Project Title

Have ruler…will travel!

 

Introduction

Humans have been using standard units to measure length for thousands of years.  Over time, the units have evolved and the accuracy of measurement has increased.   Land surveyors now have precise lasers and GPS systems to measure distances accurately.  Although as students, we are limited in our access to lasers and GPS, we will compare distance measured with a tape measure to a new technology available for free to the public.  Using satellite images and aerial photography, Google Earth offers a remarkably accurate way for us to measure distances.

 

Task

Working together with your group, you will select three rectangular locations to measure.  After measuring the length and width of each location, you will use the Pythagorean Theorem to calculate the length of the diagonal.  Then you will measure the actual distance of the diagonal.  When you have completed all of your measurements, you will check your work for accuracy by using Google Earth to measure the distances.  Finally, you will create a Google Earth Tour of your chosen locations.

 

Instructions

Solve each problem in order.  Save your work along the way, as you will create a presentation at the conclusion of the project.

 

1                    First problem:

·                     With your group, choose three, large, local rectangles or squares to measure.  You will need to pick locations where it is possible to measure the length, width, and diagonal.  Ideal locations include:  football field, baseball diamond, soccer field, etc.  Be creative.  Try to pick locations that are individual to your team. 

 

Hint:  (A city block would not be appropriate, as you would not be able to measure the diagonal with a measuring tape.  Most people tend not to like students climbing through their back yards.)

 

2                    Second problem:

·                     Once your group is happy with the three locations chosen, you will begin measuring.  First, measure the length and width of the location by either using a measuring tape or pacing off the length, if necessary.  You may measure in customary or metric units depending on your tape measure.  The measuring tape will give you the most accurate reading, but for some very large locations, you may need to pace off the lengths. Record the length and width of the location in the table below.

 

·                     Follow the link below to increase your accuracy at pacing.   

http://www.ehow.com/how_4497078_estimate-distance-using-pace-count.html

 

3          Third Problem:

·                     Using the length and width of the location, imagine drawing in the diagonal.  The diagonal would split the rectangle into two congruent, right triangles.  We could consider the length to be side a and the width to be side b.  Using the Pythagorean Theorem, substitute sides a and b into the formula to find side c.  Show your work in the table below.

 

·                     Give your answer for side c in simplified radical form and record it in the table.

 

Hint:  (Are there any perfect squares that can be factored out of the radical?)

 

·                     Now, evaluate your answer to the nearest tenth using a calculator and record.

 

            Hint:  (Although the answer in simplified radical form is exact, the answer to the nearest tenth is more meaningful for measuring distance.)

 

·                     Finally, measure or pace off the diagonal and record the measurement in the table.

 

Hint:  (Now move on to your next location.  To make the best use of your time, complete all of the above steps at one location, before moving on to the next.)

 

Location

Measurement

Length, side a

Measurement

Width, side b

Given a & b, use the Pythagorean Theorem to solve for c.

Give your answer in simplified radical form and rounded to the tenth.

Remember: 

Measurement

Diagonal, side c

1

 

 

 

 

2

 

 

 

 

3

 

 

 

 

 

4          Fourth problem:

·                     Now that you have the table filled out with your measurements, we will use Google Earth to check for accuracy.  Google Earth is a free download: http://earth.google.com/download-earth.html

 

·                     Open Google Earth and type your city and state into the “Fly to” textbox on the top left.  Then hit enter.  You should now see an aerial view of your city.   Tools for zooming in and out and panning in all directions are located at the top right of the map.  Use the tools to find your first location and zoom in as close as possible.

 

·                     Notice the toolbar with small buttons at the top of the map.  Select the “Show Ruler” button, that looks like a ruler.   Being as precise as possible, click on the map to drop your start and stop points.   The ruler is set to measure in miles as the default but can be changed to measure in feet or meters.  Measure the lengths of sides a, b, and c.   Record your results in the table below.  Repeat for the next two locations.

 

Hint:  (While zoomed in on each location, it would be helpful to mark the place by selecting the “Add Placemark” button, that looks like a thumbtack.  Then change the name of the location and click ok.  We will use the places to create a Google Earth Tour later.)

 

Location

Google Earth Measurement

Length, side a

Google Earth Measurement

Width, side b

Google Earth

Measurement

Diagonal, side c

1

 

 

 

2

 

 

 

3

 

 

 

 

Collaboration

Get together with another group to discuss the accuracy of your results.  Discuss the following:

·                     How will you determine accuracy? 

·                     Which group had more accurate results?  How do you know?

·                     Did the accuracy vary from location to location?  Why? 

 

Conclusions

Your project will be a Google Earth Tour and a presentation of your results.  You may choose to represent your results on a poster or by making a multimedia presentation.  Please make sure that both tables are neatly presented as well as the step-by-step algebra to solve for c using the Pythagorean Theorem.  Also, include a discussion of your accuracy, using the questions above for guidance. 

 

In order to make the Google Earth Tour, you need to have a place marker at each location.  See the hint for problem four if you have not already marked the places.  Now select Tour under the Add Menu at the top of the screen.  You will begin recording when you press the red record button on the lower left.  Move from place to place and hit the record button to stop.  Your tour will then play.  If you are happy with it, save the tour by selecting the save file button to the right of the playback bar. 

 

Hint:  (You can then save the tour under File, Save, Save Place As.  It can be saved on the desktop or to a flash drive.  The file saves as a .kmz file and is not easily imported into Power Point.  For this reason, it would be best to play your tour separately from the rest of your presentation.) 

 

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

 

Score

Content

Presentation

4

Your project appropriately answers each of the problems.  Tables are included and are complete.  The step-by-step solution to each Pythagorean problem is given.

 

Your project is mathematically correct as it approaches the accuracy of the measurements and comments on any sources of error.

Your project contains information presented in a logical and interesting sequence that is easy to follow.

 

Your project is professional looking with graphics and attractive use of color. 

 

3

Your project answers each of the problems.  Tables are included and are complete.  The step-by-step solution to each Pythagorean problem is given.  Minor errors may be noted.

 

Your project approaches the accuracy of the measurements and comments on any sources of error.  Minor errors may be noted.

Your project contains information presented in a logical sequence that is easy to follow.

 

Your project is neat with graphics and attractive use of color. 

 

2

Your project attempts to answer each of the problems.  Tables are included and are mostly complete.  The step-by-step solution to each Pythagorean problem is missing and/or major errors are noted.

 

Your project attempts to address accuracy of the measurements, but major mathematical errors are noted.  Your project contains little discussion of the sources of error. 

Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

 

Your project contains low quality graphics and colors that do not add interest to the project.

1

Your project attempts to answer some of the problems.  Some tables are included and are mostly incomplete.  Step-by-step solutions to each Pythagorean problem are missing and major errors are noted.

 

Your project makes little attempt to address accuracy or sources of error.

Your project is difficult to understand because there is no sequence of information.

 

Your project is missing graphics and uses little to no color.

 


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