The purpose of this curriculum guide is to provide OER lesson material and support activities for Pythagorean Theorem instruction. It is geared towards GED® requirements. Both printable and online options are provided.
This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.
This lesson unit is intended to help teachers assess how well students are able to: use the area of right triangles to deduce the areas of other shapes; use dissection methods for finding areas; organize an investigation systematically and collect data; deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem.)
This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to: use facts about the angle sum and exterior angles of triangles to calculate missing angles; apply angle theorems to parallel lines cut by a transversal; interpret geometrical diagrams using mathematical properties to identify similarity of triangles.
This lesson unit is intended to help teachers assess how well students are able to: recognize and visualize transformations of 2D shapes; and translate, reflect and rotate shapes, and combine these transformations. It also aims to encourage discussion on some common misconceptions about transformations.
An interactive applet and associated web page that show the definition and properties of a rectangle in coordinate geometry. The applet has a rectangle with draggable vertices. As the user re-sizes the rectangle the applet continuously recalculates its width, height and diagonals from the vertex coordinates. Rectangle can be rotated on the plane to show the more complex cases. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a rectangle when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Mrs. Lu has asked students in her class to find isosceles triangles whose vertices lie on a coordinate grid. For each student example below, explain wh...
Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form of x2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.
This task requires students to apply the Pythagorean Theorem.
Students use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.