Zoom: Using Geographic Scale to Apply Spatial Reasoning

Zoom, Zoom: Using Geographic Scale to Apply Spatial Reasoning

Students learn important lessons about scale as they apply spatial reasoning with linear measurement and scientific notation using different types of maps and imagery.

Author / Denise Dorn
Grade Level / 5 and 8
Duration / 1-2 class periods
National Geography Standards / Arizona Geography
Strand /
Other Arizona Standards
ELEMENT ONE: THE WORLD IN SPATIAL TERMS
1. How to use maps and other geographic representations, tools, and technologies to acquire, process, and report information from a spatial perspective. / CONCEPT 1
World in Spatial Terms
Grade 5
PO 1. Interpret information from a variety of maps:
a.  contour
b.  population density
c.  natural resource
d.  historical maps
Grade 8
PO 2 Identify purposes of, and differences among, maps, globes, aerial photographs, carts and satellite images.
PO 3 Interpret maps, charts and geographic databases using geographic information. / Mathematics Common Core Standards
Number and Operations in Base Ten
5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Measurement and Data (MD)
5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Expressions and Equations (EE)
8.EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Standards for Mathematical Practice
5.MP.2 and 8.MP.2. Reason abstractly and quantitatively.

Zoom: Using Geographic Scale to Apply Spatial Reasoning

Overview

Given images and maps with scale, students will record linear measurements of specific features in meters, kilometers and in scientific notation. In addition, students will determine appropriate maps and imagery given a linear measurement of a feature.

Purpose

In this lesson students will gain a better understanding of the magnitude of rational numbers by measuring using a map scale, converting between measurements and using scientific notation.

Materials

·  Rulers

·  How to Convert within the Metric System

·  How to Change Numbers from Standard form into Scientific Notation and Back

·  Worksheet

·  Worksheet KEY

·  Images and maps at different scales supplied in the student materials.

·  Outline maps at different scales

·  Paper, pencil

·  Strips of paper so students can reproduce the graphical scale

Objectives

The student will be able to:

1. Select appropriate imagery and maps based on resolution of different features at different map scales.

2. Measure distances between features in meters and kilometers given a scale and convert those measurements to scientific notation.

Procedures

Students should have experience in place values from millionths to millions. Students should also be familiar with scientific notation and the metric system. The handout provides rudimentary background.

Introduce the lesson with a few minutes on Google Earth.

1. This lesson's homepage has four zoom movies. (A computer display or TV in the classroom is needed to show the movies.) Simply go to the homepage and scroll down towards the bottom. Click on the links to the movies. They are QuickTime movies that provide a good anticipatory set. Zooms are created by combining satellite imagery with aerial photographs. The satellite imagery shows "big picture" features, while the aerial photographs taken from airplanes show close-up features like buildings. [Note: if your browser does not show the movies, you can go into the "lessonfile" folder and find the dorn folder. The QuickTime movies can be opened from within the dorn folder.]

2. Using an overhead or computer, review all the images and maps students will be using for the lesson. Be sure to point out the graphical scale for each image or map. Show students the features they will be measuring when they get their own set of maps. Tell them to keep in mind the four questions they will need to answer at the end of the worksheet.

distance made by using a straight line between the points. This is the distance sometimes called "as the crow flies". To find the actual distance between two points, students will use the graphical scale. The simplest method is to reproduce, and extend the scale marks on the side of a straight scrap of paper.

3. Remind students that graphical scales are a type of proportion (or ratio) that compares:

Distance on the Map

Distance on the Ground

Use the aerial photograph of Bank One Ballpark to demonstrate the use of a graphical scale. Emphasize the proportion for this map is 13mm: 100 m. Explain that you must use a ruler to measure the distance on graphical scale. Demonstrate how to measure distances on several images and maps. Tell students that they will need to measure the distance made by using a straight line between the points. This is the distance sometimes called "as the crow flies". To find the actual distance between two points, students will use the graphical scale. The simplest method is to reproduce, and extend the scale marks on the side of a straight scrap of paper.

4. For students who would like a more mathematical challenge, have them use a ruler, determine the proportion represented by the graphical scale, measure the distance between objects listed for each image, then use cross-products to find the actual distance. Students who use this method will need to round their answers.

Example: Bank One Ballpark

Graphical Scale 13 mm:100 m

Distance from X to Y: 40 mm

13  = 40 13d = 4000

100 d d = 4000 ¸13

d = 307

d = about 300 m

5. Distribute student handouts on How to Convert within the Metric System and

How to Change Numbers from Standard form into Scientific Notation and Back. Discuss or review the material on those handouts, perhaps making an overhead of them

6. Distribute the images and maps. (It may be necessary to copy and laminate a class set or sets for small groups, or the images and maps could be put on overheads, or the students could look at them in color in a computer lab.)

7. Model how to fill out the first column (Distance in Meters) on the student worksheet. Start with the aerial photograph of the Bank One Ballpark.

8. After students have completed Column 1 on the worksheet, distribute student handout on "how to convert within the metric system" and "scientific notation". Discuss or review the material on these handouts. Help students complete Columns 2, 3, and 4 for Bank One Ballpark. Have students complete Columns 2, 3, and 4 for the Bisbee map. Check their answers. Have students finish the conversions for the rest of the worksheet.

9. Closure: come together as a class and show one of the zoom movies, explaining again how different spatial scales display different types of information.

Assessment

Students fill out the student handouts. Correct answers on three out of four questions (What would you pick?) would be considered mastery. Eighty percent or higher on the Math Worksheet and/or STUDENT HANDOUT How to Change Numbers from Standard form into Scientific Notation and Back would be considered mastery.

Extensions

Have students bring in maps, have teachers supply wall maps or globes, or use Internet sources of maps such as <www.mapquest.com> and <www.esri.com>. Then, use those maps to explore issues of scale, spatial reasoning, and what maps/images are best to use for different purposes.

Another extension could be to use the same maps and images and have students measure curved distances. To do this, simply cut string and mark the string with the graphical scale. So they can compare, for example, the real length of the Mississippi River with the "as the crow flies" distance.

Sources

·  The aerial imagery and maps are courtesy of Arizona State University, NASA, and the U.S. Geological Survey.

·  Tucson Football stadium zoom

http://svs.gsfc.nasa.gov/vis/a000000/a002200/a002245/index.html

·  Washington DC pan and zoom

http://svs.gsfc.nasa.gov/vis/a000000/a001300/a001324/index.html

·  Hollywood zoom http://svs.gsfc.nasa.gov/vis/a000000/a002100/a002108/index.htm

·  World Trade Center, New York City zoom http://svs.gsfc.nasa.gov/vis/a000000/a002400/a002443/index.html

Zoom: Using Geographic Scale to Apply Spatial Reasoning