This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

In this seminar you will learn how to simplify square roots whose radicands contain factors that are perfect squares. You will learn how to perform these operations on both integers and variables. You will be able to do this by learning how to identify factors that are perfect squares.  These will be necessary skills as you continue to perform operations that contain radical expressions.   StandardsCC.2.2.8.B.1Apply concepts of radicals and integer exponents to generate equivalent expressions.

This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

Instructional Procedures:Introduction: Introduce the topic of square roots. Discuss how square roots are used in real life (Pythagorean Theorem, find square foot of homes). Instructional strategies/activities: Discuss the complete the square through the notes. Write the examples on whiteboard. Guided practice: Have students come up front of whiteboard and solve the square roots equations. After everyone have opportunity to solve the square roots equations on whiteboard. Everyone will get to work on computers to complete their tasks provide by teachers.Closure: Explain how important the complete square roots by imply to the real life situations. Use driving distance calculation as the example.Independent practice/Evaluation procedure:  I will evaluate the participation of each students through the tasks they complete in the classroom time.Modifications for special needs students: Present the more visual clues of how to solve square roots into the simplest radical form. More attentive in case if need help. Present more notes to aid.

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.