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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.

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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