Here is the presentation that guides this section: Union and Intersection.pptx
I start off the conversation around the symbols for intersection and union and support the idea with Venn Diagrams, analogy and finally practice problems. I find that the Venn Diagram is very helpful in describing the ideas of intersection and union. Without this visual tool, students confuse the two definitions, where intersections include everything that groups have in common and unions include everything in either group. I find that any variation of this explanation is almost useless with the Venn Diagram visual.
For the analogy, I might try something simple, like if have your class and another, the intersection would be empty and the union would include everyone from both classes. However, if the two groups are basketball and football teams, the intersection would be the players who play both sports and the union would be every player who plays basketball or football or both.
Then, we will begin to work on some of the sample questions in the presentation. The major hurdle for students is to find various efficient ways of finding answers. For example, in question 1 we are looking for the intersection of A and B and C. Without reading every value, we can eliminate choice 1, because 1 is not in all three sets. So, once we identify a single element not in all three groups, we move on to the next choice.
For this part of the lesson, students pick union and intersection questions from this packet:
They are allowed to try topics that we have not yet explored, but my goal is to focus specifically on questions that deal with a the intersection and union (and not so much the subset and complement).
For this part of the lesson, we review student misconceptions and algorithms. One interesting issue that frequently comes up is that many students find a union or intersection that is partially true. For example, many students circle choice 1 on question 3 because the element 5 is part of the intersection of A, B and C. However, students need to understand that the intersection of A, B and C must include all elements in the intersection, not just one. So on question 3, many students gravitate towards choice 1 since the number 5 is all three sets. Students should consider all the variables.