationships.
TRAPS & PITFALLS
There are definitely a few pitfalls found in this objective. The first is notation. The symbols for union and intersection always seem to be confusing even though I try to tell them that 'U' is for union. Also students struggle to get the concepts of union and intersection when dealing with complements. It just seems that figuring out the union between one subset and not another subset is difficult. Venn diagrams help a lot. Finally and probably the biggest pitfall - Expecting students to know what is in a deck of cards. Kids just don't play cards anymore.
The student needs to come with some basic understanding of probability. Really this is building location - from here we will introduce all of the key foundational ideas of probability.
In that this is the first objective concerning probability and it introduces the foundational concepts and ways to visualize probabilities.... everything in this objective connects to the future objectives, especially mutually exclusive, complement, intersection and union.
MY REFLECTIONS (over line l)
I guess my biggest reflection is that I needed to spend more time early one working with the visual representations of complement, intersection and union. When we started dealing with independence and conditional probability a better visual understanding of the subsets would have helped more of my students understand these more difficult idea. Slowdown early and get a real good grasp of Venn diagraming.