Set Theory and Logic Unit Plan
Set Theory and Logic
Site: | ARPDC |
Course: | ERLC Math 30-2, 2012-2014 - Candace Ketsa (Click to Enter) |
Book: | Set Theory and Logic Unit Plan |
Printed by: | Guest user |
Date: | Sunday, 1 September 2024, 3:52 AM |
Introduction to Set Theory and Logic
General Outcome: Develop critical thinking skills related to uncertainty.
SO1. Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies. [CN, ME, PS, R]
1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
- guess and check
- look for a pattern
- make a systematic list draw or model
- eliminate possibilities
- simplify the original problem
- work backward
- develop alternative approaches.
1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.
2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.
2.4 Determine the elements in the complement, the intersection or the union of two sets.
2.5 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.
2.6 Identify and correct errors in a solution to a problem that involves sets.
2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.
Mathematical Processes
- Connections [CN] Students are expected to make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines
- Problem Solving [PS] Students are expected to develop and apply new mathematical knowledge through problem solving
- Reasoning [R] Students are expected to develop mathematical reasoning
- Visualization [V] Students are expected to develop visualization skills to assist in processing information, making connections and solving problems.
- Mental Estimation [ME] Students are expected to demonstrate fluency with mental mathematics and estimation.
Types of Sets and Set Notation
Achievement Indicators
2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context, and explain the reasoning.
2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.
2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.
2.4 Determine the elements in the complement, the intersection or the union of two sets.
2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.
______________________________________________________________________
Discovery Based Learning Ideas:
1. Sets and Venn Diagram (Applet) - (Interactivate) [T]
This interactive helps students understand the terms surrounding the ideas of sets and Venn Diagrams. It also helps them understand how to arrange items in a Venn diagram.
_______________________________________________________
Lesson Links:
- Click here for ERLC Lesson Link (pdf). Please use this lesson as a framework for your own teaching environment.
______________________________________________________________________
Assessment For Learning Ideas:
1. Venn Research [CN] -- Have students find Venn Diagrams in the newspapers or internet. Once they find an example have them create questions that include the terminology empty set, disjoint sets, subsets, and universal sets. Have them provide an answer key to those questions.
_______________________________________________________
Additional Resources:
- Click here for More math notes on an Introduction to Sets (Tools4Teachers)
Exploring Relationships between Sets
Achievement Indicators
2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning. [V] [R]
2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation. [V] [C]
2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.
______________________________________________________________________
Discovery Based Learning Ideas:
1. Operations on Sets
-
- Operations on Sets from the Wolfram Demonstrations Pr
- Click here to download a student assessed exploration that can be used with this applet.
______________________________________________________________________
Lesson Links:
- Click here for ERLC Lesson Link (Notebook). Please use this lesson as a framework for your own teaching environment
_________________________________________________________
Assessment For Learning
1. Student Created Assessment [CN], [V] -- Have students think of two sets that will have some overlap and create a Venn Diagram. If students have troubles thinking of an idea, direct them to the Explore the Math on page 19. Have the students describe the four areas of the Venn diagram using the Venn Diagram they created.
______________________________________________________________________
Additional Resources to Support this Lesson
- Click here for more notes Venn Diagrams (Purple Math)
- Click here for some work sheets on Venn Diagrams (Enchanted Learning)
- Click here for an interactive for creating easy Venn Diagrams (Applet)
- Click here for some practice problems on Venn Diagrams (NLVM)
- Click here for a interactive for finding the shaded regions of two or three intersecting Venn Diagrams (Wolfram)
_____________________________________________________
Videos:
for a General video for this lesson (Youtube)
for a video on Introduction to Venn Diagrams (YouTube)
for a video on Solving problems using Venn Diagrams (Youtube)
Click here for a video on Misusing Venn Diagram (Rachell Maddow Show)
Intersection and Union of Two Sets
Achievement Indicators:
2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.
2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.
2.4 Determine the elements in the complement, the intersection or the union of two sets.
2.5 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.
2.6 Identify and correct errors in a solution to a problem that involves sets.
2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.
______________________________________________________________________
Discovery Based Learning:
1. Click here for an interactive that shows a basic example of two sets that must intersect -- Basketball and Volleyball. (Tools4Teachers) You will need to have an account with Tools4teachers to access this interactive.
2. Click here for a Venn Diagram Applet (Java Web Technology)
_________________________________________________________
Lesson Links:
- Click here for ERLC Lesson Link. (Notebook) Please use this lesson as a framework for your own teaching environment.
_________________________________________________________
Assessment For Learning
1. Set Theory Worksheet -- Chang (Word document). This worksheet is a great way for students to be creative and get a true understanding of sets and set notation. [V], [CN] (Standard of Excellence)
2. Virtual 3-set Venn Diagram Manipulative (Standard of Excellence) -- This is a nice tool to practice set notation and shading corresponding areas of the venn diagram.
3. Exit Slip Questions
-
- Have students draw Venn diagrams for P ∩ Q, P ∩ Q’, P’ U Q, P’ U Q’. [V] (Acceptable Standard)
-
- Venn diagrams are useful when three subsets are given. Construct such a diagram, given the subsets P, Q, and R. Identify each of the eight resulting areas in terms of P, Q, and R. Use the appropriate set theory symbols. [V, R] (Standard of Excellence)
_________________________________________________________
Extending Your Thinking
1. The Egg Man -- Click here to link you to an activity that challenges students in the union and intersection of sets. It is fun and creative.
_________________________________________________________
Videos:
General video for this lesson (Youtube)
Applications of Set Theory
Achievement Indicators
2.5 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.
2.6 Identify and correct errors in a solution to a problem that involves sets.
2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.
______________________________________________________________________
Lesson Links:
- Click here for ERLC Lesson Link (Notebook). Please use this lesson as a framework for your own teaching environment.
______________________________________________________________________
Videos:
General video for this lesson (Youtube)
In this section are complete unit lessons shared by colleagues:
1. Click here to download Notebook Lesson shared by Boulanger
Click here to download Word Document of the Student notes that go with the Notebook Lessons shared by Boulanger
Summative Assessments
Click here to assess the summative assessment area. You will need an enrolment key to access this portion of the site. Please email cketsa@gsacrd.ab.ca for access.
Below is a list of what is available for the Unit.
_______________________________________________________________________________________________________________________
Assignments
1. Unit Assignment with Answer Key (PDF) -- Ketsa
Quizzes
1. Logic - UNIT QUIZZY -- Anderson
2. Set Theory Quiz (Both Word and PDF) -- Degiuseppe
Exams
1. Unit Exam with Blueprint and Answer Key (PDF) -- Ketsa