Post #5

 Earlier this fall, I taught my 9th graders how to categorize real numbers using Venn diagrams. The students used art supplies to create a representation of the categories of real numbers using Venn diagrams. The previous day, they had learned the definition of each of the categories and seen examples of each. Once they made a Venn diagram, I have them a bank of numbers and asked them to write the numbers in the most specific category. The purpose of this activity was to deepen students understanding of how to use Venn diagrams to organize information logically into categories and subcategories and to assess their understanding of the categories of real numbers. My goal here was to engage my students in a hands-on activity that would be a variation from a typical worksheet.

This activity covers the following New York Stand Standard: AI.N.RN.3b: Categorize the sum or product of rational and irrational numbers.

The students had their definitions from the previous lesson to guide them:

The set of Real Numbers is made up of rational and irrational numbers.

Irrational Numbers: Non-terminating and non-repeating decimals.

Rational Numbers: Numbers that can be written as a ratio of integers (terminating and repeating decimals are included).

Integers: Whole numbers and their negatives.

Whole Numbers: Counting numbers including 0.

Natural Numbers: Counting numbers not including 0.

Students were familiar that some categories were subsets of other categories. During the previous lesson, we had discussed that 1 is a natural number, whole number, integer, rational number, and real number, but 2/3 is only a rational number and a real number. The goal was for students to represent these kinds of relationships in Venn diagrams. A correct example is below:

After students had successfully created a Venn diagram, they were given numbers to categorize into different areas of the diagram. They had to put each number into the most specific category. For example, putting 2 into the integers circle, outside the whole number and natural number circles, would not be the most specific place it could go. This further solidified their understanding that some categories fully contain others.

Reflection: This was an activity that I did during my first week of teaching. Next year, I have a lot of improvements that I would like to make to this activity. I found that the task was too big for many of the students to tackle at once. I may dissect this activity further and ask students to make a Venn diagram for just natural and whole numbers first. But overall, it did add a creative aspect to the class which not only engaged different kinds of learners but made the content more memorable as well. Let me know if you have any other tips for me when I do this next year!