This problem allows the student to think geometrically about lines and then …
This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).
This task is designed as a follow-up to the task F-LE Do …
This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry.
This task requires students to use the normal distribution as a model …
This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages. There are several ways (tables, graphing calculators, or statistical software) that students might calculate the required normal percentages. Depending on the method used, answers might vary somewhat from those shown in the solution.
In this activity, students squeeze a tennis ball to demonstrate the strength …
In this activity, students squeeze a tennis ball to demonstrate the strength of the human heart. Working in teams, they think of ways to keep the heart beating if the natural mechanism were to fail. The goal of this activity is to get students to understand the strength and resilience of the heart.
Students work with specified materials to create aqueduct components that can transport …
Students work with specified materials to create aqueduct components that can transport two liters of water across a short distance in their classroom. The design challenge is to create an aqueduct that can supply Aqueductis, a (hypothetical) Roman city, with clean water for private homes, public baths and fountains as well as crop irrigation.
The purpose of the task is to analyze a plausible real-life scenario …
The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.
Using the same method for measuring friction that was used in the …
Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct experiments to determine if the amount of area over which an object contacts a surface it is moving across affects the amount of friction encountered.
Students gain an understanding of the factors that affect wind turbine operation. …
Students gain an understanding of the factors that affect wind turbine operation. Following the steps of the engineering design process, engineering teams use simple materials (cardboard and wooden dowels) to build and test their own turbine blade prototypes with the objective of maximizing electrical power output for a hypothetical situation—helping scientists power their electrical devices while doing research on a remote island. Teams explore how blade size, shape, weight and rotation interact to achieve maximal performance, and relate the power generated to energy consumed on a scale that is relevant to them in daily life. A PowerPoint® presentation, worksheet and post-activity test are provided.
Students gain a basic understanding of the properties of media soil, sand, …
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 …
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 …
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 …
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 …
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 …
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).
Student teams find solutions to hypothetical challenge scenarios that require them to …
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.
Students' understanding of how robotic ultrasonic sensors work is reinforced in a …
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 …
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 …
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.
No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.
Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.
Your redistributing comes with some restrictions. Do not remix or make derivative works.
Most restrictive license type. Prohibits most uses, sharing, and any changes.
Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.