This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.

Students design and build prototypes for protective eyewear. They choose different activities or sports that require protective eyewear and design a device for that particular use. Students learn about the many ways in which the eyes can be damaged and how engineers incorporate different features and materials into eyewear designs to best protect the eyes.

Students experience the steps of the engineering design process as they design solutions for a real-world problem that could affect their health. After a quick review of the treatment processes that municipal water goes through before it comes from the tap, they learn about the still-present measurable contamination of drinking water due to anthropogenic (human-made) chemicals. Substances such as prescription medication, pesticides and hormones are detected in the drinking water supplies of American and European metropolitan cities. Using chlorine as a proxy for estrogen and other drugs found in water, student groups design and test prototype devices that remove the contamination as efficiently and effectively as possible. They use plastic tubing and assorted materials such as activated carbon, cotton balls, felt and cloth to create filters with the capability to regulate water flow to optimize the cleaning effect. They use water quality test strips to assess their success and redesign for improvement. They conclude by writing comprehensive summary design reports.

Students design and build their own model levees. Acting as engineers for their city, teams create sturdy barriers to prevent water from flooding a city in the event of a hurricane.

After learning about the concept of transfer of energy, specifically the loss of kinetic energy to friction, students get a chance to test friction. Student groups are each given a wooden block and different fabrics and weights and challenged to design the "best" puck. First the class defines what makes the "best" puck. They come to realize that the most desirable puck is the one that travels the farthest, thus the puck with the least amount of friction. In the context of hockey, the "best" puck is the one that travels farthest and loses the least kinetic energy to friction. Students then apply their knowledge of friction the energy transfer from kinetic to heat energy to design new, optimal pucks for the National Hockey League.

Using common materials (spools, string, soap), students learn how a pulley can be used to easily change the direction of a force, making the moving of large objects easier. They see the difference between fixed and movable pulleys, and the mechanical advantage gained with multiple/combined pulleys. They also learn the many ways engineers use pulleys for everyday purposes.

In this task sutdents use a dotplot, histogram or boxplot to summarize data.

Uncountable times every day with the merest flick of a finger each one of us calls on electricity to do our bidding. What would your life be like without electricity? Students begin learning about electricity with an introduction to the most basic unit in ordinary matter, the atom. Once the components of an atom are addressed and understood, students move into the world of electricity. First, they explore static electricity, followed by basic current electricity concepts such as voltage, resistance and open/closed circuits. Next, they learn about that wonderful can full of chemicals the battery. Students may get a "charge" as they discover the difference between a conductor and an insulator. The unit concludes with lessons investigating simple circuits arranged "in series" and "in parallel," including the benefits and unique features associated with each. Through numerous hands-on activities, students move cereal and foam using charged combs, use balloons to explore electricity and charge polarization, build and use electroscopes to evaluate objects' charge intensities, construct simple switches using various materials in circuits that light bulbs, build and use simple conductivity testers to evaluate materials and solutions, build and experiment with simple series and parallel circuits, design and build their own series circuit flashlight, and draw circuits using symbols.

Students analyze a cartoon of a Rube Goldberg machine and a Python programming language script to practice engineering analysis. In both cases, they study the examples to determine how the different systems operate and the function of each component. This exercise in juxtaposition enables students to see the parallels between a more traditional mechanical engineering design and computer programming. Students also gain practice in analyzing two very different systems to fully understand how they work, similar to how engineers analyze systems and determine how they function and how changes to the system might affect the system.

Working in small groups, students complete and run functioning Python codes. They begin by determining the missing commands in a sample piece of Python code that doubles all the elements of a given input and sums the resulting values. Then students modify more advanced Python code, which numerically computes the slope of a tangent line by finding the slopes of progressively closer secant lines; to this code they add explanatory comments to describe the function of each line of code. This requires students to understand the logic employed in the Python code. Finally, students make modifications to the code in order to find the slopes of tangents to a variety of functions.

This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s. Students studying statistics encounter the expression in this question as the standard deviation of a sampling distribution with samples of size n when the distribution from which the sample is taken has standard deviation s.

This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns.

This task has some aspects of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.

This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.

The Color Wheel is one solution that enforces uniform group expectations for conduct while also responding flexibly to the differing behavioral demands of diverse learning activities. This classwide intervention divides all activities into 3 categories and links each category to a color: green for free time/ low-structure activities; yellow for large- or small-group instruction/independent work; and red for brief transitions between activities. The student learns a short list of behavioral rules for each category and, when given a color cue, can switch quickly from one set of rules to another.

This activity can be played by pairs of students to support writing numbers.

Working individually or in pairs, students compete to design, create, test and redesign free-standing, weight-bearing towers using Kapla(TM) wooden blocks. The challenge is to build the tallest tower while meeting the design criteria and minimizing the amount of material used all within a time limit. Students experiment with different geometric shapes used in structural designs and determine how design choices affect the height and strength of structures, becoming comfortable with the concepts of structural members and modeling.

The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.

The lesson introduces students to the steps of the water cycle and rivers. They think about the effects of communities, sidewalks and roads on the natural flow of rainwater. Students also learn about the role of engineering in community planning and protecting our natural resources.