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• MCCRS.Math.Content.HSF-IF.B.4
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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.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
09/16/2014
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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.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
09/17/2013
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CC BY-NC-SA
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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.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
09/17/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
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A statistics lesson on describing and making claims from data representations, specifically linearly increasing data. Applies ideas of rate-of-change to develop writing a linear equation to fit the data, using the equation to interpolate and extrapolate additional information, and integrating the mathematical interpretation appropriately into a social sciences argument.

Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Sarah Ahmed
Johanna Langill
01/28/2016
Unrestricted Use
CC BY
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In this real world problem students solve questions based on the relationship between production costs and price.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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Educational Use
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Students create projects that introduce them to Arduino—a small device that can be easily programmed to control and monitor a variety of external devices like LEDs and sensors. First they learn a few simple programming structures and commands to blink LEDs. Then they are given three challenges—to modify an LED blinking rate until it cannot be seen, to replicate a heartbeat pattern and to send Morse code messages. This activity prepares students to create more involved multiple-LED patterns in the Part 2 companion activity.

Subject:
Applied Science
Computer Science
Career and Technical Education
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Brian Huang
02/07/2017
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Educational Use
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In the companion activity, students experimented with Arduino programming to blink a single LED. During this activity, students build on that experience as they learn about breadboards and how to hook up multiple LEDs and control them individually so that they can complete a variety of challenges to create fun patterns! To conclude, students apply the knowledge they have gained to create LED-based light sculptures.

Subject:
Applied Science
Computer Science
Career and Technical Education
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Brian Huang
02/07/2017
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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.

Subject:
Engineering
Education
Life Science
Ecology
Forestry and Agriculture
Chemistry
Physics
Material Type:
Activity/Lab
Assessment
Diagram/Illustration
Lecture Notes
Student Guide
Provider:
Concord Consortium
Provider Set:
Concord Consortium Collection
Author:
The Concord Consortium
05/16/2012
Unrestricted Use
CC BY
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The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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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.

Subject:
Education
Life Science
Ecology
Forestry and Agriculture
Material Type:
Activity/Lab
Data Set
Diagram/Illustration
Lecture Notes
Provider:
Concord Consortium
Provider Set:
Concord Consortium Collection
Author:
The Concord Consortium
01/13/2012
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Educational Use
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This activity utilizes hands-on learning with the conservation of energy and the interaction of friction. Students use a roller coaster track and collect position data. The students then calculate velocity, and energy data. After the lab, students relate the conversion of potential and kinetic energy to the conversion of energy used in a hybrid car.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Joel Daniel
09/18/2014
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Educational Use
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Students conduct an experiment to study the acceleration of a mobile Android device. During the experiment, they run an application created with MIT's App Inventor that monitors linear acceleration in one-dimension. Students use an acceleration vs. time equation to construct an approximate velocity vs. time graph. Students will understand the relationship between the object's mass and acceleration and how that relates to the force applied to the object, which is Newton's second law of motion.

Subject:
Computer Science
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Brian Sandall
Scott Burns
09/18/2014
Unrestricted Use
CC BY
Rating
0.0 stars

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: A model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition. At time \$t=0\$ her airplane is at the bottom of the ...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/30/2013
Unrestricted Use
CC BY
Rating
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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 historical estimates for the population of London. Year18011821 18411861 18811901 1921 1939 1961 London population 1,100,000 1,60...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
10/30/2013
Unrestricted Use
CC BY
Rating
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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.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/06/2015
Unrestricted Use
CC BY
Rating
0.0 stars

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.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/06/2015
Unrestricted Use
CC BY
Rating
0.0 stars

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.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/06/2015
Unrestricted Use
CC BY
Rating
0.0 stars

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.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/06/2015
Unrestricted Use
CC BY
Rating
0.0 stars

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.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics