Lesson: Measure Twice, Cut Once

Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

A black and white graphic of a man measuring slope using a 24-inch level and tape measure.
Measuring slope.
copyright
Copyright © U.S. Department of Justice, Americans with Disabilities Act, http://www.ada.gov/images/measureslope.gif

Summary

Students learn the metric units engineers use to measure mass, distance (or length) and volume. They make estimations using these units and compare their guesses with actual values. To introduce the concepts, the teacher needs access to a meter stick, a one-liter bottle, a glass container that measures milliliters and a gram scale.
This engineering curriculum meets Next Generation Science Standards (NGSS).

Engineering Connection

Engineers use many different methods of measurement, depending on the task at hand. The scales they use range from tiny to very large, and all measurements need to be accurate and precise. Both accuracy and precision are very important — whether building the cars for a new rollercoaster or developing a new type of medicine — because small mistakes can lead to big disasters!

Pre-Req Knowledge

Students should have some prior experience with the terms mass, distance, length and volume.

Learning Objectives

After this lesson, students should be able to:

  • List which units of measurement are used for different properties.
  • Estimate simple measurements of distance and length.
  • Explain how engineers use measurement and understand the importance of accuracy and precision in engineering design.

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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.

  • Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem. (Grades 3 - 5) Details... View more aligned curriculum... Do you agree with this alignment?
  • Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
  • 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. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
  • Appropriate measurement tools, units, and systems are used to measure different attributes of objects and time. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
  • Convert among different-sized standard measurement units within a given measurement system. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
Suggest an alignment not listed above

Introduction/Motivation

You are probably familiar with units such as pounds, feet, inches and gallons, but engineers also frequently use units of meters, grams and liters. These units are a part of the metric system. What kinds of things do you think engineers might need to measure? (Have students brainstorm "measuring" situations. Possible answers may include: height of a roller coaster, volume of a large aquarium, weight of a rocket, or distance across a bridge.) As young engineers, we should practice using the metric system also.

Let's start out by thinking about distance. How far away do you think I am from the back of the room? (Students will probably reply in units of feet.) As an engineer, we would use a unit called a meter to discuss this distance. This is how long a meter is. (Hold up a meter stick.) One meter equals about 3 feet. So, knowing this, how many meters from the back of the room do you think I am standing? Excellent guesses! Does someone want to use this meter stick and find out the correct measurement? (Select a student to measure the distance and write it on the white/chalk board.) Can you estimate how far from school you live in meters? Does this seem like a long way away (similar to saying I live 2,000 feet from school)? A much better unit of measurement for this is a kilometer. There are 1,000 meters in one kilometer and 0.62 miles in one kilometer. This means that one mile is longer than one kilometer. How far from school do you think you live in units of kilometers? (Take a few student estimates and write this value on the chalk/white board.) How far away do you think the sun is in kilometers? (Again, write several students' guesses on the board.) The sun is nearly 150,000,000 kilometers (about 93 million miles) away! (Write this figure on the board also.) This distance is enormous!

Let's look at something smaller. Think about the distance from your heel to your toe? Would we use a kilometer? (Answer: No) How about a meter? (Answer: You could, but that is still not the best measurement.) Actually, there is an even better unit than a meter — a centimeter. There are 100 centimeters in one meter. Look at your ruler and notice that one side has inches, and the other side might have centimeters. Can you estimate the length of your foot in centimeters? (Take a few student guesses and record this value on the chalk/white board.) Great job! Did you notice on the ruler that the centimeter is broken down into smaller parts? These are called millimeters. Between each centimeter there are 10 millimeters. Can anyone tell me how many millimeters there are in one meter? (Answer: 1,000) What would an engineer measure using millimeters? (Answers may include: the size of a bug, the length of a small piece of wire for a household appliance or even the thickness of a piece of metal.)

Do you wonder if there are even smaller units? Yes, there are (the picometer and nanometer, among others). What are some possible things you imagine might need to be measured that are smaller than a millimeter? (Possible answers: size of cells or bacteria, tiny circuits for computers and other electronic devices.) To measure in micrometers, you would need a microscope for this!

Many engineers need to measure length of distance as part of their work. For example, a civil engineer might want to measure the length of a bridge in meters or kilometers, and a biomedical engineer might want to measure the length of a small bone in centimeters or millimeters.

All of these things we have talked about so far are measurements of distance or length. There are other quantities of an object we might want to measure, also. For example, we can measure the length of a text book, but we also might want to measure its mass. Remember that mass is the amount of matter in an object. (Remind students that mass is different than weight.) What do you think the mass of this text book is? (Students' answers will probably be in pounds.) Great! These are all good guesses. As scientists and engineers, we use a unit called a gram. One pound is equal to about 454 grams. (Write this relation on the board and then ask students which unit is smaller.) A green pea, for example, has a mass of about one gram. What do you think the mass of an apple is in grams? (Record a few students' estimates on the chalk/white board.)

How about something more massive, such as a stack of dictionaries? There is a better unit to use for massive objects: a kilogram. One kilogram equals about 2 pounds or 1,000 grams (write this relation on the board). Now think of an object with very little mass, such as a grain of rice. Would you use kilograms to measure its weight? (Answer: No) How about grams? (Answer: No) We would use an even smaller unit called a milligram. There are 1,000 milligrams in one gram.

Do you notice a similarity between kilogram and kilometer? These two words have the prefix kilo (underline this portion of both words). Kilo means 1,000 in the metric system.

Can anyone think of another quantity you may want to measure? How about liquid? No, it's not temperature in this case (although temperature is a very important quantity that engineers need to measure). Let's assume you wanted to measure how much of a liquid you had. What units might you use? Think of a jug of milk. Your mom or dad may often purchase a "gallon" of milk from the store. A gallon is a unit of volume, but like inches and pounds, it is not the scientific unit of measurement. Instead, engineers use liters. This is a liter. (Show the students a one-liter bottle.) Just like meters and grams, liters are divided into larger and smaller units as well. The most common of these is a milliliter. Is a milliliter larger or smaller than a liter? (Answer: Smaller) Correct! There are 1,000 milliliters in one liter, so the milliliter is smaller. (Show the students a milliliter with a glass measuring cup. Fill the cup with a colored liquid.) Can you estimate the volume of liquid in this cup? (Have students record this guess.) What might an engineer measure in liters? (Answer: An environmental engineer might design a water storage tank to hold a certain number of liters, or a biomedical or chemical engineer might measure medicines or chemicals in milliliters.)

Now that we know how and why engineers measure different things, can you think of a reason why it would be important for an engineer to make an accurate measurement? What would happen if an aerospace engineer designed a rocket to carry humans to Mars and they made a mistake when measuring the size of the fuel tank? The astronauts might not have enough fuel to make it back to Earth and not only would we lose the rocket, we would lose the lives of the astronauts and all the hard work and money that went into the space mission! Can you think of another example of how a small mistake in measurement could result in a big disaster? (Example: If a chemical engineer measured the volume of a solution incorrectly when they were creating a new medicine, they might make people much more sick, rather than enabling them to get well.)

Let's measure the quantities that we estimated earlier. (Measure the mass of the apple, and the volume of the liquid in front of the class. Have the students measure the length of their foot.) Now that we have measured these values, compare them to your estimates. Were you close?

Lesson Background and Concepts for Teachers

Table shows prefixes, abbreviations and number of units for giga, mega, kilo, hector, deka, meter/gram/leter, deci, centi, milli, micro.
Table of metric units.
copyright
Copyright © ITL Program, College of Engineering, University of Colorado at Boulder.

Imperial to Metric Conversion (approximations):

1 pound (lb) = 0.454 kilograms (kg) = 454 grams (g)

1 foot (ft) = 0.305 meters (m)

1 mile (mi) = 1.61 kilometers (km)

1 inch (in) = 2.54 centimeters (cm)

1 gallon (gal) = 3.78 liters (l)

1 ounce (oz) = 29.6 milliliters (ml)

Metric to Imperial Conversions (approximations):

1 kilogram (kg) = 2.21 pounds (lbs)

1 meter (m) = 3.28 feet

1 kilometer (km) = 0.621 miles (mi)

1 centimeter = 0.394 inches (in)

1 liter = 0.265 gallons (g)

1 milliliter (ml) = .0338 ounces (oz)

Vocabulary/Definitions

imperial units: A system of units first developed by the British Weight and Measures Act. Also referred to as foot-pound-second units.

mass: The amount of matter in an object.

metric units: A decimalized system of units devised around the number 10. Also referred to as the International System of Units, or SI units.

Associated Activities

  • Give an Inch, Take a Foot - Students use a word-bank of measurement vocabulary to complete sentences. They also make estimations of length and distance and compare their values with the values they measure with a meter stick or ruler.
  • Mint-Mobiles - Students build small race cars made from lifesaver-shaped candies, plastic drinking straws, Popsicle sticks and index cards, as a way to explore independent and dependent variables. They also practice the engineering design process by brainstorming, planning, building, testing, and improving their "mint-mobiles."

Lesson Closure

It is very important for engineers to know what units to use to measure certain quantities. Why? This is critical when an engineer presents data or when s/he needs to recreate an experiment or rebuild a device. It is also important for communication with engineers in other cities or countries. For example, think about how hard it would be to bake a delicious cake for the first time without a recipe. How would we know how much flower or sugar to add? Knowing how to measure accurately assures that we have just the right amounts of all the ingredients.

So, as we have discussed, there are many different units of measure. It is important to have an understanding of the metric system, as it is used all over the world. It is especially important for engineers to have knowledge of units of measurement so that they can develop the safest and most effective products.

Attachments

Assessment

Pre-Introduction Assessment

Brainstorming/Prior Knowledge: Have students list some quantities that engineers might need to measure along with their corresponding units. Also, have them list reasons why measuring is important.

Post Introduction Assessment

Estimation: Have the students estimate the following quantities in metric units:

  1. The distance from their home to school (km)
  2. The length of their foot (cm)
  3. The mass of their favorite pet (kg)
  4. The mass of an apple (g)
  5. The volume of liquid in the container (mL)

Afterwards, tell the students the actual mass of the apple and the actual volume of liquid in the container and have students measure the length of their foot. Have the students compare their estimates with the actual values and comment on their predictions: "My prediction for the mass of the apple was too big," or "I thought the mass of the apple was less than the actual mass."

Lesson Summary Assessment

Class Discussion: List several types of engineers on the Board. (Possible examples could include: civil engineers, mechanical engineers, aerospace engineers, chemical engineers, environmental engineers, etc.) For each type of engineer, have students think of at least one measurement that would be important for that type of engineer's job and the units they would use. Also, have them think about the disasters that could occur if the measurements are not accurate. Encourage the students to share their answers with the class.

Homework: Have the students complete the Practice Your Units Worksheet; review their answers to gauge their mastery of the subject.

Lesson Extension Activities

Have the class measure several of the objects in the room (teacher's desk, students' desks, book cases, chalk/white boards, closets, windows, etc.) by assigning a group of students a task (for example, one group would be in charge of measuring and counting the total number of desks and tables, another group would be in charge of measuring the width of doors, windows, and chalk/white boards, etc.) After all of the objects have been measured, have each group pretend they are an architectural engineering team working to create a layout of the classroom. Students should make a scaled poster or drawing to present to the class.

Contributors

Lesley Herrmann; Malinda Schaefer Zarske; Janet Yowell

Copyright

© 2010 by Regents of the University of Colorado.

Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

Acknowledgements

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: July 31, 2017

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