Lesson 1.3 – Measurement and Statistics

Preface
The practice of measuring is older than recorded history. Every human civilization throughout history developed its own measuring tools and, along with them, its own measuring standards. It was through the establishment of measuring tools and standards that the Egyptians were able to build their giant pyramids, and the Romans were able to build their roads and aqueducts. Shared understanding and communication established through standardization played a key role in their successful outcome. Standardization is what allows many people to work individually on parts that come together to form a finished product or system. Without measurement standards, manufactured parts would not be interchangeable and mass production could not exist. Measurement is so important that the founding fathers of the United States included it in the Constitution, giving Congress the power to set uniform standards for weights and measures. Today, the American National Standards Institute serves as the unifying force system for the measurement used in the United States. This lesson provides an introduction to measurement through the study of linear distance and angles.

Since the beginning, scientists have realized the laws of nature are not bound to the borders between kingdoms or countries, and that uniform standards of measure form the foundation for changing the secrets of the universe into human knowledge. In the midst of the French Revolution, scientists developed a new system of measurement that was simple, logical, and well-suited to the needs of both scientists and engineers. Since its inception 220 years ago, the metric system has spread throughout the industrialized world, and is now the international standard for acquiring and communicating measurements.

In this lesson, students will learn about measurement and statistics. They will apply what they have learned through
  • basic dimensioning techniques.
  • reading English and metric scales.
  • converting measurements between English and metric units.
  • performing precision measurement using dial calipers.
  • recording data
  • performing basic statistical analysis.
  • creating graphs of statistical information.

Concepts
1. Measurement systems were developed out of the need for standardization.
2. Engineers apply dimensions to drawings to communicate size information.
3. Manufactured parts are often created in different countries, where dimensional values are often converted from one standard unit to another.
4. The amount of variation that can be measured depends on the precision of the measuring tool.
5. Statistical analysis of measurements can help to verify the quality of a design or process.
6. Engineers use graphics to communicate patterns in recorded data.

Standards and Benchmarks Addressed
Standards for Technological Literacy
Standard 1:
Students will develop an understanding of the characteristics and scope of technology.
BM B:
All people use tools and techniques to help them do things.
Standard 2:
Students will develop an understanding of the core concepts of technology.
BM K:
Tools and machines extend human capabilities, such as holding, lifting, carrying, fastening, separating, and computing.
Standard 3:
Students will develop an understanding of the relationships among technologies and the connections between technology and other fields of study.
BM A:
The study of technology uses many of the same ideas and skills as other subjects.
BM F:
Knowledge gained from other fields of study has a direct effect on the development of technological products and systems.
Standard 7:
Students will develop an understanding of the influence of technology on history.
BM E:
The design and construction of structures for service or convenience have evolved from the development of techniques for measurement, controlling systems, and the understanding of spatial relationships.
Standard 17:
Students will develop an understanding of and be able to select and use information and communication technologies.
BM Q:
Technological knowledge and processes are communicated using symbols, measurement, conventions, icons, graphic images, and languages that incorporate a variety of visual, auditory, and tactile stimuli.

National Science Education Standards
Unifying Concepts and Processes Standard K-12: As a result of activities in grades 9-12, all students should develop
  • Change, constancy, and measurement
Science as Inquiry Standard A: As a result of activities in grades 9-12, all students should develop
  • Abilities necessary to do scientific inquiry
Science and Technology Standard E: As a result of activities in grades 9-12, all students should develop
  • Abilities of technological design

Principles and Standards for School Mathematics
Number Operations:
Instructional programs from pre-kindergarten through grade 12 should enable all students to understand numbers, ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and how they relate to one another; and compute fluently and make reasonable estimates.
Measurement:
Instructional programs from pre-kindergarten through grade 12 should enable all students to understand measurable attributes of objects and the units, systems, and processes of measurement; and apply appropriate techniques, tools, and formulas to determine measurements.
Data Analysis and Probability:
Instructional programs from pre-kindergarten through grade 12 should enable all students to formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
Representation:
Instructional programs from pre-kindergarten through grade 12 should enable all students to create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena.

Standards for English Language Arts
Standard 4:
Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.
Standard 8:
Students use a variety of technological and informational resources (e.g., libraries, databases, computer networks, video) to gather and synthesize information and to create and communicate knowledge.
Standard 12:
Students use spoken, written and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Performance Objectives
It is expected that students will:
  • Research and design a CD cover or book jacket on the origins of the measurement systems.
  • Measure and record linear distances using a scale to a precision of 1/16 inch and 1 mm.
  • Measure and record linear distances using a dial caliper to a precision of 0.001 inch.
  • Add and subtract U.S. standard and metric linear measurements.
  • Convert linear distance measurements from inches to millimeters and vice versa.
  • Apply linear dimensions to a multiview drawing.
  • Calculate the mean, mode, median, and range of a data set.
  • Create a histogram of recorded measurements showing data elements or class intervals, and frequency.

Assessment
Explanation
1. Students will explain the history of measurement to a younger student using their book jacket or CD cover as an example.
Application
2. Assess a student’s journal for evidence of effective communication of ideas such as,
a. Do students’ sketches and drawings clearly communicate their ideas?
b. Have students used a variety of methods to communicate their ideas?
c. Have students integrated information from a variety of sources into their work?
3. Students will demonstrate and explain to another student how to measure objects using a scale or dial caliper.
Interpretation
4. Students will make journal entries reflecting on their learning and experiences. Example of prompts for the general entries: Write about what you learned in class today. How do you know when your sketches are ready to transfer into a drawing? What is something you learned today that you did not understand or know before?
Self-Knowledge
5. Students will be required to reflect on their work in their journals by recording their thoughts and ideas. They may use their self-assessments as a basis for improvement. Ideas and questions students may pose and answer in their journals are:
  • Today, the hardest part for me to understand was…
  • When I work in a group, I find that…
  • When I work by myself, I find that…
  • What did I accomplish today?
  • Now that I have done this, what is next?
Perspective
6. Students will select an engineering blunder and prepare an essay that expresses two points of view about the role played by measurement.

Essential Questions
1. Why did our ancestors create measurement standards?
2. Who is responsible for establishing measurement standards that are used by engineers and manufacturers today?
3. What methods do engineers use to communicate an object’s dimensional information?
4. What problems could result from incorrectly converting measurements from one system to another?
5. What factors influence the precision of a measuring tool?
6. What information can a designer use from a statistical analysis of a product?

Key Terms
Data Set
A group of individual values or bits of information that are related in some way or have some common characteristic or attribute.
Dimension
A measurable extent, such as the three principal dimensions of an object is width, height, and depth. Length and thickness are not used because they cannont be applied in all cases. The front view of an object shows only the height and width and not the depth. In fact, any one view of a three-dimensional object can show only two dimensions, the third dimension will be found in an adjacent view.
Dimension Lines
Lines that are thin lines capped with arrowheads, which may be broken along their length to provide space for the dimension numerals.
English System
Also referred to as the U.S. Customary system. The measuring system based on the foot, second, and pound as units of length, time, and weight or mass.
Extension Lines
Thin lines used to establish the extent of a dimension. Extension lines begin with a short space from the object and extend to about .125 inches past the last dimension line. Extension lines may cross object lines, center lines, hidden lines, and other extension lines, but may not cross dimension lines.
Foot
A unit of linear measure equal to 12 inches or 30.48 cm.
Frequency
The rate at which something occurs over a particular period or in a given sample.
Graph
A diagram showing the relation between variable quantities, typically of two variables measured along a pair of lines at right angles.
Histogram
A graph of vertical bars representing the frequency distribution of a set of data.
Inch
A unit of linear measure equal to one twelfth of a foot or 2.54 cm.
International Organization for Standardization (ISO)
A non-governmental global organization whose principal activity is the development of technical standards through consensus.
Mean
The average or central value of a set of quantities.
Measure
To determine the size, amount, or degree of something by comparison with a standard unit.
Median
Referring to the middle term or mean of the middle two terms of a series of values arranged in order of magnitude.
Meter
The fundamental unit of length in the metric system, equal to 100 centimeters or approximately 39.37 inches.
Metric System
The decimal measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass.
Millimeter
A metric unit of linear measure equal to 1/1000 of a meter.
Mode
The value that occurs most frequently in a given data set.
Normal Distribution
A function that represents the distribution of variables as a symmetrical bell-shaped graph.
Numeric Constraint
A number value, or algebraic equation that is used to control the size or location of a geometric figure.
Precision
Exact in measuring, recording, etc.
Scale
1. A straight-edged strip of rigid material marked at regular intervals and used to measure distances. 2. A proportion between two sets of dimensions used in developing accurate, larger or smaller prototypes, or models of design ideas.
Standard
Something considered by an authority or by general consent as a basis of comparison.
Statistics
Collection of methods for planning experiments, obtaining data, organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on data.
Two-Dimensional
Having the dimensions of height and width, height and depth, or width and depth only.
Unit
A standard quantity in terms of which other quantities may be expressed.
Variation
A change or slight difference in condition, amount, or level.