Math Motivaton

 

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 possibly 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 site 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.

· Distribute a copy of each Property Sheet to each student.

· Before beginning each block of group exercises, review the properties that apply to these exercises and do examples.  For example, before doing the Complex Numbers Activities, review the Properties of Complex Numbers and do examples matching the properties. Have students jot down these examples in the margins or on separate sheets.

· Have students break up into their groups. Have each member responsible for a specific task in the group. Rotate the students often so roles of group members are switched and their is uniform participation.

· Reveal the exercises one at a time. Allow groups to compete to be the ones to do the problem on the board. Use a game format, extra credit, or other innovation to make this as fun as possible. My initial thought on this was to make this much like a reality TV show or game show - if you have ideas, drop me an email.

Property Sheets - Follow the links and print out a copy of each sheet for each group.
Properties of Real Numbers
Properties of Equations
Properties of Complex Numbers
Properties of Inequalities
Properties of Graphs
Properties of Functions
Properties of Polynomial Functions
Properties of Exponential and Logarithmic Functions

NOTE ABOUT PROPERTIES:  It is not important that the student be burdened with memorizing the exact property number, but rather to simply cite the property. For example, if they are citing Property BP10 to justify that (x+3)(x +1) = x2 + 3x +1x + 3, simply stating The Distributive Property should  be sufficient. Doing several steps in one seems reasonable as well so the student could state (x+3)(x +1) = x2 + 4x + 3 with justification of The Distributive Property and Like Terms May Be Combined. I shy away from using the common acronym FOIL in this example since it seems to stray away from the true property used a bit much, but with proper explanation, using FOIL as justification should be OK as well.  The objective here is to encourage a deductive approach that uses solid mathematical justification as well as to 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.
Exponents & Radicals
Factoring Review
Rational Expressions