Testing is critical to any design, whether the creation of new software or a bridge across a wide river. Despite risking the quality of the design, the testing stage is often hurried in order to get products to market. In this lesson, students focus on the testing phase of the software/systems design process. They start by exploring existing examples of program testing using the CodingBat website, which contains a series of problems and challenges that students solve using the Java programming language. Working in teams, students practice writing test cases for other groups' code, and then write test cases for a program before writing the program itself.

Students gain a basic understanding of the properties of media soil, sand, compost, gravel and how these materials affect the movement of water (infiltration/percolation) into and below the surface of the ground. They learn about permeability, porosity, particle size, surface area, capillary action, storage capacity and field capacity, and how the characteristics of the materials that compose the media layer ultimately affect the recharging of groundwater tables. They test each type of material, determining storage capacity, field capacity and infiltration rates, seeing the effect of media size on infiltration rate and storage. Then teams apply the testing results to the design their own material mixes that best meet the design requirements. To conclude, they talk about how engineers apply what students learned in the activity about the infiltration rates of different soil materials to the design of stormwater management systems.

Following the steps of the iterative engineering design process, student teams use what they learned in the previous lessons and activity in this unit to research and choose materials for their model heart valves and test those materials to compare their properties to known properties of real heart valve tissues. Once testing is complete, they choose final materials and design and construct prototype valve models, then test them and evaluate their data. Based on their evaluations, students consider how they might redesign their models for improvement and then change some aspect of their models and retest aiming to design optimal heart valve models as solutions to the unit's overarching design challenge. They conclude by presenting for client review, in both verbal and written portfolio/report formats, summaries and descriptions of their final products with supporting data.

Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct an experiment to determine if weight added incrementally to an object affects the amount of friction encountered when it slides across a flat surface. After graphing the data from their experiments, students can calculate the coefficients of friction between the object and the surface it moved upon, for both static and kinetic friction.

In the first part of the activity, each student chews a piece of gum until it loses its sweetness, and then leaves the gum to dry for several days before weighing it to determine the amount of mass lost. This mass corresponds to the amount of sugar in the gum, and can be compared to the amount stated on the package label. In the second part of the activity, students work in groups to design and conduct new experiments based on questions of their own choosing. These questions arise naturally from observations during the first experiment, and from students' own experiences with and knowledge of the many varieties of chewing and bubble gums available.

This task asks students to write a proof that applies the properties of parallel lines and congruent triangles to prove a parallelogram property. It can be used in the classroom as an individual, small group, or whole-group practice problem or as an assessment question. More examples of its use in the classroom can be found in the "Public Remarks" section below. Illustrative Mathematics provides this summary: "This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS triangle congruence theorem, and the fact that opposite sides of parallelograms are congruent."

The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).

How does infrastructure meet our needs? What happens when we are cut off from that supporting infrastructure? As a class, students brainstorm, identify and explore the pathways where their food, water and energy originate, and where wastewater and solid waste go. After creating a diagram that maps a neighborhood's inputs and waste outputs, closed and open system concepts are introduced by imagining the neighborhood enclosed in a giant dome, cut off from its infrastructure systems. Students consider the implications and the importance of sustainable resource and waste management. They learn that resources are interdependent and that recycling wastes into resources is key to sustain a closed system.

Student teams find solutions to hypothetical challenge scenarios that require them to sustainably manage both resources and wastes. They begin by creating a card representing themselves and the resources (inputs) they need and wastes (outputs) they produce. Then they incorporate additional cards for food and energy components and associated necessary resources and waste products. They draw connections between outputs that provide inputs for other needs, and explore the problem of using linear solutions in resource-limited environments. Then students incorporate cards based on biorecycling technologies, such as algae photobioreactors and anaerobic digesters in order to make circular connections. Finally, the student teams present their complete biorecycling engineering solutions to their scenarios in poster format by connecting outputs to inputs, and showing the cycles of how wastes become resources.

This art history video discussion looks at Donald Judd's "Untitled", 1969, ten copper units, each 9 x 40 x 31 inches with 9 inch intervals (Guggenheim Museum, New York).

This art history video discussion examines Donatello's "St. Mark", 1411-13, marble, 93" (236 cm), Orsanmichele, Florence.

This art history video discussion examines Donatello's "David", bronze, late 1420s to the 1460s, likey the 1440s (Museo Nazionale del Bargello, Florence).

In this Smarthistory video Dr. Beth Harris and Dr. Steven Zucker discuss Donatello's "Equestrian Monument of Gattamelata" (Erasmo da Narni), 1445-53, bronze, in the Piazza del Santo, at Padua.

This art history video discussion examines Donatello's "Feast of Herod", panel on the baptismal font of Siena Cathedral, Siena, Italy, Gilded bronze,1423--1427.

This art history video discussion examines Donatello's "Madonna of the Clouds", c. 1425--35, marble, 33.1 x 32 cm / 13 1/16 x 12 5/8 inches (Museum of Fine Arts, Boston).

After watching video clips from the Harry Potter and the Goblet of Fire movie, students explore the use of Punnett squares to predict genetic trait inheritance. The objective of this lesson is to articulate concepts related to genetics through direct immersive interaction based on the theme, The Science Behind Harry Potter. Students' interest is piqued by the use of popular culture in the classroom.

Students' understanding of how robotic ultrasonic sensors work is reinforced in a design challenge involving LEGO MINDSTORMS(TM) NXT robots and ultrasonic sensors. Student groups program their robots to move freely without bumping into obstacles (toy LEGO people). They practice and learn programming skills and logic design in parallel. They see how robots take input from ultrasonic sensors and use it to make decisions to move, resulting in behavior similar to the human sense of sight but through the use of sound sensors, more like echolocation. Students design-test-redesign-retest to achieve successful programs. A PowerPoint® presentation and pre/post quizzes are provided.

Students investigate the difference between qualitative and quantitative measurements and observations. By describing objects both qualitatively and quantitatively, they learn that both types of information are required for complete descriptions. Students discuss the characteristics of many objects, demonstrating how engineers use both qualitative and quantitative information in product design.

Student groups are provided with a generic car base on which to design a device/enclosure to protect an egg on or in the car as it rolls down a ramp at increasing slopes. During this in-depth physics/science/technology activity, student teams design, build and test their creations to meet the design challenge, and are expected to perform basic mathematical calculations using collected data, including a summative cost to benefit ratio.

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.