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How to Engage Adult Students in the Pythagorean Theorem

In Mathematics, the use of theories and formulas is common practice. The Pythagorean Theorem is a geometric theory used in the calculations of right triangles. The Pythagorean Theorem states that the sum of the squares of the two sides of the right triangle is equal to the square of the hypotenuse. The hypotenuse is the side opposite the right angle. The equation for Pythagoras’ Theory is a2 + b2 = c2.

As you work with your students, it is important to ensure that they understand all of the terminology, know the equation and how to properly create and label diagrams for problem solving. Your lessons should allow numerous opportunities for students to practice with word problems and diagrams. This can be accomplished through a combination of classroom instructional activities and online practice.

### Instructional Activities

Instruction on the Pythagorean Theorem should not be limited to mere lecture and note-taking. Creating opportunities for your students to engage with the information will yield a greater chance for success. Some ideas for classroom activities are:

#### How Big is the Screen?

Televisions, tablets and cell phone screens are measured on the diagonal. Create a lesson that allows students to use the theorem to measure the screen sizes of various electronics, including their own.

#### Problem Centered Practice

Studies have shown that learners learn and retain information that is used to solve a problem. Teach the theory using problems that are related to real life. Examples include determining television size for a particular space, ladder usage to reach certain windows or roofs, and calculating distances on a road trip.

#### Open Discovery

Consider allowing students to discover the theory on their own. Start the lesson by providing a problem to be solved. Allow students to work through various ways of solving the problem using the tools you provide. Follow their attempts with direct instruction and additional practice once the concept has been formally learned. An example of this open discovery lesson can be found on The Teaching Channel.

### Online Practice

Many effective tools for review and practice of the Pythagorean Theorem can be found online. You can choose resources that demonstrate the content in a particular way that best aligns with your students’ learning styles. You may also opt to access a variety of sites so that your students get used to seeing the theory in practice in many different applications. A few online resources include:

• Khan Academy offers in depth math tutorials for students of all ages. The videos are organized by concept and feature multiple episodes for additional instruction. The videos feature an instructor writing notes and sharing examples on the board, just as in a classroom. An area for interactive practice is also available.
• Regents Prep provides multiple choice practice questions for student practice. Given the information in the word problems and diagrams, students are required to use the theory to provide correct answers. Each question also features an explanation of how the correct answer is derived.
• Braining Camp delivers multiple activities for the Pythagorean Theorem. A lesson provides visual models accompanied by audio narration. The second activity offers an opportunity to work with manipulatives to demonstrate the proof. The remaining activities offer students a chance to practice their skills through questions and problem solving.

The Pythagorean Theorem can be taught and reinforced in a number of ways. Exposure in a myriad of settings will allow students to build their confidence in applying the skill. The theory moves from a seemingly foreign concept to a practical function, correlated with regular life activities.