Standard 5 : Apply properties from Set Theory to solve problems.



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General Information

Number: MA.912.LT.5
Title: Apply properties from Set Theory to solve problems.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Logic and Discrete Theory

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.LT.5.1: Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.
MA.912.LT.5.2: Given a relation on two sets, determine whether the relation is a function, determine the inverse of the relation if it exists and identify if the relation is bijective.
MA.912.LT.5.3: Partition a set into disjoint subsets and determine an equivalence class given the equivalence relation on a set.
MA.912.LT.5.4: Perform the set operations of taking the complement of a set and the union, intersection, difference and product of two sets.
Clarifications:
Clarification 1: Instruction includes the connection to probability and the words AND, OR and NOT.
MA.912.LT.5.5: Explore relationships and patterns and make arguments about relationships between sets using Venn Diagrams.
MA.912.LT.5.6: Prove set relations, including DeMorgan’s Laws and equivalence relations.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Taxes using Venn Diagrams, Lesson 1:

Students will review constructing and solving Venn diagrams with two and three data sets. Students will then convert text about the collection of taxes from the local, state, and federal governments into a Venn diagram. This is lesson 1 of a three-part integrated mathematics and civics mini-unit.

Taxes using Venn Diagrams, Lesson 2:

Students will discuss, recognize, and be challenged to list unions, intersections, and complements related to a Venn diagram created by three data sets. The data is the type of taxes assessed to citizens by the local, state, and federal governments. This is the second lesson in a 3-part integrated mathematics and civic mini-unit.

Can You Walk in My Shoes?:

Students use real-life data to create dot-plots and two-way tables. Students will collect data at the beginning of the lesson and use that data to create double dot plots and frequency tables, finding and interpreting relative frequencies.

The assignment allows students to work collaboratively and cooperatively in groups. They will communicate within groups to compare shoes sizes and ages to acquire their data. From the collection of data they should be able to predict, analyze and organize the data into categories (two-way tables) or place on a number line (dot-plot).

As the class assignment concludes, a discussion of the final class display should take place about the purchasing of shoes versus ages and the relationship that either exists or doesn't exist.

Human Venn Diagram:

Students will physically interact with Venn diagrams. The students will physically interact with Venn diagrams; the students in the class become the data to arrange. Students will physically move and see how and why elements belong in each section of the Venn diagram.

Perspectives Video: Expert

Name Description
B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.