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Identifying Functions
Unrestricted Use
CC BY
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This task emphasizes the expectation that students know linear functions grow by constant differences over equal intervals and exponential functions grow by constant factors over equal intervals.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
In the Billions and Exponential Modeling
Unrestricted Use
CC BY
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This problem provides an opportunity to experiment with modeling real data. Populations are often modeled with exponential functions and in this particular case we see that, over the last 200 years, the rate of population growth accelerated rapidly, reaching a peak a little after the middle of the 20th century and now it is slowing down.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Intro to Systems of Linear Equations
Conditional Remix & Share Permitted
CC BY-NC
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In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they've learned to similar situations.

Subject:
Algebra
Mathematics
Material Type:
Lesson Plan
Author:
Shawn Dykstra
Date Added:
11/14/2017
Linear Functions
Unrestricted Use
CC BY
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This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Linear Or Exponential?
Unrestricted Use
CC BY
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This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Linear function graph display
Read the Fine Print
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An interactive applet that allows the user to graphically explore the properties of a linear functions. Specifically, it is designed to foster an intuitive understanding of the effects of changing the two coefficients in the function y=ax+b. The applet shows a large graph of a quadratic (ax + b) and has two slider controls, one each for the coefficients a and b. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Subject:
Geometry
Mathematics
Material Type:
Reading
Simulation
Provider:
Math Open Reference
Author:
John Page
Date Added:
02/16/2011
Modeling Dynamics and Control I
Conditional Remix & Share Permitted
CC BY-NC-SA
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This course is the first of a two term sequence in modeling, analysis and control of dynamic systems. The various topics covered are as follows: mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices, analytical and computational solution of linear differential equations, state-determined systems, Laplace transforms, transfer functions, frequency response, Bode plots, vibrations, modal analysis, open- and closed-loop control, instability, time-domain controller design, and introduction to frequency-domain control design techniques. Case studies of engineering applications are also covered.

Subject:
Applied Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dubowsky, Steven
Trumper, David
Date Added:
02/01/2005
Molecular Models and 3D Printing
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Educational Use
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Students are challenged to use computer-aided design (CAD) software to create “complete” 3D-printed molecule models that take into consideration bond angles and lone-pair positioning. To begin, they explore two interactive digital simulations: “build a molecule” and “molecule shapes.” This aids them in comparing and contrasting existing molecular modeling approaches—ball-and-stick, space-filling, and valence shell electron pair repulsion (VSEPR)—so as to understand their benefits and limitations. In order to complete a worksheet that requires them to draw Lewis dot structures, they determine the characteristics and geometries (valence electrons, polar bonds, shape type, bond angles and overall polarity) of 12 molecules. They also use molecular model kits. These explorations and exercises prepare them to design and 3D print their own models to most accurately depict molecules. Pre/Post quizzes, a step-by-step Blender 3D software tutorial handout and a worksheet are provided.

Subject:
Chemistry
Physical Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Conrad Faine
Kerlyn Prada
Date Added:
03/14/2017
Newton's Law of Cooling
Unrestricted Use
CC BY
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The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Numerical Methods for Partial Differential Equations (SMA 5212)
Conditional Remix & Share Permitted
CC BY-NC-SA
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A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Khoo, Boo
Patera, Anthony
Peraire, Jaime
White, Jacob
Date Added:
02/01/2003
PEMDAS: Algebraic Order of Operations
Read the Fine Print
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Watch this music video to help you learn about PEMDAS (Please Excuse My Dear Aunt Sally). Does this sound familiar? If not, this is an excellent device to memorize the algebraic order of operations. This video is produced by Mr. Davis Productions and plays music by Odyssey Sound Lab.

Subject:
Algebra
Mathematics
Material Type:
Reading
Provider:
SMARTR
Provider Set:
SMARTR: Virtual Learning Experiences for Youth
Date Added:
03/15/2009
PVSTEM9 Slow Car Challenge - How Slow Can You Go?
Conditional Remix & Share Permitted
CC BY-NC
Rating
0.0 stars

Build the slowest moving LEGO car (or other vehicle dependent on gears and moves at a constant velocity), predict exactly when and where that will crash into another one a set distance apart.
Combines Physics, Tech Ed, and Algebra I concepts very well.

Subject:
Applied Science
Engineering
Physical Science
Physics
Material Type:
Activity/Lab
Date Added:
12/06/2018
Review Worksheets: Linear and Quadratice Equations, Unit Conversion, Significant Figures, and Trigonometry- Barbara Gilbert, CNM
Unrestricted Use
CC BY
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These worksheets, provided by Barbara Gilbert, review mathematics concepts that are necessary in physics, including linear equations, quadratic equations, unit conversion, significant figures, and trigonometry.

Subject:
Applied Science
Mathematics
Material Type:
Homework/Assignment
Date Added:
09/12/2016
Rising Gas Prices Đ Compounding and Inflation
Unrestricted Use
CC BY
Rating
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The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
02/13/2013
A Saturating Exponential
Unrestricted Use
CC BY
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The context of this task is a familiar one: a cold beverage warms once it is taken out of the refrigerator. Rather than giving the explicit function governing this warmth, a graph is presented along with the general form of the function. Students must then interpret the graph in order to understand more specific details regarding the function.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
02/04/2013