The purpose of this task is to give students experience in using simulation to determine if observed results are consistent with a given model (in this case, the Ňjust guessingÓ model). Part (i) also addresses the role of random assignment in the design of an experiment and assesses understanding of this concept.

This task involves two aspects of statistical reasoning: providing a probabilistic model for the situation at hand, and defining a way to collect data to determine whether or not the observed data is reasonably likely to occur under the chosen model. When guessing between two choices, there is no reason to suspect that one outcome is more likely than the other. Thus, a model that assumes the two outcomes to be equally likely (such as flipping a coin) is appropriate.

This task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task models a satellite orbiting the earth in communication with two control stations located miles apart on earthsŐ surface.

The context of this task is a familiar one: a cold beverage warms once it is taken out of the refrigerator. Rather than giving the explicit function governing this warmth, a graph is presented along with the general form of the function. Students must then interpret the graph in order to understand more specific details regarding the function.

Students learn about various natural hazards and specific methods engineers use to prevent these hazards from becoming natural disasters. They study a hypothetical map of an area covered with natural hazards and decide where to place natural disaster prevention devices by applying their critical thinking skills and an understanding of the causes of natural disasters.

Student teams practice water quality analysis through turbidity measurement and coliform bacteria counts. They use information about water treatment processes to design prototype small-scale water treatment systems and test the influent (incoming) and effluent (outgoing) water to assess how well their prototypes produce safe water to prevent water-borne illnesses.

Students develop an understanding of the concepts of "push" and "pull" as they "save" stuffed animals from danger using LEGO MINDSTORMS(TM) NXT robots. After learning more about the concepts through a robot demonstration, students explore the concepts themselves in the context of saving stuffed animala from the table edges. They choose to either push or pull the animal to safety, depending on the orientation of the robot and toy. They see the consequences of their choices, learning the importance of understanding these force concepts and the differences between them.

In this challenging instructional task students relate addition and subtraction problems to money and to situations and goals related to saving money.

Students use their knowledge about how healthy heart valves function to design, construct and implant prototype replacement mitral valves for hypothetical patients' hearts. Building on what they learned in the associated lesson about artificial heart valves, combined with the testing and scoring of their prototype heart valve designs in this activity, students discover the pros and cons of different types of artificial heart valves based on materials, surgery requirements, and lifespan.

This brief activity leads students through analysis of an archaeologist's sketch of the grave of an African buried in colonial New York.

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Students gain an understanding of the layers of the Earth by designing and building clay models.

Students learn how to determine map distances and areas using the map scale. They get a feel for how much an area represents on the map in relation to the size they are suggesting for their underground caverns to shelter the Alabraska population.

This word problem may be used for instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them.

Students use data acquisition equipment to learn about force and displacement in regard to simple and complex machines. In the engineering world, materials and systems are tested by applying forces and measuring the resulting displacements. The relationship between the force applied on a material, and its resulting displacement, is a distinct property of the material, which is measured in order to evaluate the material for correct use in structures and machines.

Students learn what a pendulum is and how it works in the context of amusement park rides. While exploring the physics of pendulums, they are also introduced to Newton's first law of motion about continuous motion and inertia.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Students employ the full engineering design process to research and design prototypes that could be used to solve the loss of sea turtle life during a hurricane. During Hurricane Irma, Florida lost a large proportion of its sea turtle nests. Protecting these nests from natural disasters or even human influence is an essential component of conservation in Florida, since only one hatchling in every thousand survives to adulthood. In this activity, students learn about sea turtle nesting behaviors and environmental impacts of hurricanes. Students work collaboratively to build structures that could protect a single sea turtle nest, or an entire beach, in the event of a hurricane or other similar weather disaster. Then, students present their solutions to concerned stakeholders. As an optional extension, students can build prototypes using 3D printers or 3D pens.

Students embark on a scavenger hunt around the school looking for indoor air pollution and mapping source locations.