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Country Borders and Area

By: Kirstin Bittel, Brink Harrison, Sally Rusk, and Rachel Hughes



Time: 2-3 class periods
Preparation Time: 10 minutes to copy Activity sheets
Materials:

Activity sheets:
Acticity sheet 1
Activity sheet 2
Activity sheet 3

 


Abstract
A math lesson applying unit analysis to deal with metric units when analyzing the percentage of land use in a specific country.

Purpose: To determine the perimeter and area of a country and find out what percentage of each is used for specific purposes. (explore)

Objectives
First class period students will be able to:

1. Use unit analysis to set up ratios to compute measurements
2. Convert empirical measurements to metric
3. Judge the reasonableness of results when converting to metric

Second class period students will be able to:

4. Calculate the perimeter of a country
5. Calculate the area of a country
6. Calculate the percentage of perimeter that borders other features (neighboring countries, oceans, etc.)
7. Calculate the percentage of area in the country that is water (lakes and rivers.)
8. Calculate what percentage of land is used for agriculture and other uses.

Third class period students will be able to:

9. Use proportions to calculate the portion of a pie-graph that represents a specific percentage of land use
10. Construct pie-graphs to represent data on borders and land use

National Science Education Standards
Measurement:
Apply appropriate techniques, tools, and formulas to determine measurement
Use unit analysis to check measurement computations
Understand measurable attributes of objects and the units, systems, and processes of measurement.

Number and Operations

Judge the reasonableness of numerical computations and their results

Representation
Use representations to model and interpret physical, social, and mathematical phenomena


Teacher Background
If applicable

Resource Websites

http://www.cia.gov/cia/publications/factbook/
 

 

Activity:

Day 1

When the students walk into the room, ask them, “How many seconds are there in a regular year?” Allow a few minutes for students to respond. Do not judge answers.

Put the digit 1 on the board and tell them, “I’m going to start putting zeros behind the 1, and you to tell me when to stop so we’ll know your estimate of the number of seconds in a year.” It might be a good idea that you and the class reach agreement on how many answers you will accept. Don’t take a guess from each student in the class or else you will be adding zeros for the whole period.

Begin and keep adding zeros until someone tells you to stop. Ask the class if they want to stop there or keep going. If they want to go on, mark the first zero in a different color and add more zeros until someone else says, “Stop.” Have the students put commas in the appropriate places in the number and ask the students to read the numeral they have chosen.

Tell the students, “ As a class we will now calculate the number. Anybody have any suggestions?” Allow a few minutes for students to respond and have them write their answers on the board. Hopefully someone will come up with the correct procedure, but they may not include the units of measure with the numbers. As you go over the procedure, make sure to write in the units in the appropriate spots and show how the units cancel out to get the answer, explaining that this technique is called unit analysis.

If nobody suggests the correct procedure, point out that unit analysis can be used to compute the answer this question. Hand out Activity sheet or put it on the overhead and have the students do the work in their notebooks.

Activity sheet 1

Day 2
Ask students. “Do you think the size of a country or of the number of neighbors it has affects its status or economy? Why?” Allow a few minutes for students to respond. Do not judge answers.

Show students the data on the United States from the Infrared Analyst's Guide to Worldwide Environments web page. http://www.iriacenter.org/irworld.nsf/Frameset%201?OpenFrameSet&Frame=Target&Src=_
15tkn4trfe9m68bjeedj2ut35edq3ujrgcln50ob7ckj42tbkdt374obdcli00_

http://www.cia.gov/cia/publications/factbook/
If you use the first website, the distances will be given in miles and area in square miles. The second website uses a different format and uses metric units. Both provide useful information.

Homework
Have students calculate the same information for their country. Remind them that this data will be a part of the country display so that it should be presented accurately and neatly. (This might be information they wish to graph for their country displays.)

Activity sheet 2

Day 3
Tell the students, “Being able to present data in an appropriate manner is one of the standards in mathematics. Simply having the data is not enough; you need to be able to communicate it to others. Given the data that you found yesterday about your country, what forms of representation would you choose to make the data clear? Why would you choose this form?” Allow a few minutes for students to respond. Do not judge answers.

Homework
Have students make pie-graphs of the same information for their country. Remind them that this data will be a part of the country display so that it should be presented accurately and neatly. (This might be information they wish to graph for their country displays.)

Activity sheet 3

Closure
The students reach closure as they work on the graphs for their country displays.

Embedded Assessment

The first day of this lesson will be assessed through informal discussion of ways to apply unit analysis and guided practice as the students do the Activity sheet. The second day of the lesson will be assessed by guided practice as the class as a whole finds the information for Brazil. Individual or small group assessment can be done by informal observation as the students do the calculations for their country displays. The third day will be assessed by guided practice as the class as a whole makes the pie-graphs for Brazil. Individual or small group assessment on the third day can be done by informal observation as the students do the calculations for their country displays.

Things to check with embedded assessments:

  • Can students convent measurements from empirical to metric?
  • Can students calculate percentages?
  • Can students calculate ratios?
  • Can the students measure angles in the pie-graphs

 

 



PULSE is a project of the Community Outreach and Education Program of the Southwest Environmental Health Sciences Center and is funded by:


an
NIH/NCRR award #16260-01A1
The Community Outreach and Education Program is part of the Southwest Environmental Health Sciences Center: an NIEHS Award

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Supported by NIEHS grant # ES06694


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Last update: November 10, 2009
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