Post #6

In the following probability activity, students will have the opportunity to explore intersections, unions, and complements using Venn diagrams. This covers the New York State Standard HSS.CP.A.1: "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")."

My goal for this activity is to use visuals to support logical thinking. Venn diagrams are a strong visual that can help students understand relationships between sets. These graphic organize can help students solve real-world problems and understand more abstract logic skills.

Students will be expected to have knowledge of how a Venn diagram works before this lesson.

Students will receive a word bank containing the following words:

• Snow
• Ice
• Christmas
• Valentine's Day
• Easter
• Thanksgiving
• Hot Chocolate
• New Year's Day
• Snowman
• Candy canes
• Blizzard

They will sort these words into the following Venn diagram:

We will then discuss the definitions of union, intersection, and complement in the context of these Venn diagrams. 

• The definition of intersection directly relates to the visual. The set of the intersection of holidays and things related to winter are the items listed in the intersection of the two circles. This relates to the word AND. The items have to be holidays AND related to winter.
• The definition of union has to do with the word OR. The set of the union of holidays and things related to winter can be any holiday OR anything related to winter. It has to fall into at least one of those categories. So, everything listed throughout the Venn diagram is included.
• Finally, complements include items that are only ever listed in one category. It can be thought of things that are not in the category. The complement of things related to winter includes just Easter and Thanksgiving. The complement of Holidays is snow, ice, hot chocolate, snowman, candy canes, and blizzard.

Once students have seen this model, they will receive another Venn diagram. Individually, they will have to find the intersection, union, and complements of the sets.

Finally, students will be partnered up and will receive a list of items. Their task will be to come up with their own two categories and find the intersection, union, and complements of each set.

Reflection:

I like how this activity builds up from a model to more challenging levels, but each one is grounded in the same visual to help students understand more abstract logical organizational skills. I think that this activity could be great for middle school students but could be adapted for higher level math students who need to practice their logic skills for sophisticated proof writing. I think that I achieved my goal of using visuals by keeping the same visual consistent through each part of the activity.