Unit 7: Exploring Relationships with Venn Diagrams

This unit introduces the concept of set theory and operations involving sets. It will also explore the relationship between sets and Venn diagrams, in addition to using set theory to solve problems.

Unit Focus

Reading Process

Vocabulary Development

• The student will use new vocabulary that is introduced and taught directly.
• The student will listen to, read, and discuss familiar and conceptually challenging text.
• The student will relate new vocabulary to familiar words.

Writing Process

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style.

Algebra Body of Knowledge

Quadratic Equations

• Graph quadratic equations with and without graphing technology.
• Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.
• Use quadratic equations to solve real-world problems.
• Use graphing technology to find approximate solutions of quadratic equations.

Discrete Mathematics Body of Knowledge

Set Theory

• Perform set operations such as union and intersection, complement, and cross product.
• Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.

Lesson 1: Sets

We will become more familiar with Venn diagrams as a mathematical tool while learning to use operations relative to set theory.

Reading Process

Vocabulary Development

• The student will use new vocabulary that is introduced and taught directly.
• The student will listen to, read, and discuss familiar and conceptually challenging text.
• The student will relate new vocabulary to familiar words.

Writing Process

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style.

Lesson 2: Unions and Intersections

Reading Process

Vocabulary Development

• The student will use new vocabulary that is introduced and taught directly.
• The student will listen to, read, and discuss familiar and conceptually challenging text.
• The student will relate new vocabulary to familiar words.

Writing Process Strand

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style.

Discrete Mathematics Body of Knowledge

Set Theory

• Perform set operations such as union and intersection, complement, and cross product.
• Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.

Lesson 3: Complements

Reading Process

Vocabulary Development

• The student will use new vocabulary that is introduced and taught directly.
• The student will listen to, read, and discuss familiar and conceptually challenging text.
• The student will relate new vocabulary to familiar words.

Writing Process

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style.

Discrete Mathematics Body of Knowledge

Set Theory

• Perform set operations such as union and intersection, complement, and cross product.
• Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.

Lesson 4: Cartesian Cross Products

Reading Process

Vocabulary Development

• The student will use new vocabulary that is introduced and taught directly.
• The student will listen to, read, and discuss familiar and  conceptually challenging text.
• The student will relate new vocabulary to familiar words.

Writing Process

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style.

Discrete Mathematics Body of Knowledge

Set Theory

• Perform set operations such as union and intersection, complement, and cross product.

Lesson 5: Using Venn Diagrams for Three Categories

Reading Process

Vocabulary Development

• The student will listen to, read, and discuss familiar and conceptually challenging text.

Writing Process

Prewriting

• The student will prewrite by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal  organizational style.

Discrete Mathematics Body of Knowledge

Set Theory

• Perform set operations such as union and intersection, complement, and cross product.
• Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.