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(Part I of III, area, surface area, and volume)
Activity summary:
This activity is used to encourage creative thinking and problem solving by applying previously learned skills to a new situation. They are able to reinforce their ability to solve for the area of simple shapes by estimating the area of more complicated and irregular shapes. They can also find or estimate the perimeters.
Subject:
Math: Geometry, Measurement, Problem Solving, Area.
Grade Level:
Target Grade: 8th
Upper Bound: 8th
Lower Bound: 6th
Materials:
___ Area worksheet
___ Rulers
___ Lengths of String (optional for perimeter)
___ Calculators (optional)
___ Shape stencils
___ Paper for students to work on (at least 8x10, there are advantages to both small and large sheets)
___ Accurate scale (optional)
Activity Introduction/Motivation:
Explain to students that often in life you may not be able to get exact answers to problems and the ability to accurately estimate can be important. For example; you want to know how many acres there are on a plot of land that is broken up by rivers or lakes and has some oddly shaped borders. If you have an aerial photograph you would be able to estimate the amount of land, but how can you be as accurate as possible?
Activity Plan:
Prior to class, get poster board or cardboard and cut out a few different shapes to act as stencils. Remember, your students are going to have to find a way to estimate the area, so the more intricate you make it the more time it will take. Have paper ready for the kids, after you introduce the activity; tell them they are going to have to estimate the area of one of the stencils. Let them attempt the activity on their own, give guidance only if the students are well off track. Also have them calculate the perimeter if you wish.
Note: you may want to ask them to round there measurements to the nearest inch or centimeter unless they have calculators. They will use a lot of time simply multiplying to find the areas of the more basic shapes.
After they have had some time to try their method, give them a demonstration of two popular methods. In the PowerPoint I choose to break the shape down into simple shapes such as triangles, rectangles and parallelograms. Then add up the area of each shape. The second method I chose was to create a grid over the shape and count squares; whole squares first, then the extra bits. For the perimeter, show them they can lay sting down along the edge, then measure the string for a relatively accurate measurement.
If you have time ask your students to try one of the methods they hadnt used the first time and see how close their two answers are. Make sure they pay attention to if they are over or underestimating, and explain why this is important to know (say buying paint, you dont want to underestimate or it may not match, etc.).
The finally; take one of the shapes on paper and cut it out carefully, then cut out a shape that is of a known size, 10 by 10 maybe. This way you can weight the piece of known size and get a weight per square inch or centimeter. Now weigh the cutout shape, and you can find the area, this is very accurate assuming you cut it out well.
Learning Objectives:
8th grade Math TEKS:
8.7 (A)
8.14 (A)
8.14 (B)
8.14 (C)
8.14 (D)
7th grade Math TEKS:
7.8 (C)
7.9
7.13 (B)
7.15 (B)
Prerequisites:
The students must be comfortable finding the area of shapes such as triangles, rectangles, and parallelograms.
Attachments:
___ link to HYPERLINK "../../../../Local%20Settings/Temp/Area%20Estimate%20Worksheet"Area Estimation Worksheet (only works if you saved the files to your temp folder, otherwise you need to locate it to open).
___ ling to HYPERLINK "../../../../Local%20Settings/Temp/Estimating%20Areas.ppt"PowerPoint presentation (to use during activity)
Authors: Graduate Fellow Name: Kevin Brink Teacher Mentor Name: Jessica BelcherDate Submitted: 2/4/07 Date Last Edited: 2/4/07
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