Multi-Media Lesson: Area of Circles and Probability

Multi-Media Lesson: Area of Circles and Probability

Summary

Unit Name: Measurement of Two-Dimensional Figures

Lesson Name: Area of Trapezoids

Teacher Name:Joan Carter

Grade Level:8th Grade, Pre-Algebra

Classroom Layout:Students will work individually or in pairs on wireless laptops.

Prerequisite Knowledge of Students: Students should be able to:

1)Calculate the area of various polygons including trapezoids,

2) Draw a trapezoid with given area, and

3) Work independently on laptop with Safari (or other web-browser).

Prerequisite Knowledge of Teachers: Teachers should have:

1)Working knowledge of GeoGebra and dynamic worksheets,

2)Working knowledge of wireless laptop cart, and

3)Introduced the topics of area of trapezoids

Objectives of the Lesson: After completion of this lesson, students will be specifically able to:

1)Find the area of trapezoids.

2)Use technology as a tool to solve a problem.

Time Frame of the Lesson: 1 day for review of prerequisite knowledge

1 day for exploration of website and dynamic worksheet

List of Materials:Hardware: wireless laptop cart, teacher computer, LCD projector

Software: GeoGebra, web-browser, html worksheets, HotPotatoes Jclose activity

Other: calculator, paper, pencil, class set of dry erase boards and markers

Description of content: This activity will present a different strategy for finding the areas of trapezoids in an interactive activity that the students will perceive as fun. Instead of using the area formula, the html worksheet will attempt to show students that the area can be found by multiplying the median of the trapezoid by the height of the trapezoid. This lesson plan includes links to mathopenref.com and to Universal Streaming, a website that offers full-length videos, video clips, and lesson plans on a variety of topics. The School Board of Broward County has made the website available to all Broward County schoolteachers.

SSS: A.1.3.1, B.1.3.1, B.1.3.3, B.3.3.1, C.3.3.1, E.1.3.2

List of Key Words:Area, trapezoid, base, height, parallel, average (mean), median of trapezoid, midpoint, complex figure

Multi-Media Lesson: Area of Trapezoids

Lesson Plan

1)Introduction to the Lesson:

To introduce the lesson, I have students view the following videoclip from Universal Streaming. The full video is a great review activity at the end of this lesson or at the end of the unit.

In addition, to introduce the lesson, I would have students visit the following website, This is an interactive website where students can manipulate the polygons to change the dimensions and area. Also, this website helps to achieve the goal of this lesson which is to teach students to calculate the area of trapezoids without the rote memorization of and substitution into the area formula.

Following are screen shots of the 3 important webpages:

2)Explanation of the math involved

My seventh and eighth grade students have had trouble in the past calculating the area of trapezoids. The formula, , is troublesome for some of my students due to the order of operations involved. If the formula is broken down into its components and explained to the students, it seems to make more sense to them. The concept of finding the average of the two bases (or the median of the trapezoid, the segment created where the midpoints of the legs are connected to find a third parallel segment) is visually easy for students to see. I draw a rough sketch similar to the one below on the board to illustrate the concept of the “average base” where the perpendicular lines are drawn through the midpoints of the legs and the “extra triangular pieces” fit perfectly in missing triangular pieces.

3) Instructional methods

I use a teacher-centered approach when I present formal notes to the class via PowerPoint presentation on my LCD projector. For this unit on area of trapezoids and complex figures, I use the 8th Grade Prentice Hall Pre-Algebra interactive software. This software allows for teacher led examples and student practice as well. Then, using a student-centered approach, students explore the website, and finally complete the html worksheet.

4)Step by step procedure:

Step One: I present the PowerPoint presentation that includes the following:

1. Review the definition of trapezoids and different appearances of trapezoids.
2. Review and label the parts of trapezoid including a new term, median.
3. Review how to calculate area of a trapezoid using the formula .
4. Explain components of area formula. Use drawing above to demonstrate the concept of “average base”.
5. Review how to find the area of complex figures.

Step Two: For a quick assessment activity regarding trapezoids, I use my class set of dry-erase boards and markers. Students are asked to draw and label trapezoids on the dry erase boards and I can quickly assess if they are correct

Step Three: The students will work individually or in pairs on wireless laptop computers to view the website, Trapezoids on the website can be manipulated to change of dimensions and area.

Step Four: Students then work with the GeoGebra html worksheet and answer the questions as set forth on the dynamic worksheet. Students should record their answers on a piece of paper or you may print out worksheets for them to write on. As students complete the worksheets using the computers, I move around the classroom addressing concerns or problems as they arise. I redirect students’ questions to the entire class.

Screen shots of the dynamic worksheet follow:

Closure of lesson:

I review all the steps with the students and will calculate the areas. Since these topics are so important in the Pre-Algebra curriculum, I remind students that they will see these topics again. Students will hand in their written observations and solutions from the worksheet.

Assignments: Students will be instructed to use dynamic worksheet to create 3 different trapezoids. Noting dimensions, students will also calculate area using traditional formula and new method using the median.

Students will also complete the following JClose vocabulary assignment:

:TITLE:Trapezoids

A trapezoid is a (1)______with exactly (2)______pair of parallel sides. These parallel sides are its (3)______. Every (4)______has two bases. The non-parallel sides are called legs. Every trapezoid has two legs. The attitude or height of a trapezoid is the perpendicular distance from one base to the other. The (5)______of a trapezoid is the line joining the midpoints of the two legs. The area of a trapezoid can be found by multiplying the median by the height. A trapezoid with one pair of opposite congruent sides is classified as an isosceles trapezoid.

:ANSWERS:

:ANSWER1:quadrilateral

:ANSWER2:one

:ANSWER3:bases

:ANSWER4:trapezoid

:ANSWER5:median

Assessments: Informal assessment is performed during activity and through written solutions from worksheet. Formal assessment will take place on the chapter test.

Feedback to students: Verbal feedback will be provided on during activity. Written feedback will be provided on the solution page that is submitted for grading.

Answer keys to assignments:

Student answers may vary.

Supplemental activities lesson:

Be sure to pair up ESE or ESOL students with students with stronger abilities if using collaborative learning.