Summary
Continuing the Asteroid Impact challenge, students use their knowledge of scales and areas to determine the best locations in Alabraska for the underground caverns. They cut out rectangular paper pieces to represent caverns to scale with the maps. They place the paper cutouts on the maps to determine feasible locations. This is activity 4 of the Asteroid Impact curricular unit and builds on the previous activities in the the unit.Engineering Connection
Engineers usually propose multiple solutions to problems, and then analyze each solution before selecting the one that best meets the criteria for success.
PreReq Knowledge
Understanding of length, width and area; ability to read a map.
Learning Objectives
After this activity, students should be able to:
 Explain that the same area can be represented by various shapes.
 Determine the length and width of a rectangle when given the area of a rectangle.
 Apply the map scale to create a cavern area.
 Synthesize multiple pieces of information and make a decision based on all the information.
More Curriculum Like This
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To kickoff the Adventure Engineering Asteroid Impact unit, students learn of the impending asteroid impact scenario, form teams and begin to study the situation in depth. A simple inclass simulation shows them the potential for destruction and disaster. They look at maps and complete a worksheet an...
Student teams determine the size of the caverns needed to house the population of the state of Alabraska from the impending asteroid impact. They make measurements and calculate area and volume from individual bedroom size to classroom size to large enough to house all Alabraskans. They convert betw...
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards  Science

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.
(Grades 6  8)
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This standard focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Define a design problem that can be solved through the development of an object, tool, process or system and includes multiple criteria and constraints, including scientific knowledge that may limit possible solutions. The more precisely a design task's criteria and constraints can be defined, the more likely it is that the designed solution will be successful. Specification of constraints includes consideration of scientific principles and other relevant knowledge that is likely to limit possible solutions. All human activity draws on natural resources and has both short and longterm consequences, positive as well as negative, for the health of people and the natural environment.The uses of technologies and any limitations on their use are driven by individual or societal needs, desires, and values; by the findings of scientific research; and by differences in such factors as climate, natural resources, and economic conditions. 
Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales.
(Grades 6  8)
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This standard focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Construct a scientific explanation based on valid and reliable evidence obtained from sources (including the students' own experiments) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. The planet's systems interact over scales that range from microscopic to global in size, and they operate over fractions of a second to billions of years. These interactions have shaped Earth's history and will determine its future.Water's movements—both on the land and underground—cause weathering and erosion, which change the land's surface features and create underground formations. Time, space, and energy phenomena can be observed at various scales using models to study systems that are too large or too small.
Common Core State Standards  Math

Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.
(Grade 6)
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Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
(Grade 7)
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Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.
(Grade 8)
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International Technology and Engineering Educators Association  Technology

Make twodimensional and threedimensional representations of the designed solution.
(Grades 6  8)
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Requirements for design are made up of criteria and constraints.
(Grades 6  8)
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State Standards
Colorado  Math

Fluently add, subtract, multiply, and divide multidigit decimals using standard algorithms for each operation.
(Grade
6)
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Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
(Grade
7)
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State the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.
(Grade
8)
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Colorado  Science

Develop and communicate an evidence based scientific explanation around one or more factors that change Earth's surface
(Grade
5)
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Analyze and interpret data identifying ways Earth's surface is constantly changing through a variety of processes and forces such as plate tectonics, erosion, deposition, solar influences, climate, and human activity
(Grade
5)
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Gather, analyze, and communicate data that explains Earth's plates, plate motions, and the results of plate motions
(Grade
7)
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Materials List
 paper
 scissors
 rulers
 calculators
 3 handouts: Possible Locations Worksheet, Alabraska General Map, Alabraska Geology Map
Introduction/Motivation
Today, your engineering team's task is to identify your best possible locations in Alabraska to locate your caverns. As you do this, you will get a lot of practice thinking about length, width and area!
First, figure out the shape and dimensions of the cavern you imagine, making sure to size it to provide enough shelter space. Then, make rectangular paper pieces that represent the caverns—to scale—which you can place on the Alabraska map to find three possible locations.
Let's get going!
Procedure
Background
As necessary, refresh students' knowledge on how to use map scales.
Before the Activity
Gather materials and make copies of the worksheet.
With the Students
 Hand out the materials to each group.
 This activity builds upon of the relationship between length, width and area. As necessary, review how to calculate area when given a length and a width AND how to calculate possible combinations of length and width when given an area.
Tip: Draw various rectangular shapes on the board (with dimensions) and ask the class to come up with other possible combinations of equal areas.
 It is important to spend some time discussing possible shape combinations to match the total area of the cavern. It is okay if some teams want long skinny caverns and others envision square caverns. Some creative groups may choose triangular caverns or circular caverns. The key is that each shape must provide the necessary area.
Tip: After completing worksheet question 3, have each group show the class its proposed cavern shapes—its cutout piece(s) of paper.
 To complete question 4, student teams must synthesize all the information they have gathered thus far and propose three locations. As needed, provide assistance and prompts.
 Have teams share their identified locations with the class and explain why they chose those locations.
Worksheets and Attachments
Assessment
Worksheet: Review students' answers on the Possible Locations Worksheet to gauge their comprehension of the material and concepts covered. Refer to the Asteroid Impact Student Workbook Example Answers provided in the unit document for example worksheet answers.
Activity Extensions
Have students compare the sizes of different U.S. states or different countries in the world.
Copyright
© 2013 by Regents of the University of Colorado; original © 2005 Colorado School of MinesSupporting Program
Adventure Engineering, Colorado School of MinesAcknowledgements
Adventure Engineering was supported by National Science Foundation grant nos. DUE 9950660 and GK12 0086457. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.
Last modified: April 3, 2018
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