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 objectivespecific 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 stepbystep 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 gamelike 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 & OnetoOne Functions
Intro to Functions Graphs
 Exercise #2  Graphing a 2part 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 NonFactorable 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.
