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Image1.gif (5877 bytes)Area & Perimeter
Determining and Distinguishing

By Ronda Barnes
University of Idaho
GRADES 4-6

 

ITV Series: Math Talk by Square One, Lesson #13: Area & Perimeter

Overview
Students are often confused about which measurement is area and which is perimeter. This units purpose is to assist students in making a clear distinction between area and perimeter. The video defines and demonstrates differences; plus, hands-on activities with manipulatives will engage students in learning. The math strand for this unit is measurement. This unit provides review and application for the concept of area and perimeter. However, the focus is to very clearly decipher between the two. The problem posed begins with area and then is reversed to be solved from the perimeter perspective. The unit also serves as a review and application of the formula for area and as a prerequisite for learning additional formulas. The lessons are set up to be customized to your needs - one day at a time or a week long unit.  Four activities to be used individually or as a whole unit on area and perimeter.


Learning Objectives

  • Students will be able to define area and define perimeter.
  • Students will be able to demonstrate their understanding of the concepts concretely, with manipulatives, and describe with words, their strategies and thought processes.

Materials

  • Video Cassette
  • Math Learning Logs
  • Pencil and paper for calculations
  • 1" cubes, 30 per student
  • A four-foot long piece of cord per two children
  • Graph paper
  • Scissors
  • "Math Check-up" (Quiz)

Pre-Viewing Activity

As a whole group, have students brainstorm and agree upon a definition for area and one for perimeter. Record the definitions on the board.

  • Area: is the measure of the inside of a polygon; the number of units needed to fill the interior of a shape.
  • Perimeter: the distance around the outside of a polygon; the total length of a shapes sides; it is a linear measure.

Provide a focus for students:
Have the students listen carefully for a definition and the question and or problem the video states.

Viewing Activities

Play the video from the beginning through the demonstration with the cubes. Pause the video when the definition is given, talk about it, replay if necessary, record definition on board; repeat procedure for the question:

If two shapes have the same area, do they have the same perimeter? Record predictions of the answer.

Discuss how well the definitions provided by the students match the definitions given on the video. Have the students create 2 or 3 (as time allows) polygons of their own, similar to those on the video. Have students trade with a partner then calculate the area and perimeter of each polygon. Discuss why perimeter and area are different?  (Some squares are surrounded by others, and so, contribute to the area, but not to the perimeter.)


Activity 2

Pre-viewing activity
Have the children experiment with the cords to determine a prediction for the question posed on the video: If two shapes have the same perimeter, can they have the same area?


Provide a focus for students 
Have the students listen carefully and record solutions to the problem/question posed.

Viewing Activities
Play the video, beginning at The Math Mimes. Pause the video after the problem/question is stated, discuss interpretation and if they match one another or not. Continue the video through The Math Mimes.

Post-Viewing Activities
In pairs, have the students further investigate the relationship of area to perimeter. Have students determine strategies for distinguishing area from perimeter. Share strategies through a whole class discussion.
Ask for volunteers to demonstrate their strategies on the board. Have the students record, in their Math Learning Logs, their favorite strategies.
Prompt question for discussion:   What are some uses, in the world, for these measurements?

 

BS01044_.WMF (1338 bytes)

Activity 3

Pre-Viewing Activities
Have students predict how to double the area of a rectangle and record their predictions. Allow students a few minutes to discuss this with a partner. Have the students investigate the problem/question using graph paper, pencils and/or scissors.

Provide a focus for students 
Assign each table to record a concept, a rule, and a formula demonstrated on the video, as they watch and listen.
Play the video beginning at segment General Mathpital. Pause the video after the demonstration on the "operating table" and again after the demonstration at the "x-ray screen." Check with students to be sure that they are able to follow and record assigned information. Example:

  • Determine measurements, 2 ft. wide x 5 ft. long.
  • Formula for Area- L x W.
  • Double L and double W.
  • Double one dimension, L or W, not both.
  • Determine measurements,
    4 x 5 = 20 or 2 x 10 = 20.

Post Viewing Activities
Have each table list a concept, rule, or formula on the board. Discuss what was learned and how that matches the predictions and discoveries made earlier. Record final information, concepts/rules/formula for area in Math Learning Logs. Play end of video (from General Mathpital) to pose the final question/problem:   When we double the length and the width, the rectangles look the same. With twice the area, the rectangles look very different. Can we double the area and keep the same shape?" Have students work on this as homework and be prepared to share results.


Activity 4

Pre-Viewing Activities
Have the students demonstrate the solutions to the homework problem using cubes and/or the board. Discuss discoveries and results. Students will record the answer to this question and how they arrived at the answer in their logs.

Provide a focus for students
Review of concepts and strategies learned. Have the students record any questions or observations that may not be clear.

Viewing Activities
Replay entire video (10 minutes), pausing if someone needs time or clarification.

Post Viewing Activities 
Whole class discussion to answer questions and discuss observations; allow students to conduct the discussion. After discussion pass out "Math Check-up" to be completed in class.

Extensions

  • Estimate and then measure the area and perimeter of the playground, a section of sidewalk, the gym, etc. Have the students choose a unit, standard or otherwise, that would be appropriate. Estimates should be recorded in Math Learning Logs and later the actual measurements. Prompt questions: How close were the estimates? How exact do we think these measurements are? Why is it critical or not to be exact?
  • Have the students use the Internet or Geological sources to determine the area and/or perimeter of a topic of choice: the earth, an ocean, a nearby lake, the county boundaries, the Kibbie Dome, etc.
  • Investigate how scientists determine and utilize measurements of area and perimeter.
  • For additional lesson plans and ideas relating to this topic and many others try TeacherSource!   You will find activities, lesson plans, teacher guides and links to other great educational web sites!  Search the database by keyword, grade level or subject area! 
  • Mathline and Scienceline are also great resources for teachers seeking teaching tips, lesson plans, assessment methods, professional development, and much more!  Look for a localized version of Mathline and Scienceline on IdahoPTV next year!

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