Even when we model the dynamics of the abundances of molecules inside …
Even when we model the dynamics of the abundances of molecules inside biological systems using calculus, it is important to remember that underlying behavior can be apparently random ("stochastic"). Even a deterministic system containing components moving in periodic ways can, at early times, support dynamics that appear disordered. The behavior of systems containing complicated collections of interacting parts can be difficult to predict with accuracy (chaos). Finally, systems can display stochasticity because the outcomes of measurements on quantum systems are indeterminate in a fundamental way. Random processes are modeled using Markov models.
Students are introduced to Hooke's law as well as stress-strain relationships. First …
Students are introduced to Hooke's law as well as stress-strain relationships. First they learn the governing equations, then they work through several example problems, first individually, then as a class. Through the lesson's two-part associated activity, students 1) explore Hooke's law by experimentally determining an unknown spring constant, and then 2) apply what they've learned to create a strain graph depicting a tumor using Microsoft Excel®. After the activities, the lesson concludes with a stress-strain quiz to assess each student's comprehension of the concepts.
This article describes an approach designed to decrease math anxiety and teach …
This article describes an approach designed to decrease math anxiety and teach students about the use of mathematical symbols simplifying radicals. A deck of cards is used in a demonstration, and a problem set using real life examples to master the use of radicals is included. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
This article discusses how the Multi-angle Imaging SpectroRadiometer (MISR) instrument found on …
This article discusses how the Multi-angle Imaging SpectroRadiometer (MISR) instrument found on the Terra satellite is used to understand how particles in the atmosphere interact with sunlight and how particle pollution affects Earth's climate. Directions for building a demonstration model of MISR out of cardboard tubes is included, along with short activities to show how it's multiple viewing angles allow MISR to differentiate the kinds of particles in the air because they scatter light differently, depending on their size, shape, and composition.
In this activity, student teams design and conduct a scientific investigation in …
In this activity, student teams design and conduct a scientific investigation in which they explore the conditions necessary for life. They conduct observations of environmental conditions both indoor and outdoor, and determine the range of variation they see. They compare these data with published temperature data for Earth, Mars, Pluto and Venus. The activity supports inquiry into the real world challenge of searching for life in extreme environments. The resource includes several student data sheets, data table and images, and a teacher's guide. Materials needed for this activity include weather instruments (e.g., thermometers, barometers, anemometers). This is Activity A of two activities in the first module, titled "Temperature variations and habitability," of the resource, "Earth Climate Course: What Determines a Planet's Climate?" The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
In this activity, student teams create a knowledge map of the essential …
In this activity, student teams create a knowledge map of the essential characteristics or factors of a planet with a habitable climate, identifying range of inputs, outputs and variables of a planetary environmental system. Identified characteristics are compared to extreme environments on Earth, such as the Antarctic or the Sahara desert, and are used to consider the real life challenge of searching for life in extreme environments. The resource includes a student data sheet, questions, teacher's guide and scoring rubric. This is Activity B of two activities in the first module, titled "Temperature variations and habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
Prior to reaching households, water is exposed to a variety of treatments …
Prior to reaching households, water is exposed to a variety of treatments designed to render it fit for human consumption and use. One of the first treatment steps is the removal of suspended solids using chemical additives called flocculants. In this activity, students learn about two commonly used flocculants and clean water collected from a local pond or river. They experiment with flocculant, stirring and pH variables.
In this problem-based learning activity, students will examine opposing views on the …
In this problem-based learning activity, students will examine opposing views on the Amazon Rainforest and will take a position on land-use and species conservation in one of the last areas of biodiversity on Earth. This activity is part of Exploring the Environment.
In the first video segment, we estimate properties of a parent distribution …
In the first video segment, we estimate properties of a parent distribution (i.e. mean and standard deviation) from a sample of a finite collection of data measurements, and we describe the standard error (SE). In the second segment, we derive the famous square-root of n factor that appears in the SE formula. The third video segment describes the visual comparison of error bars, and the fourth segment warns against a mistake that can generate inappropriate claims of statistical significance during this kind of analysis.
Students explore the response of springs to forces as a way to …
Students explore the response of springs to forces as a way to begin to understand elastic solid behavior. They gain experience in data collection, spring constant calculation, and comparison and interpretation of graphs and material properties to elucidate material behavior. Conduct this activity before proceeding to the associated lesson.
In this activity, student teams learn about research design and design a …
In this activity, student teams learn about research design and design a controlled experiment exploring the relationship between a hypothetical planet, an energy source, and distance. They analyze the data and derive an equation to describe the observations. Includes student data sheets, a teacher's guide, and a tutorial on how to use the spreadsheet program Excel. This is Activity A in module 3, titled "Using Mathematic Models to Investigate Planetary Habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
In this activity, students build a simple computer model to determine the …
In this activity, students build a simple computer model to determine the black body surface temperature of planets in our solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Experiments altering the luminosity and distance to the light source will allow students to determine the energy reaching the object and its black body temperature. The activity builds on student outcomes from activity A, "Finding a Mathematical Description of a Physical Relationship." It also supports inquiry into a real-world problem, the effect of urban heat islands and deforestation on climate. Includes a teacher's guide, student worksheets, and an Excel tutorial. This is Activity B of module 3, titled "Using Mathematic Models to Investigate Planetary Habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
Students explore how mathematical descriptions of the physical environment can be fine-tuned …
Students explore how mathematical descriptions of the physical environment can be fine-tuned through testing using data. In this activity, student teams obtain satellite data measuring the Earth's albedo, and then input this data into a spreadsheet-based radiation balance model, GEEBITT. They validate their results against published the published albedo value of the Earth, and conduct similar comparisons Mercury, Venus and Mars. The resource includes an Excel spreadsheet tutorial, an investigation, student data sheets and a teacher's guide. Students apply their understanding to the real life problem of urban heat islands and deforestation. The activity links builds on student outcomes from activities A and B: "Finding a Mathematical Description of a Physical Relationship," and "Making a Simple Mathematical Model." This is Activity C in module 3, Using Mathematical Models to Investigate Planetary Habitability, of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
In this activity, students take the age old concept of etch-a-sketch a …
In this activity, students take the age old concept of etch-a-sketch a step further. Using iron filings, students begin visualizing magnetic field lines. To do so, students use a compass to read the direction of the magnet's magnetic field. Then, students observe the behavior of iron filings near that magnet as they rotate the filings about the magnet. Finally, students study the behavior of iron filings suspended in mineral oil which displays the magnetic field in three dimensions.
Prepared with pre-algebra or algebra 1 classes in mind, this module leads …
Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.
Students discuss several human reproductive technologies available today pregnancy ultrasound, amniocentesis, in-vitro …
Students discuss several human reproductive technologies available today pregnancy ultrasound, amniocentesis, in-vitro fertilization and labor anesthetics. They learn how each technology works, and that these are ways engineers have worked to improve the health of expecting mothers and babies.
This is a lesson about characteristics necessary for life. Learners will identify …
This is a lesson about characteristics necessary for life. Learners will identify the top candidates for life in the solar system by examining Habitability Cards, which discuss each planet and the six large moons in terms of water temperature, atmosphere, energy, and nutrients. A math extension is provided on the Inverse Square Law. Includes background reading for teachers, student activity guide, reflection questions, and blackline masters. This is activity 3 of 5 in the educators guide, Astrobiology in your Classroom: Life on Earth..and Elsewhere?
Students will use this activity to determine what keeps our bones strong. …
Students will use this activity to determine what keeps our bones strong. Soaking the bones in vinegar will remove the calcium from the bones causing them to become soft and rubbery. Students will find that when we age, calcium is depleted from our bones faster than we can restore it. They will then determine what complications can arise from it.
Students learn how to take blood pressure by observing a teacher demonstration …
Students learn how to take blood pressure by observing a teacher demonstration and then practicing on fellow classmates in small groups. Once the hands-on component of this activity is completed, the class brainstorms and discusses how blood pressure might affect a person's health. This activity acts as hook for the second lesson in this unit, in which blood pressure is presented in detail, as well as how variances in blood pressure can affect a person's cardiovascular system.
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