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Free Math Worksheets Using Deductive Reasoning - Teaching Mathematics In a Group Setting

Introduction
The goal here is to have students being actively involved in the learning process and to become proficient in the deductive problem solving process.  Students will work in groups with group members switching roles constantly to insure uniform participation. Groups will compete to correctly fill in the study guides first. The students must justify all work with existing properties.

Procedure

  • Begin each class day with a motivational resource from this page or anywhere else you can find one. If there is a resource matching your objective, use that resource.  For example, for complex numbers, use the Complex Numbers Application.  If no objective-specific application is available, then use some other resource.
  • At the beginning of the lesson, review the basic properties as needed.
  • Before beginning each block of group exercises, present a fairly traditional short lecture that stresses justification of step and refers to any relevant properties and do appropriate examples. All lectures may be found here as well as from the links below. Have students take notes! The lectures I provide are in in PDF and  also in MS Word format - the MS Word files may be modified to your liking!
  • Have students break up into their groups. Present the problems from this page (or your own variations) in a step-by-step manner and have students help each other in their groups. Have each student do the problems. Walk around the room and help students as needed. Stress justification, especially early on in the course where basic algebra skills are reviewed.
  • Bonus problems are nice for livening things up. The way I do these is to award the first group to get the correct response 1 pt extra credit per member. And if an incorrect response is given then that group is disqualified. So it is a game-like atmosphere. If you find that some students are coming to this site in advance, drop me an email. and I will send you the address where there are alternate video problems.
  • As additional extra credit (or not extra credit), you can post a problem worth 1 pt at the end of the group work. This problem should be similar to the group work - this is a way to award students that are paying attention!

Property Sheets
Properties of Real Numbers
Properties of Equations
Properties of Complex Numbers
Properties of Inequalities
Properties of Graphs
Properties of Rational Functions
Properties of Functions
Properties of Polynomial Functions
Properties of Exponential and Logarithmic Functions

NOTE ABOUT JUSTIFICATION WITH PROPERTIES:  The objective here is to teach a deductive method of problem solving that serves as a basis for higher level mathematics and/or mathematical proofs. Also, this method will help familiarize students with important properties. Here is a sample of a completed group exercise.

Preliminary Activities - These are properties and operations you may wish to review in the first few class periods. You should do some examples illustrating these properties and operations. I plan on covering these in the first week without splitting students into groups.
Exponents & Radicals
Factoring Review
Rational Expressions

Group Activities Note that activities using movies are designated with  .  Activities where graphing calculators may optionally be used are designated with .
 

UPDATE: I have created two alternative sets of Bonus Questions that are saved in a different location so students can not obtain answers in advance.  If you are an instructor and would like access to these alternate problems, email me at m.sakowski@lsc.edu and I will send you a page with links to the alternates.


Complex Numbers Application - Analyzing A Car Suspension System
Lecture on Complex Numbers - PDF Form - MS Word Form
Complex Numbers - Exercise #1
Complex Numbers - Exercise #2
Complex Numbers - Bonus Question
Complex Numbers - Exercise #3
Complex Numbers - Exercise #4
Complex Numbers - Exercise #5

Lecture on Linear Equations - PDF Form - MS Word Form
Linear Equations - Exercise #1
Linear Equations - Exercise #2
Linear Equations - Application Problem - Profit in Internet Marketing
Linear Equations - Bonus Question

Lecture on Absolute Value Equations - PDF Form - MS Word Form
Absolute Value Equations - Exercise #1
Absolute Value Equations - Exercise #2
Absolute Value Equations - Bonus Question

Quadratic Application - Greenhouse Construction
Lecture on Quadratic Equations - PDF Form - MS Word Form
Quadratic Equations - Exercise #1 - Factoring
Quadratic Equations - Exercise #2 - Factoring
Quadratic Equations - Exercise #3 - Extract Square Roots
Quadratic Equations - Exercise #4 - Extract Square Roots
Quadratic Equations - Exercise #5 - Completing The Square
Quadratic Equations - Exercise #6 - Completing The Square
Quadratic Equations - Bonus Question
Quadratic Equations - Application Problem - Dimensions of a Box

Lecture on Other Equations - PDF Form - MS Word Form
Other Types of Equations - Exercise #1 - Higher Power Polynomials
Other Types of Equations - Exercise #2 - Higher Power Polynomials
Other Types of Equations - Exercise #3 - Rational Expressions
Other Types of Equations - Exercise #4 - Rational Expressions
Other Types of Equations - Exercise #5 - Radical Equations
Other Types of Equations - Exercise #6 - Rational Exponents
Other Types of Equations - Exercise #7 - Quadratic Form Equations
Other Types of Equations - Application Problem - Maximum Height of Built in Bookshelf
Other Types of Equations Bonus Question

Lecture on Inequalities - PDF Form - MS Word Form
Inequalities - Exercise #1
Inequalities - Exercise #2
Inequalities - Exercise #3
Inequalities - Exercise #4
Inequalities Bonus Question

Lecture on Variation - PDF Form - MS Word Form
Application of Variation - An Accident Scene
Variation - Exercise #1
Variation - Exercise #2
Variation Bonus Question
Variation - Application Problem - Stream Current Experiment

Lecture on Elementary Graphing - PDF Form - MS Word Form
Elementary Graphs - Exercise #1 - The Distance Formula
Elementary Graphs - Exercise #2 - The Circle Formula

Lecture on Intro To Functions - PDF Form - MS Word Form
Application of Functions - Functions and National Security
Definition of Functions - Exercise #1 - Evaluating a Function
Definition of Functions - Exercise #2 - Evaluating a Function
Definition of Functions - Exercise #3 - Finding The Domain
Definition of Functions Bonus Question

Lecture on Intro to Graphing of Functions - PDF Form - MS Word Form
Intro to Functions Graphs - Exercise #1 - Identifying Functions & One-to-One Functions
Intro to Functions Graphs - Exercise #2 - Graphing a 2-part Function
Intro to Function Graphs - Exercise #3 - Graphing a Polynomial

Lecture on Linear Functions - PDF Form - MS Word Form
Linear Functions - Exercise #1 - Finding an Equation
Linear Functions - Exercise #2 - Finding an Equation
Linear Functions Bonus Question

Lecture on Function Graphing Rules - PDF Form - MS Word Form
Graphs of Functions - Exercise #1 - Determining Even or Odd and Graphing
Graphs of Functions - Exercise #2 - Determining The Equation of a Function's Graph
Graphs of Functions - Exercise #3 - Determining The Equation of a Function's Graph
Graphs of Functions - Exercise #4 - Determining The Equation of a Function's Graph
Graphs of Functions - Exercise #5 - Determining The Graph Using Function Properties
Graphs of Functions Bonus Question

Lecture on Graphing Quadratic Functions - PDF Form - MS Word Form
Graphs of Quadratic Functions - Exercise #1 - Standard Form
Graphs of Quadratic Functions - Exercise #2 - Graphing Using Vertex Formula
Graphs of Quadratic Functions - Exercise #3 - Solving a Maximum Minimum Problem
Graphs of Quadratic Functions Bonus Question
Quadratic Functions - Application Problem - Archery

Lecture on Function Operations - PDF Form - MS Word Form
Algebra of Functions - Exercise #1 - Function Operations
Algebra of Functions - Exercise #2 - Composition of Functions
Algebra of Functions - Exercise #3 - A Special Composition of Functions
Algebra of Functions - Bonus Question

Lecture on Inverse Functions - PDF Form - MS Word Form
Inverse Functions - Exercise #1 - Verifying Inverses
Inverse Functions - Exercise #2 - Finding an Inverse Function
Inverse Functions - Exercise #3 - Graphing Inverse Functions
Inverse Functions Bonus Question
Inverse Functions - Application Problem - Fixing an Egg Beater

Lecture on Polynomial Division & Factoring - PDF Form - MS Word Form
Polynomial Application - How Polynomials Power Our Calculators and Computers
Polynomial Division and Factorization - Exercise #1 - Polynomial Division
Polynomial Division and Factorization - Exercise #2 - Synthetic Division
Polynomial Division and Factorization - Exercise #3 - Justify Synthetic Division
Polynomial Division and Factorization - Exercise #4 - Remainder Theorem
Polynomial Division and Factorization - Exercise #5 - Factor a Polynomial
Polynomial Division and Factorization - Exercise #6 - Factor a Polynomial
Polynomial Division and Factorization Bonus Question

Lecture on Graphing Polynomials - PDF Form - MS Word Form
Polynomial Graphs - Exercise #1 - Graphing a Factorable Polynomial
Polynomial Graphs - Exercise #2 - Predicting The Graph of a Non-Factorable Polynomial
Polynomial Graphs - Exercise #3 - Graphing a 3rd Degree Polynomial
Polynomial Graphs - Exercise #4 - Find The Equation From a Polynomial Graph
Polynomial Graphs Bonus Question

Lecture on Advanced Polynomial Properties - PDF Form - MS Word Form
Polynomial Advanced Properties - Exercise #1 - Listing Rational Zeros
Polynomial Advanced Properties - Exercise #2 - Rational Zeros and Descartes' Rule of Signs
Polynomial Advanced Properties - Exercise #3 - Upper and Lower Bounds
Polynomial Advanced Properties - Exercise #4 - Factoring a Polynomial
Polynomial Advanced Properties - Exercise #5 - Complex Conjugate Zeros

Lecture on Rational Functions - PDF Form - MS Word Form
Rational Functions - Exercise #1 - Graphing a Rational Function
Rational Functions - Exercise #2 - Graphing a Rational Function
Rational Functions - Exercise #3 - Graphing a Rational Function Having Slant Asymptotes
Rational Functions - Exercise #4 - Explanation of a Horizontal Asymptote Rule
Rational Functions - Exercise #5 - Explanation of a Slant Asymptote Rule
Rational Functions - Bonus Question
Rational Functions - Application Problem - Ohm's Law

Lecture on Exponential Functions - PDF Form - MS Word Form
Exponential Functions - Application Problem - Penny Doubling Problem
Exponential Functions - Exercise #1 - Graphing an Exponential Function
Exponential Functions - Bonus Question
Exponential Functions - Exercise #2 - Exponential Growth in Compounded Interest
Exponential Functions - Exercise #3 - Deriving The Formula For Continuous Compounding

Lecture on Logarithmic Functions - PDF Form - MS Word Form
Logarithmic Functions - Exercise #1 - Converting Log Form to Exponential Form
Logarithmic Functions - Exercise #2 - Converting Exponential Form to Log Form
Logarithmic Functions - Exercise #3 - Graphing Log Functions
Logarithmic Functions - Bonus Question
Logarithmic Functions - Exercise #4 - Applying Properties of Logs
Logarithmic Functions - Exercise #5 - Applying Properties of Logs

Lecture on Exponential and Log Equations - PDF Form - MS Word Form
Exponential & Log Equations - Exercise #1 - Solving Exponential Equations
Exponential & Log Equations - Exercise #2 - Solving Exponential Equations
Exponential & Log Equations - Exercise #3 - Solving Log Equations
Exponential & Log Equations - Exercise #4 - Solving Log Equations
Exponential & Log Equations - Bonus Question

Lecture on Exponential and Log Applications - PDF Form - MS Word Form
Exponential & Log Applications - Exercise #1 - Population Growth
Exponential & Log Applications - Exercise #2 - Inflation of Housing Costs
Exponential & Log Applications - Exercise #3 - Acid Rain
Exponential & Log Applications - Bonus Question
Exponential Functions - Application Problem - The National Debt
Feel Free To Print Out, Copy, Or Modify These Free Math Worksheets As You See Fit

A breakdown of my tentative plan for assessment is given here.

A Groupwork FAQ's Page is given here.

An example of how to split a class into groups is given here.

 

 

 

 

 

 

 

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