Measurement Resources

Middle School Lessons & Materials for Teachers

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The lessons and materials available here come from a variety of sites and organizations. Some include offers for video or software, and some are lesson plans. Where the originals are Claris or Acrobat (PDF) documents, we have for the most part converted them to HTML, leaving a link back to the parent page from which you can download the formatted version.

For more on measurement, search or browse the measurement pages in the Internet Mathematics Library.

 Geometry and Trigonometry

Area of a Sphere (Jewell)
A hands-on demonstration of the formula for the surface area of a sphere that uses a ball and a piece of wrapping paper to turn the formula for the area of a rectangle into the formula for the area of a sphere.
Circling Around (Jewell)
A hands-on demonstration of the relation between diameter and circumference, and why the formula pi x diameter works every time.
Discovering Pi (Eckley)
Students measure the circumference and diameter of an object to the nearest millimeter; explain how the number 3.14 for pi was determined; demonstrate that by dividing the circumference of an object by its diameter you end up with pi; discover the formula for finding circumference using pi, and demonstrate it.
Eratosthenes Finds Diameter of Earth! (Donovan)
Students learn to estimate the diameter and circumference of the Earth by repeating Eratosthenes' experiment; exchange measured data and results; and use the Internet to research the mathematical and scientific contributions of Eratosthenes.
Geometry and Measurement: Volume (instructional video) (Explorer)
Using the LxWxH formula, students invent ways to determine how many baseball boxes will fit a display case and how much water an aquarium will hold. They also learn that a formula is a shortcut for other methods of measurement and that the answer is always in cubic units.
How Tall is it? (Jungkeit, Caniglia)
Introduces the meaning behind approximate measure by using triangles and trigonometric ratios to compute the approximate height of a school smokestack or tall structure near the school. Uses computer technology to create experimental heights, as well as statistical analysis to predict the actual height of the stack.
No. 28: Rectangle Perimeter (NASA)
From a 9th grade math proficency test. A rectangle with a perimeter of 24 inches might have adjacent sides measuring...
Measuring Distances - Triangulation (Michal)
Students learn to determine the distance to an object by sighting a distant object from 2 different locations and knowing the distance between them (parallax). Optional: use trigonometry to determine an unknown distance.
The Mathematics of Cartography (Lanius)
Maps and measuring the earth: the history and math of mapmaking, some problems to solve, a list of cartography resources, and information on map-related careers.

 Length, Area, and Volume

Area of a Sphere (Jewell)
A hands-on demonstration of the formula for the surface area of a sphere that uses a ball and a piece of wrapping paper to turn the formula for the area of a rectangle into the formula for the area of a sphere.
Area and Volume (Welch)
Students will be able to describe the difference between area and volume and to understand how various units of measure relate to one another.
Area: What's a Square Foot? (Energy Conservation Enhancement - Louisiana)
Students will be able to: define area, explain how area is computed, and find the area of basic figures and objects. They will also determine the proper amount of glassed area to be placed on a structure for maximum energy efficiency.
Cube Coloring Problem (Dickerson)
Students investigate what happens when cubes of different sizes are constructed from unit cubes, the surface areas are painted, and the large cubes are taken apart. How many of the 1x1x1 unit cubes are painted on 3 faces, 2 faces, 1 face, no faces?
Geometry and Measurement: Volume (instructional video) (Explorer)
Using the LxWxH formula, students invent ways to determine how many baseball boxes will fit a display case and how much water an aquarium will hold. They also learn that a formula is a shortcut for other methods of measurement and that the answer is always in cubic units.

  Metric Units and Unit Conversions

How Do You Measure Up? (Carroll County M.S. teachers)
A lesson and an activity from a booklet prepared by 20 teachers as part of a project funded under the Goals 2000: Educate America Act in Tennessee. Students collect and analyze data.
No. 1: Adding Feet and Inches (NASA)
From a 9th grade math proficiency test. If Sally places a rocket 3' 6" tall atop a launchpad 1' 8" tall, how tall will the entire unit, rocket and launchpad, be when she is done?
No. 2: Measuring Boards (NASA)
From a 9th grade math proficiency test. Lewis needs 1,500 boards to build a small rocket. Each board must be 3' long.If boards are sold in 12' lengths, how many boards must Lewis buy and cut into 3' pieces to get the 1,500 boards he needs?
No. 9: Road Map - Scale (NASA)
From a 9th grade math proficiency test. If the scale on a road map is 1 inch = 250 miles, how many inches would represent 1250 miles?
No. 17: Measuring Things (NASA)
From a 9th grade math proficiency test. Which object is matched with its appropriate unit of measure?
No. 18: Unit Conversions (NASA)
From a 9th grade math proficiency test. Which statement is not correct?
No. 19: Tons and Pounds (NASA)
From a 9th grade math proficiency test. A loaded moving van weighs 5 tons. How many pounds would 10 loaded moving vans weigh?
Metric Conversions (Caniglia)
A board game that offers practice in converting one unit of metric length to another, and in the interpretation of abbreviations.
Metric Equivalents (Tresino)
Students use a shortcut method to change one metric unit to another (ex: kilometers to centimeters), through a diagram that supplies words that are easy to remember.
Smile Metric Style (Metder)
An activity that enables students to practice working with the metric system, which can be confusing and difficult for many.

 Natural Phenomena

Finding Elevation (Limberg)
Finding the height of a hill has long been a task of surveyors. The method of leveling used in this activity is essentially what has been used for hundreds of years - the only major difference is that the level is supported by a tripod and the straw is replaced by a small telescope. (Modern methods use a portable laser in place of the telescope but the method is essentially the same.) This activity is well suited to a camp situation.
How Much Further? (What Good is Math?)
A game for car trips - how long will it take to get to your destination? From a site designed to show middle school students how math is useful in their everyday lives.
Just How Cold Is It? (Great Lakes Collaborative)
In this lesson the students use a thermometer to collect, record, and graph daily temperatures for two weeks.
Measuring Plant Growth (DeRoo)
Illustrates how certain seeds grow into plants and reproduce seeds at very rapid rates. A variety of bean seeds are planted in flower pots or milk cartons, watered, and placed in a sunny window. As the bean plant grows up an attached support string, its height may be measured in either inches or meters and the number of days recorded on graph paper that has been placed behind the plant.
Seeds Using Stored Food Supply (DeRoo)
Provides practice in measuring circumference and diameter in centimeters.
Tell Time with Your Feet (Addington)
Students tell time by measuring their shadows and using a shadow table.
Tree Measurement (Vratil)
Students demonstrate measurement of the trunk, crown, and height using vertical and horizontal measurement; compare results with other groups; create a graph of their findings for the trunk, crown, and height of the tree; and define horizontal, vertical, and circumference.

 Statistics

Data Sets (Daley)
Data sets that can be downloaded as ClarisWorks spreadsheets by simply clicking on the desired title. The downloaded lists can then be sorted, manipulated, and graphed on your computer in the same way that any Clarisworks spreadsheet is manipulated.
How Do You Measure Up? (Hedge, Carlton)
A lesson and an activity from a booklet prepared by twenty Carroll County Middle School teachers as part of a project funded under the Goals 2000: Educate America Act in Tennessee. Students collect and analyze data.
Measurement and Frogs (Caniglia)
This activity focuses on a measurement activity that incorporates the concept of mean, median, and range using the Statistics Workshop.
Population Hunt (Great Lakes Collaborative - Jewell)
Students use World Almanacs to look up statistics about different cities in the U.S. After writing statistics found in both standard and expanded form, they are asked to compare, order and list the cities from greatest to least population.

Other Resources

 Sites where you can find more lessons and materials

Lessons by Susan Boone
Lessons developed by Susan Boone, a participant in GirlTECH '95, a program funded by CRPC Rice University and the RUSMP. A Functional Housing Market asks students to search the Internet for housing prices and compare them to the area of a house, thus deriving a linear equation. The Internet Pizza Server lets students order pizzas, calculating their area and determine the better buy. With Pop Clock, students look at the census site, study data and make predictions on future populations. Find the mean and median speeds for racers in the INDY 500. Study rates and speeds by using the Real-Time Traffic Report.
Secondary Resource and Assessment Database
The assessments and resources in this database are mostly classroom tested. Teachers can submit materials of their own. You can browse the database, or search for specific topics:
  1. Area
  2. Length
  3. Time
  4. Volume and Mass

  Reference Materials

Anglo-Saxon Weights and Measures (Proot)
How the system emerged, its long history, its many different units, whys, and whens of length, area, volume and capacity, weight, and miscellaneous units.
Math2.org (formerly Dave's Math Tables) (Manura)
A table of areas, volumes, and surface areas from a collection of useful math reference tables, formatted especially for the Web.
How Many? A Dictionary of Units of Measurement (Rowlett)
A dictionary of both metric (SI) and English measurement units, with history, links to related sites, and a bibliography.
Metric Conversion Factors
This list from the Washington State Department of Transportation provides conversions between U.S. customary units and SI (International System) units.
Metric System/International System of Units (SI) (Proot)
How the metric system and the SI correlate with other systems, and the physical and engineering units: history of systems; basic units (length, weight, time, temperature); secondary units (area and volume); physics (force, pressure, work & energy, power).
Metric System and Unit Conversion (Logan)
Advantages of the metric system: it was based on a decimal system (i.e.: powers of ten) and therefore simplifies calculations; it is used by most other nations of the world, and therefore has commercial and trade advantages. If an American manufacturer with domestic and international customers is to compete, it must absorb the added cost of dealing with two systems of measurement. List of prefixes, types of measure.
SI - The International System of Units (Kemp)
Introduction to the Metric System. The International System of Units (SI) is a modernized version of the metric system established by international agreement. SI provides a logical and interconnected framework for all measurements in science, industry, and commerce. The metric system is much simpler to use than the existing English system since all its units of measurement are divisible by 10. More metric information; GAO report on highway signs, FAQ.

 Projects and Competitions

Measurement in Motion Math/Science Competition (Learning in Motion)
Pose an interesting math or science question, based on either a supplied QuickTime movie or a QuickTime movie of your own. Then use Measurement in Motion to investigate and analyze the movie, and present your results. Eligible students must be enrolled in a K-12 school within the United States or its territories, and be sponsored by a teacher. Entries can be submitted by a single student or a group of students.
The Noon Observation Project - March 1996 or
The Noon Observation Project - March 1997 (Levin, Rogers, Waugh & Smith)
A joint effort among interested schools worldwide in accurately estimating the circumference of the earth. Mathemetics (algebra, geometry, trigonometry, elementary statistics), science, social science, social studies, and geography can be enhanced through this project. How to compute local noon at your location; a form for submitting your Noon Observations; an explanation of the formulas for computing the Earth's circumference from the shadow lengths; Eratosthenes.
 
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Mara Landers

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