**Title**

Ve Vant Your Blood (Greta Lawlor)

**Goals**

1) Students will explore the concept of sets using Venn diagrams to problem solve.

2) Students will be able to present and justify their solution using Venn diagrams.

**Abstract**

This activity asks students to use the concept of Venn diagrams to categorize patients according to blood type and antigens. They are given uncategorized data from a hospital and asked to determine the total number of patients, the number of each blood type, and those with exactly two antigens. The students are expected to present and justify their solution with Venn diagrams.

**Problem Statement**

Discuss with your students how many people they know who have needed blood because of an accident or surgery, etc. Help the students to articulate the fact that each of us belongs to a certain blood group and within that blood group is a subgroup depending on antigens. Go over the explanation in the problem of blood types and antigens and have the students use Venn diagrams to help them find and justify a solution.

**Instructor Suggestions**

1) Discuss with the students any part or parts of the problem which may give them trouble. In the discussion, make sure they understand the different blood types and antigen types.

2) Have students form small groups.

3) Distribute "Ve Vant Your Blood" handout with a transparency and a marker.

4) Have one group share their answer and then ask other groups who did it differently to share their work.

**Materials**

"Ve Vant Your Blood" activity sheet, transparencies, markers.

**Time**

Introduction (5 min.) small group work (25 min.), presentation and large group presentation (20 min.)

**Mathematical Concepts**

*Discrete Mathematics Concepts*

Counting, logic and sets

*Related Mathematics Concepts*

Categories and relationships, problem solving, set theory

**NCTM Standards Addressed**

Problem Solving, Communication, Reasoning, Discrete Mathematics

**Colorado Model Content Standards Addressed**

Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

**Curriculum Integration**

This activity would be useful in an Algebra 1 class when discussing sets. It could also be extended to use in a Probability and Statistics course.

**Further Investigation**This activity could be extended by using the percentages of each blood type in the population as a whole to make inferences in the classroom and from the data in the activity.

**Variations/Comments**

This activity is relatively simple as an exercise in set theory, but could easily be extended to the entire population or the classroom and would easily extend into probability and statistics. A simpler version could be done before the activity using hair color, gender, eye color or other easily categorized attributes for a collection of items.

**References/Resources**

Herr, Ted, & Johnson, Ken. __Crossing the River With Dogs and Other Mathematical Adventures__. Key Curriculum Press, 1994.

Kenney, M.J., & Hirsch, C.R. (Eds.) 1991. __Discrete Mathematics Across the Curriculum__, __K-12.__ Reston, VA: National Council of Teachers of Mathematics.