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Secondary Math Lesson Plans9 chapters | 176 lessons

Instructor:
*Christopher Muscato*

Chris has a master's degree in history and teaches at the University of Northern Colorado.

With this lesson plan, your students are going to explore the concepts of sets, Venn diagrams and probability. They will apply their knowledge by organizing and analyzing a collection of data.

Upon completion of this lesson, students will be able to:

- Define the concept of sets and Venn diagrams
- Distinguish between mutually exclusive and non-mutually exclusive events
- Organize a collection of data into sets and determine probability

90-120 minutes

- CCSS.MATH.CONTENT.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

- CCSS.MATH.CONTENT.6.SP.B.5

Summarize numerical data sets in relation to their context.

- CCSS.MATH.CONTENT.6.RP.A.3.C

Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

- Copies of the lesson quiz
- Lists of 50 animals that live in the Amazon Rainforest
- Basic calculators

- Start by giving students a list of 50 animals that are found in the Amazon Rainforest. Ask students to look over the list.
- Imagine you are a scientist whose job is studying the diversity of animals in the Amazon. You've encountered all of these animals, so how do you begin to organize all of this data? How do you turn this list into something useful?

- Begin the video lesson Set Theory, Venn Diagrams & Exclusive Events.
- Pause the video at 1:53 and discuss this information as a class.
- What is a set of data? How are sets identified?
- Why are Venn diagrams useful? How might a scientist use a Venn diagram to study sets? How might a mathematician use a Venn diagram to study sets?

- Resume and complete the video. Discuss this information as a class.
- What does it mean for two things to be mutually exclusive? Look at the list of animals in the Amazon. If we were to organize these into mutually exclusive sets, what might we come up with? (Try to encourage students to consider things like mammals vs. birds, things with scales vs. things with fur, things that only eat meat vs. things that only eat plants).

- You may test student understanding with the lesson quiz.

- Break the class into small groups.
- Inform students that they are going to organize their list of Amazon animals according to three different criteria, according to the following instructions (which should be written on the board):
- First, select two mutually-exclusive sets (i.e. mammals and amphibians). Go through the list of animals and write, in brackets, the elements of each set. Draw two circles, and place the elements of each set in the corresponding circle.
- Next, select two non-mutually exclusive sets (i.e. things with fur and things that are black). Go through the list of animals and write, in brackets, the elements of each set. Remember that since these are non-mutually exclusive, a single animal may be an element in each set. Create a Venn diagram, and place the elements of each set in the corresponding circle, being aware of what overlaps.
- Third, select two different non-mutually exclusive sets and create a third Venn diagram with those elements.

- Give students time to create their Venn diagrams.

- Cover the concept and basic rules of ratios and probability. If there are 100 coins, and 50 of them are pennies, there is a 50 out of 100 chance of randomly selecting a penny. Teach students how to calculate this using a calculator.
- Students will then go through each of their three charts from the prior activity, and calculate the probability of encountering the animals in each set while in the Amazon. Each set should be calculated based on the entire list of 50 animals. Each chart will ultimately produce four calculations:
- The probability of encountering animals from Set A
- The probability of encountering animals from Set B
- The probability of encountering animals from either Set A or Set B (add both numbers)
- The probability of encountering animals from both Set A and Set B (use the number from the intersecting portion of the Venn diagram) - Note: for the mutually exclusive chart, the probability of encountering both will be zero.

- Once students have completed this, talk about their results. What did they see? How is this useful? How did would this help a researcher organize and understand their data about animals in the Amazon?

- As an out-of-class extension, ask students to select one of their Venn diagrams and add a third set to it. They will go through the list of 50 animals, identify the animals that fit into that set, and create a Venn diagram with a third circle. They will also calculate the probability of encountering animals in Set C, as well as the overlap AC, BC, and ABC.

Mutually Exclusive Events & Non-Mutually Exclusive Events

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