**Algebra-Based Physics:** Measurement and the Language of Physics Units

This topic contains a selection of units designed to help you to teach physics. In physics, using precise measurements and standard units is important in comparing physical quantities and understanding basic concepts.

### Frames of Reference (4)

#### Lesson Plans:

Any measurement of position, distance, or speed must be made with respect to a reference frame. This item is 3-part module for teaching frames of reference. It contains background information, warm-up questions, and step-by-step procedures for lessons on the aberration of starlight and a non-mathematical introduction to the Theory of Relativity.

**Item Type:**Lesson Plan

**Level:**High School Physics

**Duration:**2-3 class periods

#### Activities:

All motion is relative to a frame of reference. This interactive animation is a great introduction to a topic that is often difficult for students to grasp. It shows how the motion of a bouncing basketball looks different depending on whether the observer is standing still, walking in the same direction as the player, or walking in the opposite direction. It offers nine scenarios (frames of reference), and students must answer questions from the observer's viewpoint.

**Item Type:**Interactive Tutorial

**Level:**Grades 7-12

**Duration:**20-30 minutes

When introducing frames of reference, it helps if your students have a sense of scale. In this wonderful update of "Powers of 10", your students view images of the Milky Way at 10 million light years from Earth, then move through space at successive orders of magnitude until they reach an oak tree in Florida. After that, the applet decreases in progression down to molecular structure of one leaf, and on to chromatin, DNA, and subatomic particles.

**Item Type:**Image Set

**Level:**Grades 4-12

**Duration:**15 minutes

#### Student Tutorials:

This unique website compares the magnitude and size of a broad variety of objects, using colored histograms for ease of visual comparison. Objects range from the nanoscale to distances between galaxies. Most items are linked to annotated reference pages.

**Item Type:**Online Tutorial

**Level:**Grades 9-12

**Duration:**30 minutes

### Physics Terminology (3)

#### Activities:

If you've never visited the award-winning *Hyperphysics* web site, put it on your list. It is a set of online tutorials that features concept maps laid out in a web-like fashion for easy navigation. This page describes units of measurement, unit conversions, dimensional analysis, and basic mechanical quantities. Some of the maps are "active graphics", which link to capsules of background information. Remarkably easy to use!

**Item Type:**Reference Material

**Level:**Teacher Support

#### References and Collections:

As the name implies, this web page offers non-scientists a guide to SI. The materials are written so that a user with little prior experience with metrics can comprehend the measurements and how they are applied mathematically. ****NOTE: This is a 1.5MB download.*

**Item Type:**Reference Material

**Level:**Teacher Support

#### Student Tutorials:

To a beginning student, the unfamiliar language of physics can seem like a foreign tongue. This tutorial, part of the respected *Physics Classroom* collection, is an interactive introduction to some basic terminology. It focuses on scalars, vectors, distance, and displacement.

**Item Type:**Interactive Tutorial

**Level:**Grades 9-12

**Duration:**30 minutes

### Units of Measure (7)

#### Activities:

This item provides rules and "how-tos" for calculating both the relative and absolute uncertainty in a measurement.

**Item Type:**Tutorial

**Level:**Teacher Support

This resource is a digital tool for performing unit conversions with the extra feature of displaying cancellation of terms, helping students to gain a deeper understanding of the mathematical processes involved. Students can convert among 25 physical quantities, including units such as force, temperature, energy, and current.

**Item Type:**Mathematical Tool

**Level:**Grades 6-12

#### References and Collections:

All mechanical quantities can be expressed in terms of three quantities: length, mass, and time. This item is part of the highly-regarded *Hyperphysics* concept maps. It describes units of measurement, unit conversions, dimensional analysis, and basic mechanical quantities. Some of the maps are "active graphics", which link to capsules of background information. Remarkably easy to use!

**Item Type:**Reference Material

**Level:**High School

Information at the foundation of modern science and technology from the Physics Laboratory of NIST

**Item Type:**Reference Material

**Level:**Teacher Support

This comprehesive guide on SI encompasses tables, charts, drawings, and a coherent set of text explanations of base units, derived units, common quantities, equivalencies, and prefixes. It is written so that a user with no prior experience with metrics can comprehend the measurements and how they are applied mathematically.

**Item Type:**Reference Material

**Level:**Teacher Support

Teachers will find in-depth information on base units, derived units, and relationships among SI units in this free web site developed and maintained by NIST (the National Institute for Science and Technology). Don't miss the link to the "Digital Dutch" unit converter. It is amazingly easy to use.

**Item Type:**Reference Material

**Level:**Teacher Support

#### Assessment:

This resource is a formal study addressing two research questions: 1) Does student understanding of measurement processes change through active lab participation, and 2) What patterns exist in how students understand this topic prior to intensive lab participation. This resource links to the full article at no cost to the user.

**Item Type:**Scholarly Article

**Level:**Teacher Support

### Applying Measurement in Physics (13)

#### Lesson Plans:

This 3-day inquiry-based lesson is a great way for students to discover what "accuracy" and "precision" mean in measurement. Fun hands-on activities include measuring objects using ancient "cubit" units and tossing foam darts to gather data. The lesson concludes as students work cooperatively to explore using significant figures in an Internet project.

**Item Type:**Cooperative Learning

**Level:**Grades 7-12

**Duration:**3 class periods

An exceptional resource collection on how to integrate "direct measurement videos". These high-speed short videos feature tools for easy analysis of various physical situations: rulers, grids, frame-counters, and screen overlays for making precise measurements. Includes 9 teaching modules with lesson plans, assessments and answer keys, and pedagogical background. *Does not require purchase or installation of video analysis software.*

**Item Type:**Video Analysis Lessons

**Level:**Grades 8-12

#### Activities:

This cost-free web page allows teachers and learners to easily create and print graphs for use as visual communication tools. With one click, the students may choose from five graph types: bar, line, area, pie, and X/Y. Various patterns, colors, grids, and label choices are available to allow customization.

**Item Type:**Graph-Making Tool

**Level:**Grades 4-12

A simple online game to help beginning students get a feel for the rules of significant figures. The score is automatically tallied, with explanations given for incorrect responses. ***After completing this activity, try the resource directly below in cooperative learning groups. For background info, see the tutorial below from the University of Guelph.*

**Item Type:**Interactive Game

**Level:**High School

**Duration:**20-30 minutes

After introducing the rules of significant figures, students can test their skills in this interactive drill & skill. We suggest setting up cooperative learning groups to make it a game. *NOTE FROM THE EDITOR: beginning students often misunderstand or overestimate the usefulness of significant figures. In real-world research laboratories, practicing scientists commonly express uncertainty quantities as a separate numeral. Good examples of how to express uncertainty can be found in the NIST Fundamental Physical Constants (Reference below).*

**Item Type:**Problem Set

**Level:**High School

**Duration:**30 minutes

How small is the error between two and three significant digits? How about three and four digits? Can the error be ignored? This activity would be a great choice for students who have already been exposed to the basics of significant figures. They enter a number, then select the number of significant digits from 1-5. The resultant numbers are automatically displayed, plus the percent error.

**Item Type:**Interactive Problem Set

**Level:**High School

**Duration:**30 minutes

This is a really nice interactive simulation to give students virtual practice in using a micrometer, a device for doing ultra-precise measurement down to the level of 1 micrometer. Each time the "reset" button is pressed, a random-size object appears on screen. Students use sliders to move the object into place, perform the measurement, and check the accuracy of their reading.

**Item Type:**Interactive Simulation

**Level:**Grades 7-12

**Duration:**30 minutes

This Java-based activity lets students manipulate a 3-D rectangular prism or triangular prism to explore surface area and volume. It's designed to help secondary students visualize the relationship of width, depth, and height in calculating and estimating volume/surface area.

**Item Type:**Interactive Simulation

**Level:**Grades 5-10

**Duration:**30 minutes

#### References and Collections:

This resource is a formal study addressing two research questions: 1) Does student understanding of measurement processes change through active lab participation, and 2) What patterns exist in how students understand this topic prior to intensive lab participation. This resource links to the full article at no cost to the user.

**Item Type:**Scholarly Article

**Level:**Teacher Support

Values of the fundamental physical constants, recommended for international use, are provided at this web site. These are the latest values of the constants recommended by CODATA (updated in 2006). Need background information? It's all there, in an easily-searchable format.

**Item Type:**Reference Material

**Level:**Grades 9-12

#### Student Tutorials:

This item, part of the Open Door website, discusses the role of uncertainty in measurement. Students learn the difference between systematic and random error, and gain practice in quantifying the error. Also find high-quality sections on the Vernier scale, "best-fit line", and sampling frequency.

**Item Type:**Online Tutorial

**Level:**High School

**Duration:**One class period

Measurement of physical objects is, by nature, imprecise. When rounding numbers, you must use enough digits to minimize errors. However, if too many digits are used, errors can be easily made keeping track of all the numerical values. This tutorial will help students with the basic rules. ***Under Activities above are two applets to give students interactive practice in significant figures.*

**Item Type:**Interactive Tutorial

**Level:**High School

**Duration:**30 minutes

Converting between units doesn't have to be frustrating to your students. This tutorial, part of an award-winning collection, is the best we found for demonstrating how to use unit cancellation to solve problems involving unit conversions.

**Item Type:**Online Tutorial

**Level:**Grades 8-12

### For the New Teacher (4)

#### Activities:

This digital unit converter offers students more than the typical online conversion resource. It allows conversion among 25 physical quantities, from more common applications (force, energy, current, voltage) to lesser-used conversions such as illuminance and magnetic flux. It provides the additional feature of displaying cancellation of terms, helping beginners to gain a deeper understanding of the mathematical processes involved.

**Item Type:**Mathematical Tool

**Level:**Grades 6-12

#### References and Collections:

This resource is a comprehensive guide on SI for teachers and students. It contains tables, charts, and text explanations of base units, derived units, equivalencies, common quantities, and prefixes. To aid the learner in visualizing quantities, drawings of common multiples are provided for each of the base units. The materials are written so that a user with no prior experience with metrics can comprehend the measurements and how they are applied mathematically.

**Item Type:**Reference Material

**Level:**Teacher Support

This is a comprehensive set of tutorials for learning algebra-based introductory physics, organized by topic. It could be quite useful for students who need extra help or for crossover teachers seeking content support. A $5.00 annual feel gives access to additional simulations and resources.

**Item Type:**Tutorial Collection

**Level:**High School Physics

#### Content Support For Teachers:

This item, part of the Open Door website, discusses the role of uncertainty in measurement. Review the difference between systematic and random error, and gain practice in quantifying the error. Also find high-quality sections on the Vernier scale, "best-fit line", and sampling frequency.

**Item Type:**Online Tutorial

**Level:**Teacher Support

### Teaching Tools (4)

#### Activities:

A helpful online unit converter for teachers and students.

**Item Type:**Mathematical Tool

**Level:**Grades 6-12

This cost-free web page allows teachers and learners to easily create and print graphs for use as visual communication tools. With one click, the students may choose from five graph types: bar, line, area, pie, and X/Y. Various patterns, colors, grids, and label choices are available to allow customization.

**Item Type:**Graph-Making Tool

**Level:**Grades 4-12

#### References and Collections:

A site that lists the constants with all types of units and gives a tutorial on calculating uncertainty.

**Item Type:**Reference Material

**Level:**Teacher Support

#### Content Support For Teachers:

A good resource that gives the teacher tools to get at students' prior knowledge about measurement and uncertainty.

**Item Type:**Scholarly Article

**Level:**Teacher Support

### Dimensional Analysis (5)

#### Activities:

Dimensional analysis (DA) is a technique that is used to change any unit from one to another and to validate equations. Students who understand DA have a definite advantage in solving problems. This terrific interactive tutorial starts with slowly-paced guidance, then progresses with conversion problems. Cool tools include a "Pencil & Eraser" allowing students to draw lines to cancel units, and a "Balance" tool to tell them whether their conversion factors are valid. *Requires Shockwave plug-in.*

**Item Type:**Interactive Tutorial

**Level:**Grades 9-12

**Duration:**One class period

#### Content Support For Teachers:

This web page is part of the highly-regarded *Hyperphysics* concept maps. It describes units of measurement, unit conversions, dimensional analysis, and basic mechanical quantities. Some of the maps are "active graphics", which link to capsules of background information. Remarkably easy to use!

**Item Type:**Reference Material

**Level:**Teacher Support

#### Student Tutorials:

Dimensions of a quantity refer to the combination of units or *base quantities* that make it up. Most physical quantities can be expressed in terms of five basic dimensions and their combinations: mass, length, time, electrical current, and temperature. Often, students have difficulty understanding why dimensions are different than units. This tutorial contains basic information, 3 short quizzes and one longer post-test. Your students can move at their own pace or work in cooperative groups. ***NOTE: This activity can be done without computers, as all components are printable.*

**Item Type:**Instructional Module

**Level:**Grades 9-12

**Duration:**2-3 class periods

Your students will need to understand how to cancel units before they can solve problems using dimensional analysis. Beginning with simple one-step conversions, it progresses to problems requiring multiple conversions. Students will like the informal writing style by the author, whose motto is "If I can do this stuff, then so can you!"

**Item Type:**Online Tutorial

**Level:**Grades 8-12

#### Assessment:

This resource is a formal study assessing student understanding of measurement and uncertainty. It was administered to more than 500 students at two large research universities to address these questions: 1) How does student understanding change over one semester from participating in an introductory physics course with a lab, and 2) What patterns exist in student reasoning pertaining to measurement and uncertainty prior to instruction?

**Item Type:**Scholarly Article

**Level:**Teacher Support

### Scale, Order of Magnitude, and Estimation (4)

#### Activities:

Students explore size estimation in 1, 2, and 3 dimensions. Multiple levels of difficulty allow for progressive skill improvement. CAUTION: This activity is addictive!

**Item Type:**Interactive Animation

**Level:**Grades 6-12

**Duration:**One class period

An updated version of "Powers of 10". View the Milky Way at 10 million light years from Earth, then move through space at successive orders of magnitude until you reach an oak tree in Florida. After than, move from a single leaf to the cell nucleus, chromatin, DNA, and subatomic particles.

**Item Type:**Image Set

**Level:**Grades 4-12

**Duration:**15 minutes

Interactively explore various specimens as they appear under a scanning electron microscope (SEM). SEM can produce very high-resolution photos of details as small as 1-5 nanometers. Students can adjust the focus, brightness, and contrast, and choose from a cockroach, pollen grain, diatom, a gecko foot, a jellyfish, and more. Each successive image doubles the magnitude of the magnification.

**Item Type:**Images/Illustrations

**Level:**Grades 5-12

**Duration:**30 minutes

This newer and beautifully designed version of Powers of 10 takes students on a "nano-journey" inside a carbon-based cell, an LED diode, and a laptop microchip. At each descending level, you can click on background information and additional Flash simulations. Kids can choose from 3 images and send "postcards" to friends about their journey. *Fair warning: this resource is so engaging, be prepared to spend at least an hour on your trip.*

**Item Type:**Interactive Tutorial

**Level:**Grades 6-12

**Duration:**One Class Period

### Assessments (2)

#### References and Collections:

The National Assessment of Educational Progress (NAEP) is the only nationally administered, continuing assessment of what America's students know and can do in various subject areas. This website provides free access to the most recent assessment questions, organized by topic and level. Teachers can view an analysis of the results to see short-term and long-term trends in samples of students at ages 9, 13, or 17 years.

**Item Type:**Assessment Tool

**Level:**Grades K-12

#### Assessment:

This activity helps students understand concepts of position and coordinates. Students must locate points on a graph paper using either components or distance and angle.

**Item Type:**Problem Set

**Level:**Grades 9-12

**Duration:**One class period