Performance+Assessment+1

** Due Date: Odd Periods 1/14/14 Even Periods 1/15/14 ** Your assignment is to write a student Quadrilateral Handbook. The handbook will be used as a study guide for future classes of Geometry students. Other students will use your handbook to learn about quadrilaterals and their properties. Materials needed: graph paper, straight edge, pencil, calculator, textbook, binding material Your handbook will be completed on standard graph, notebook, or printer paper and bounded. You will create one chapter for each of the five quadrilaterals: __parallelogram__, __rectangle__, __trapezoid__, __rhombus__, and __square__. Each chapter will include the following four items: 1. On graph paper, draw a coordinate plane, roughly the size of one full page. Draw the quadrilateral accurately on the coordinate plane, using any four points of your choosing. Include the diagonals. Label the (x,y) coordinates of each vertex. 2. Explain the properties of the polygon in a clear, easy-to-read format. Be sure to include the following information: · __Properties of the Sides__ (Which sides are congruent? Which sides are parallel or perpendicular?) · __Properties of the Diagonals__ (Do the diagonals bisect? Are they congruent?) · __Properties of the Angles__ (Which angles are congruent? Are there any right or supplementary angles?) 3. Prove all of the properties of the __sides__ and the __diagonals__ by applying the following formulas to the quadrilateral on your graph. Show how you arrive at your conclusions. a. Using the (x,y) coordinates of your quadrilateral, how can you use the __distance__ formula to prove the properties of the sides and of the  diagonals? b. Using the (x,y) coordinates of your quadrilateral, how can you use the __slope__ formula to prove whether the sides of your polygon are parallel,  perpendicular or neither? 4. Write three example problems, referencing your diagram, to solve for missing parts: a. Give one angle measure and calculate the remaining three b. Give one or two side lengths and calculate the remaining side lengths c. Give one diagonal section and calculate the remaining three Show how each problem is solved in a step-by-step format and reference the quadrilateral’s properties when you use one. Keep in mind you are teaching another student how to solve the problem. In the next chapter, create a summarization page that compares and contrasts each of the 5 quadrilaterals with every other. Be sure to highlight at least one similarity and one difference between each pair of polygons. In the last chapter, choose one of the quadrilaterals and write a short paragraph about an example of it in the real world. How do its properties help make that object useful or better? Example: A window and a window pane are rectangles. A rectangle has 4 right angles, which keeps the window pane “square” or insures a perfect, tight fit between the pane and the window. This is important because gaps can cause air or moisture leakage. Make your handbook look attractive and presentable for distribution to other students with you as the author. Feel free to add pictures of these polygons, either hand-drawn or taken from magazines, the internet, etc. to add interest.
 * Performance Assessment: Creating a Quadrilateral Handbook **
 * Performance Assessment: Creating a Quadrilateral Handbook **

** Scoring Rubric **

4 Demonstrates an excellent performance or complete understanding 3 Demonstrates a competent performance or general understanding 2 Makes some errors; shows incomplete understanding or misconceptions 1 Demonstrates serious errors; shows major misunderstanding


 * ** Category ** || ** Criteria **  ||  ** Points Earned (1 to 4) **  ||
 * 1. Drawings || Drawings are geometrically correct; the vertices are the proper distance apart and coordinates are labeled correctly, parallel and perpendicular sides are drawn correctly; diagonals are shown; parts are labeled correctly ||  ||
 * 2. Polygon properties || Each polygon’s properties are listed completely and accurately and are separated visually by side, angle, and diagonal properties ||  ||
 * 3. Formula application || Slope, distance, and midpoint formulas are applied correctly. The connection between the formulas and the polygon properties is well demonstrated. Every property regarding sides, diagonals, parallelism, or perpendicularity is proven by an appropriate formula. ||  ||
 * 4. Correctness of calculations || Formulas are correct and yield correct answers. No mathematical errors are made. ||  ||
 * 5. Example problems || The examples are mathematically correct and shown in step-by-step format. The polygon properties are referenced as justification for the steps, where appropriate. ||  ||
 * 6. Summarization page || The information is accurate and clearly presented. At least one comparison and one contrast is made between each polygon and every other. ||  ||
 * 7. Usefulness in teaching || The handbook would serve as a useful, complete, and accurate a guide for students who are studying the properties of polygons. ||  ||
 * 8. Presentation || The student followed the directions for creating the handbook. The handbook is well organized and easy to read. It is neat and attractive. ||  ||
 * || ** TOTAL POINTS **  ||   ||