This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.

Students use their understanding of projectile physics and fluid dynamics to find the water pressure in water guns. By measuring the range of the water jets, they are able to calculate the theoretical pressure. Students create graphs to analyze how the predicted pressure relates to the number of times they pump the water gun before shooting.

Students perform one of the first steps that environmental engineers do to determine water quality sampling and analysis. Student teams measure the electrical conductivity of four water samples (deionized water, purified water, school tap water and a salt-water solution) using teacher-made LED-conductivity testers and commercially available electrical conductivity meters. They use multimeters to also measure the resistance of the samples. They graph their collected data to see the relationship between the conductivity and resistance. Then, all students measure the conductivity of tap water samples brought to school from their homes; they organize and average their data by sub areas within their local school district to see if house location has any relationship to the water conductivity in their community.

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions. The task is designed to encourage students to communicate their findings in a narrative/report form in context Đ not just simply as a computed number.

By this point in the unit, students have learned all the necessary information and conceptualized a design for how an optical biosensor could be used to detect a target strand of DNA associated with a cancer-causing gene as their solution to the unit's challenge question. Now student groups act as engineers again, using a poster format to communicate and prove the validity of the design. Successful posters include a description of refraction, explanations of refraction in a thin film, and the factors that can alter the interference pattern of a thin film. The posters culminate with an explanation of what is expected to be seen in a biosensing device of this type if it were coupled to a target molecule, proven with a specific example and illustrated with drawings and diagrams throughout. All the poster elements combine to prove the accuracy and viability of this method of gene detection. Together with its associated lesson, this activity functions as part of the summative assessment for this unit.

Students learn about the major factors that comprise the design and construction cost of a modern bridge. Before a bridge design is completed, engineers provide overall cost estimates for construction of the bridge. Students learn about the components that go into estimating the total cost, including expenses for site investigation, design, materials, equipment, labor and construction oversight, as well as the trade-off between a design and its cost.

This word problem is based estimating the height of a person over time. Note that there is a significant amount of rounding in the final answer. This is because people almost never report their heights more precisely than the closest half-inch. If we assume that the heights reported in the task stem are rounded to the nearest half-inch, then we should report the heights given in the solution at the same level of precision.

The second volume in a four-part series, this Open Educational Resource (OER) continues a
collection of melodies to support beginning and intermediate ear training study. The melodies in
this resource contain musical attributes in major and minor, simple and compound meters, and
bass and treble clefs, with melodic contours that include large and frequent leaps, and rhythmic
motives with multiple subdivisions of the pulse.

The fourth volume in a four-part series, this Open Educational Resource contains melodies to
support intermediate ear training study. The melodies are organized primarily with melodic
considerations, beginning with diatonic melodies, followed by melodies in C-clefs, then
melodies with chromaticism, and ending with modulations. Many of the melodies have
significant rhythmic motives, with a variety of subdivisions for the pulse. Instructors will notice
several Russian melodies that use the Russian alphabet for the title, followed by the translation.
When I came across the collection of Russian melodies, I could not resist learning a little about
the Russian alphabet and including it in the resource. There are also several Scottish melodies;
the less-challenging Scottish melodies explore the C-clefs, presented first in either the bass or
treble clef, followed by a C-clef to illustrate the relationship between the two clefs.

This Open Educational Resource (OER) was originally inspired to make sight-singing materials
more accessible for the students at The Hartt School, University of Hartford. This is the first of a
four-part resource.

The third volume in a four-part series, this Open Educational Resource (OER) contains melodies
to support intermediate ear training study. The melodies are separated into simple and compound
meter, organized with rhythmic considerations. A few melodies may seem out of place regarding
meter, but are appropriate regarding rhythmic characteristics, for example, the exercises in 5/4
and 7/4 are placed with simple meter. The 3/8 example was intended to bridge the gap between
simple and compound meter, but formatting dictated the 3/8 melody be placed in the 3/2 and 2/2
section. The order is not a prescription, but a presentation of melodies with similar characteristics
that should be applied appropriately to respective curricular objectives. Melodies have been
presented in the treble and bass clefs, in major and minor key signatures through five sharps and
four flats, ensuring an accessible range from A3 to D5 (with middle-C as C4), with the exception
of songs with a broad range that leave no alternative. One note: The first eight measures of #7,
Deign My Voice to Hear, is used in Sight-Singing Level I for Beginning Ear Training Study (#6)
because of the appropriate musical attributes for the first level, and included here with the rest of
the melody applicable at this level.

Why do the lights turn on in a room as soon as you flip a switch? Flip the switch and electrons slowly creep along a wire. The light turns on when the signal reaches it.

Why do the lights turn on in a room as soon as you flip a switch? Flip the switch and electrons slowly creep along a wire. The light turns on when the signal reaches it.

Subject provides a solid theoretical foundation for the analysis and processing of experimental data, and real-time experimental control methods. Includes spectral analysis, filter design, system identification, simulation in continuous and discrete-time domains. Emphasis on practical problems with laboratory exercises. Subject is designated as a d'Arbeloff Laboratory "gateway" subject.

This course covers the fundamentals of signal and system analysis, focusing on representations of discrete-time and continuous-time signals (singularity functions, complex exponentials and geometrics, Fourier representations, Laplace and Z transforms, sampling) and representations of linear, time-invariant systems (difference and differential equations, block diagrams, system functions, poles and zeros, convolution, impulse and step responses, frequency responses). Applications are drawn broadly from engineering and physics, including feedback and control, communications, and signal processing.

This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products. The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier transform and its generalizations, which are explored in detail. Filtering and filter design, modulation, and sampling for both analog and digital systems, as well as exposition and demonstration of the basic concepts of feedback systems for both analog and digital systems, are discussed and illustrated.

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar Ňfinding the solutionÓ problem to thinking about what it really means for a number to be a solution of an equation.

Benjamin Franklin was sixteen years old and working as an apprentice in the Boston print shop of his older brother James when, in April 1722, he began writing a series of essays to be published in the New-England Courant under the pseudonym of “Silence Dogood.” In his Autobiography, Benjamin remembered slipping these essays, written in disguised handwriting, under the door of the Courant, which James was publishing; he assumed (probably correctly) that James would refuse to print an essay from him if he simply asked or submitted it under his own name. James published the essays, which became very popular among the newspaper’s readers. Benjamin kept his authorship of the series a secret, even from his brother, until after he finished writing them in October 1722, at which point James printed an advertisement asking for “Silence Dogood” to come forth. Benjamin confessed that he was the author, which seems to have annoyed his older brother. It was not too long after that that Benjamin left his brother’s shop–breaking his apprenticeship–and moved to Philadelphia.

Student teams make polymers using ordinary household supplies (glue, borax, water). They experiment with the semi-solid material when warm and cold to see and feel its elastic and viscous properties. Students will begin to understand how the electrical forces between particles change as temperature or the force applied to the substance changes. Is it a solid, a liquid, or something in between? How might it be used?