### Summary

Student teams determine the size of the caverns necessary to house the population of the state of Alabraska from the impending asteroid impact. They measure their classroom to determine area and volume, determine how many people the space could sleep, and scale this number up to accommodate all Alabraskans. They work through problems on a worksheet and perform math conversions between feet/meters and miles/kilometers.### Engineering Connection

Engineering teams begin the design process by thoroughly defining the problem at hand. This process involves identifying, through group brainstorming, discussion and research, the technical, financial and social criteria for successful design. When designing underground spaces, civil, mining and architectural engineers perform similar analyses as is done in this activity to determine the necessary space requirements.

### Learning Objectives

- Measure length, width and height of a room using a tape measure or ruler.
- Calculate area and volume from length, width and height measurements.
- Convert simple English units to metric units.
- Determine proportion by comparing a smaller area to a larger area.
- Represent a measurement on graph paper.

### More Curriculum Like This

**How Big?**

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Filtering is the process of removing or separating the unwanted part of a mixture. In signal processing, filtering is specifically used to remove or extract part of a signal, and this can be accomplished using an analog circuit or a digital device (such as a computer). In this lesson, students learn...

**Discovering Relationships between Side Length and Area**

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheetsâ€”which ...

**Adventure Engineering Challenge: Asteroid Impact**

Through this earth science curricular unit, student teams are presented with the scenario that an asteroid will impact the Earth. In response, their challenge is to design the location and size of underground caverns to shelter the people from an uninhabitable Earth for one year.

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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 K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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*.

###### Common Core State Standards - Math

- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Make two-dimensional and three-dimensional representations of the designed solution. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Colorado - Math

- Fluently add, subtract, multiply, and divide multidigit decimals using standard algorithms for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio reasoning to convert measurement units. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving the four operations with rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

- rulers, meter sticks, tape measures
- graph paper
- calculators
- (optional) helium balloons, each with~12 ft (3.7 m) of string (or at least ceiling height amount of string)
- (optional) masking tape, to mark off the size of a bed on the floor
- How Big? Worksheet
- Reference Page (contains 12 vocabulary words and definitions, formulas, unit conversions)
- butcher block paper and colored pencils, for drawing cavern designs

### Introduction/Motivation

Student engineering teams calculate how large caverns need to be in order to accommodate all the citizens of the state of Alabraska.

### Procedure

- Distribute materials to each group, including a ruler or tape measure.
- Have students measure and record on the worksheet the length, width and height of the classroom. There are several different ways to determine room height. One entertaining way is to give each group a helium balloon with a string tied to it. Let the balloon float to the ceiling, mark on the string where the floor is, then haul in the balloon and measure the string!
- Have students calculate the area (l x w) and volume (l x w x h) of the classroom. As necessary, provide explanation of a rectangle and a cube. Remind students that area involves multiplying two units of measurements together so the answer will be in units (meter, kilometer) with a raised number 2 ("squared," such as m
^{2}, km^{2}). Volume is found by multiplying length by width by height. Since three units are multiplied together the units of the answer will be represented by a cube (m^{3}).**TIP:**It is helpful to use a ruler or meter stick to draw a square foot or square meter on the classroom board. Also draw an area 1 m by 2 m and explain how it equals 2 m^{2}.**TIP**: If students have not studied area and volume, work these problems with them on the oard. It is also beneficial for teams to compare answers; and for the teacher to give them a "correct" answer to move forward with. - Give student teams time to discuss and answer worksheet questions 3 through 9. Either let them work through the problems as teams and then discuss as a class -OR- discuss answers as a class after each question. By the nature of the open-ended questions, the answers will vary. This is okay!! Explain that engineering design often leads to
*many correct answers*.**TIP:**If students have a hard time conceptualizing how many beds will fit in the classroom, use masking tape to make an outline of a bed (1 m x 2 m) on the floor. This should aid students in answering question three.**TIP:**Teams will use the answer to question 8 in later lessons. Although it is not necessary, you may want to give each team the same answer to move forward with. - Some common comparisons to help explain question 9: (a) One mile is equivalent to the length of about 7.5 city blocks. (b) 56 city blocks in a 1 km
^{2}. (c) School grounds usually take up 4 to 8 blocks. So, if your school takes up 4 blocks, it would take 14 schools to equal 1 mi^{2}. (d) A football field is about 90 m (300 ft) long by 45 m (150 ft) wide. It would take about 250 football fields to equal 1 km^{2}. - As time permits (or as a homework assignment), have students draw a plan for their team's cavern design. Give each team a large sheet of butcher block paper and colored pencils. Encourage them be creative think about what sorts of things they would want in their caverns!
**TIP:**Build on this task by later by having each team re-create this initial cavern drawing to scale (next lesson/activity topic).

### Attachments

### Assessment

- Review students' worksheet answers to gauge their math skills and understanding of the engineering challenge.
- Examine students' drawings to evaluate their comprehension of the project.

### Activity Extensions

- Determine the area and volume of rooms in their houses.
- Search the Internet to see where Alabraska would rank in terms of population and size.
- Visit www.asae.org and write a report about agricultural engineers.
- Determine the number of people in their state; then, calculate the necessary cavern size.

### Copyright

© 2013 by Regents of the University of Colorado; original © 2005 Colorado School of Mines### Supporting Program

Adventure Engineering, Colorado School of Mines### Acknowledgements

Adventure Engineering was supported by National Science Foundation grant nos. DUE 9950660 and GK-12 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: May 25, 2017

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