Students explore Hooke's law while working in small groups at their lab benches. They collect displacement data for springs with unknown spring constants, k, by adding various masses of known weight. After exploring Hooke's law and answering a series of application questions, students apply their new understanding to explore a tissue of known surface area. Students then use the necessary relationships to depict a cancerous tumor amidst normal tissue by creating a graph in Microsoft Excel.
Construct and measure the energy efficiency and solar heat gain of a cardboard model house. Use a light bulb heater to imitate a real furnace and a temperature sensor to monitor and regulate the internal temperature of the house. Use a bright bulb in a gooseneck lamp to model sunlight at different times of the year, and test the effectiveness of windows for passive solar heating.
In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.
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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend's house with a full battery. The pictures below sho...
Students act as Mars exploratory rover engineers, designing, building and displaying their edible rovers to a design review. To begin, they evaluate rover equipment and material options to determine which parts might fit in their given NASA budget. With provided parts and material lists, teams analyze their design options and use their findings to design their rovers.
In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.
This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).
Use a series of interactive models and games to explore electrostatics. Learn about the effects positive and negative charges have on one another, and investigate these effects further through games. Learn about Coulomb's law and the concept that both the distance between the charges and the difference in the charges affect the strength of the force. Explore polarization at an atomic level, and learn how a material that does not hold any net charge can be attracted to a charged object. Students will be able to:
This task requires students to use functions to calculate how to best benefit from a pizza promotion.
Students are presented with a biomedical engineering challenge: Breast cancer is the second-leading cause of cancer-related death among women and the American Cancer Society says mammography is the best early-detection tool available. Despite this, many women choose not to have them; of all American women at or over age 40, only 54.9% have had a mammogram within the past year. One reason women skip annual mammograms is pain, with 90% reporting discomfort. Is there a way to detect the presence of tumors that is not as painful as mammography but more reliable and quantifiable than breast self-exams or clinical breast exams? This three lesson/three activity unit is designed for first-year accelerated or AP physics classes. It provide hands-on activities to teach the concepts of stress, strain and Hooke's law, which students apply to solve the challenge problem.
In this activity the temperature of a reaction is monitored for different concentrations of reactants.
Students will be reviewing and learning points/lines, slope formula, slope-intercept form, and standard form. over four days. Day five will be an accumulation of everything learned where students will use GeoGebra, an assistive technology tool, to graph linear models they create and will represent the linear model in both slope-intercept and standard form.*This work was made possible by the generous support of the National Science Foundation, grant #1755631, and the University of St. Francis Noyce STEM Educators Program
In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4). They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions. They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3). Students identify appropriate types of functions to model a situation. They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as, the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions, is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.
This lab demonstrates Ohm's law as students set up simple circuits each composed of a battery, lamp and resistor. Students calculate the current flowing through the circuits they create by solving linear equations. After solving for the current, I, for each set resistance value, students plot the three points on a Cartesian plane and note the line that is formed. They also see the direct correlation between the amount of current flowing through the lamp and its brightness.
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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: The table below shows the temperature, $T,$ in Tucson, Arizona $t$ hours after midnight. When does the temperature decrease the fastest: between midnig...
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.
This concept-building activity contains a set of sequenced simulations for investigating how atoms can be excited to give off radiation (photons). Students explore 3-dimensional models to learn about the nature of photons as "wave packets" of light, how photons are emitted, and the connection between an atom's electron configuration and how it absorbs light. Registered users are able to use free data capture tools to take snapshots, drag thumbnails, and submit responses. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology.
Explore how populations change over time in a NetLogo model of sheep and grass. Experiment with the initial number of sheep, the sheep birthrate, the amount of energy sheep gain from the grass, and the rate at which the grass re-grows. Remove sheep that have a particular trait (better teeth) from the population, then watch what happens to the sheep teeth trait in the population as a whole. Consider conflicting selection pressures to make predictions about other instances of natural selection.