To learn the pattern of the side lengths of a 45-45-90 triangle, students complete a gallery walk, a card sort activity starting with using the Pythagorean theorem, and activity to locate if there is an error in a presented problem and if so to identify what the error is.

The lesson will provide a conceptual basis for illustrating the parallelism between solving multi-step equations and translating literal equations into solutions for specified variables.

Students will prove: Two triangles are congruent using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates.

This lesson is a student discovery lesson that culminates in square root regression with technology. Students will use their study of inverses, the relationship between quadratic and square root functions, their previous knowledge of regression, and determine how to find the square root regression of real-world data.

The students will be able to graph quadratic functions using key attributes of quadratic equations.