Browse the PA State Standards

Browse the PA state standards and select the standards on which you would like to base your unit. In a separate document, write two to three paragraphs explaining how your unit of instruction supports local guidelines and student academic content standards. Remember to submit this with your task.

Geometry:

Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.

Draw, label, measure and list the properties of complementary, supplementary and vertical angles.

Classify familiar polygons as regular or irregular up to a decagon.

Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.

Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles).

The standard that I wish to base my unit is on the standards that apply for geometry for grade 8 mathematics. Geometry is one of the most crucial components for the 8th grade level because it supports understanding of higher mathematics at the high school level. Not only is it a very basic component of understanding calculus and linear algebra, but it is the fundamental basis for most science and computer technology classes as well.

The unit that I will create focuses on exploring the properties of the polygon. The polygon has many unique properties and it is a very important unit because it shows students that the squares, rectangles and even circles that they are so familiar with fits within the framework of a greater geometrical understanding, polygons. This essentially ties together all of the random "shapes" that they have had to master into a unified rule for application. According to Pennsylvania standards students need to be able to perform five different functions for polygons, they have to be able to classify polygons as regular or irregular up to the decagon. Identify, name and draw the properties of many different polygons. The unit that I will construct focuses on teaching students the tools necessary for constructing and understanding the properties of polygons. It shows the universality of these shapes and how they can be constructed in accordance with their specific characteristics. My focus will be on understanding the "universal" application of polygons and then applying them to specific shapes so that students do not engage in "memorization" so much as understanding of the root concept of polygons.

My unit fits specifically into the purpose of the PA standards for 8th grade math, and specifically attacks the need for students to have strong geometry experience going into high school. Therefore this unit is critical for the success of students in general and especially when focusing in core understanding.

B. Write four instructional goals for your unit (two for each lesson plan). Enter the goals in the Objectives field in the Unit and Lesson Builder templates.

Unit: Understanding the properties of a polygon (Geometry)

Lesson Plans:

Focus on polygons

Goals:

Understand what makes an object a polygon

Actual definition of polygon

Identify different polygons by name

Understand formula for basic polygon for parameter and area (rectangle, pentagon, hexagon, etc.)

How to construct a polygon make a rectangle make a polygon of more than 6 points measurement of circumference and area in construction

Understanding Squares

Goals:

Understand special properties of squares

Define square in context of polygon

Understand the equal properties of squares

Being able to construct a square

Understand calculating properties of a square calculate area of square using "square rule" calculate parameter of square (width x 4) calculate diagonal of square (pythagoran equation)

C. Write twelve measurable objectives (three for each goal). Enter the objectives in the Objectives field in the Unit and Lesson Builder templates.

D. Browse the sites given below, as well as any Internet resources you may be aware of, for ideas related to the Procedures section of your lesson plans. Review two separate Internet resources. In a separate document, write two or three paragraphs, per source, evaluating the resource by at least three of the following standards: age-appropriateness, the accuracy of the content, usability of the resource in the classroom, and the accommodation of different learning styles. Cite the resources you evaluated. http://www.scienceu.com/geometry/classroom/buildicosa/index.html

This resource is very good for my lesson plan because it focuses on engaging students in the actual properties of a polygon. It is age appropriate at the 8th grade level for several reasons. First it is a very sophisticated project in that the instructions for constructing this polygon is complex, therefore it takes high cognitive skills in order to build such a project. It is ambitious enough that the entire class is engaged and that at this grade level students will have enough knowledge to be both challenged in its construction while still feeling that they are doing something productive and not overwhelmed.

The content is very pertinent to the discussion of polygons by identifying that constructing a polygon requires not only understanding that there are many points but that there are precise mathematical instructions for the properties of a polygon. This exercise applies both the math as well as the theory behind polygons together into an interactive exercise which makes it very accurate in allowing students to practice precisely how they are going to build their polygon.

Finally, it accommodates many different types of learning styles because it engages students on different levels. For students who learn through repetition, this exercise forces students to do the mathetical concepts over and over again in order to perfect the polygon. Students who are at a lower level will be intrigued by the building stage of this exercise and thus still be actively engaged and better understand the concept because it is engaging. While students who are already exceeding this level will be challenged by the interactivity and the actual immensity of the project and can engage from a project management perspective. Thus this project fully utilizes the skill levels of all students in the class and blends the sophisticated with the simplistic at the same time. http://www.scienceu.com/geometry/activities/tetrapuzzles/index.html