# Lesson:How Big?

### Summary

Continuing the Asteroid Impact challenge, student teams determine the size of the caverns needed to protect the population. Students measure their classroom to determine overall area and volume, how many people could comfortably sleep in that space, and then up their numbers to find the necessary area to house all Alabraskan citizens. The lesson and associated activity provide a good application of area and volume concepts. Students also perform math conversions between feet, meters, miles and kilometers.

### Engineering Connection

Engineering teams always begin the design process by defining the problem. This process involves identifying, through group discussion and research, the technical, financial and social criteria for successful design. When designing underground spaces, civil, mining and architectural engineers would perform analyses that are similar to what students do in this lesson/activity to determine the appropriate space requirements.

### Pre-Req Knowledge

Fifth-grade reading level; some knowledge of length, width, area and volume; metric units; multiplication; familiarity with the inquiry-based learning process.

### 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.

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### 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.

###### Common Core State Standards - Math
• Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
• 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?
• Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
• Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. (Grade 7) 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 word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
###### International Technology and Engineering Educators Association - Technology
• 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?
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### Introduction/Motivation

Student teams calculate how large the caverns need to be to accommodate all the people of Alabraska.

### Lesson Background and Concepts for Teachers

Familiarize students with the concepts of area and volume, as well as example units associated with them. Write on the board the formulas for calculating area and volume:

area = length x width

volume = length x width x height

Area examples: a rectangle, the area of a rug, classroom floor space; such as 6 m x 6 m = 36 square meters).

Volume examples: a cube, the interior space in a box, the space in a classroom; such as 6 m x 6 m x 9 m 324 cubic meters).

Common size comparisons:

• 1 mile equals ~7.5 city blocks
• 56 city blocks in 1 km2
• School grounds usually take up 4-8 blocks, so if your school takes up 4 blocks, it would take 14 schools to equal 1 mi2
• A football field is ~90 m (300 ft) long x 45 m (150 ft) wide, so it would take ~250 football fields to equals 1 km2 <

### Associated Activities

• How Big? - Students determine the necessary size of the caverns to house the population of Alabraska. 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.

### Assessment

Review students' answers on the How Big? Worksheet to gauge their mastery of the subject matter.

### Lesson Extension Activities

• 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.