Two-Way Tables and Venn Diagrams (Lesson 5.3)

Chapter 5 - Day 3

Learning Targets
  • Use a two-way table to find probabilities. 
  • Calculate probabilities with the general addition rule. 
  • Use a Venn diagram to find probabilities. 
Activity: Can You Taco Tongue and Evil Eyebrow?
Activity:
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Experience First

To start, you will want to make sure students are familiar with taco tongue and evil eyebrow. It’s best if you model each of these for your students. If you aren’t quite this talented, you can use these images:

 

 

 

 

 

 

The first part of this activity is the fun part. Have students work in pairs. Each student needs to decide if their partner is a "Yes" or "No" for Taco Tongue and a "Yes" or "No" for Evil Eyebrow. Students then go to the front whiteboard to record the data by recording a tally mark for themselves in the correct part of the two-way table. 

Here are some important teaching tips to keep in mind:

  • Students may get confused about how the two-way table works. They often think they need to put two tally marks on the board (one for Taco Tongue and one for Evil Eyebrow). Inform them that they are each only putting 1 tally mark on the board and there are four possibilities (Yes/Yes, Yes/No, No/Yes, and No/No). 

  • This activity works best if there are nonzero values for all four cells in the two-way table. If you notice one cell is empty, you might decide to “include Mrs. Stecher from the next classroom over who just happens to fall into that category”.

Ask students to give all answers as unreduced fractions for the activity today. This will help make the debrief cleaner.

Formalize Later

Make sure to point out the close connection between the two-way table and the Venn Diagram (after all, they are totally BFFs). You can also use this example to define the 4 regions of a Venn Diagram: left pacman, the football, the right pacman, and the outside.

When you get to question #3, give students a visual representation of the probabilities:​

  • "If you are Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are No Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are Yes Evil Eyebrow OR No Evil Eyebrow, please stand up." Count them out loud then have them sit.

No problem here. We could have simply added the counts from the first two groups.


When you get to question #4, give students a visual representation of the probabilities:

  • "If you are Yes Taco Tongue, please stand up." Count them out loud then have them sit.

  • "If you are Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are Yes Taco Tongue OR Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.


Big problem here. We can't simply add the counts from the first two groups. Why not? Because some people were double counted (like Turner)! Call out the names of the students that were double counted and have them stand (these are the most talented people in the room). Subtract them out and you will arrive at the correct answer. The purpose of this activity is to get students thinking and reasoning about the General Addition Formula, rather than just memorizing a formula (Experience First, Formalize Later).

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