Sound familiar? In an arithmetic class, you can point out many applications like retail markup, gas mileage, medical doses, etc. but what about algebra? For example, where will the average person make use of methods used to solve algebraic equations? Why would the average person need to know how to find the inverse of a function?

Hopefully, after viewing the examples on this site, your students will clearly see that the process of learning higher mathematics provides valuable skills in deductive reasoning and symbolic reasoning in addition to math skills used directly in science and engineering applications.

## Free Math Worksheets Using Deductive Reasoning

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 ensure 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 there 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.

## Goals for Students

Active role in learning as opposed to a passive one

Familiarization with important mathematical properties

Ability to deductively reason and construct mathematical proofs