Lesson Standard(s): 6.NS.1 Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real- world situations). Process Standard (s):4: Connect mathematical ideas and real-world situations through modeling.b) Interpret mathematical models in the context of the situation.d) Evaluate the reasonableness of the model and refine if necessary.Lesson Objective(s):Students will exhibit their prior knowledge of dividing whole numbers using area models.After exploration through videos, manipulatives, and drawings, students will represent the quotient of a whole number divided by a fraction using area models.See attachments for lesson plan, PowerPoint presentation, and worksheet. 

This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.

The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.

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 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 problem complements the problem ``Do two points always determine a linear function?''

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 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 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 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 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. 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, 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.

In this problem-based learning module, students will explore the importance of sleep and the impact sleep has on their lives.  During the launch phase students can choose to record sleep data via downloaded apps or in a sleep diary.  Days 2 through 4 have students explore the concept and necessity of living organisms need to sleep. On day 2 the participants will take a series of cognitive test for baseline data.  Through station rotation and a jigsaw activity learners will become familiar with circadian rhythm and sleeping disorders. Finally, days 5-7 have the students produce a video or infographic to communicate the importance of sleep and its relationship to performance both physically and academically.

This is a Lesson about Domain and Range for Secondary Math I students. The lesson was built in the Desmos classroom.