Create and evaluate expressions involving variables and whole number exponents.

b. Evaluate expressions at specific values of the variables.

d. Write and evaluate algebraic expressions.

In this video lesson, students will learn about linear programming (LP) and will solve an LP problem using the graphical method. Its focus is on the famous "Stigler's diet" problem posed by the 1982 Nobel Laureate in economics, George Stigler. Based on his problem, students will formulate their own diet problem and solve it using the graphical method. The prerequisites to this lesson are basic algebra and geometry. The materials needed for the in-class activities include graphing paper and pencil. This lesson can be completed in one class of approximately one hour. If the teacher would like to cover the simplex algorithm by George Dantzig as an alternative solution method, an additional whole class period is suggested.

Students explore the relationship between the flapping frequency, the amplitude, and the cruising speeds of a variety of animals to calculate their Strouhal numbers.Key ConceptsStudents are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills. Students will:Try a variety of strategies to approaching different types of problems.Devise a problem-solving plan and implement their plan systematically.Become aware that problems can be solved in more than one way.See the value of approaching problems in a systematic manner.Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.Make connections between previous learning and real-world problems.Create efficacy and confidence in solving challenging problems in a real-world setting.Goals and Learning ObjectivesAnalyze the relationship between the variables in an equation.Write formulas to show how variables relate.Communicate findings using multiple representations including tables, charts, graphs, and equations.

This lesson has students create, compare, and solve linear, quadratic, exponential, and cubic functions based on a primary source from Weather Underground about the melting of the polar ice caps. If the formatting is an issue, contact me at rob.leichner@gmail.com for a Google drive link to the lesson plan.

In this video segment from Cyberchase, the CyberSquad must get into a vault before Hacker, Buzz and Delete by cracking a code of shapes and numbers.

In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

Students play an Expressions Game in which they describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners try to write the correct expressions based on the descriptions.Key ConceptsMathematical expressions have parts, and these parts have names. These names allow us to communicate with others in a precise way.A variable is a symbol (usually a letter) in an expression that can be replaced by a number.A term is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus).A coefficient is a symbol (usually a number) that multiplies the variable in an algebraic expression.An exponent tells how many copies of a number or variable are multiplied together.A constant is a number. In an expression, it can be a constant term or a constant coefficient. In the expression 2x + 3, 2 is a constant coefficient and 3 is a constant term.Goals and Learning ObjectivesIdentify parts of an expression using appropriate mathematical vocabulary.Write expressions that fit specific descriptions (for example, the expression is the sum of two terms each with a different variable).

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

This activity allows students to practice solving one and two step equations by using an interactive tool teaching zero pairs to eliminate constant values and division and mulitplication properties to eliminate coefficient values.

This course provides a general overview of databases, including topics such as database history, modern database systems, the different models used to design a database, and Structured Query Language (SQL), which is the standard language used to access and manipulate databases. Upon successful completion of this course, the student will be able to: compare and contrast the database approach and the file system approach; explain what a database management system is as well as the various components; identify the various people involved in database management systems; explain the historical background of database management systems; compare the various database models; describe the functions of a database management system; explain the three-schema database architecture; describe what tables, indexes, and views are as well as discuss the differences among them; explain the entity-relationship model; develop an entity-relationship model based on user requirements; describe the relational database model; explain the process of normalization; convert an entity-relationship diagram to a set of normalized relations; explain referential integrity; identify how relational algebra is used to construct queries; describe and use data definition commands; describe and use data manipulation commands; explain how to join tables together for queries. (Computer Science 403)

An interactive applet and associated web page showing how to find the area and perimeter of a trapezoid from the coordinates of its vertices. The trapezoid can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. 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.

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
Acknowledgement
Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.

In this activity, students interpret the motion of a car using its related velocity and acceleration vectors.

This math problem demonstrates the concept of geometric progression, through an example of a million dollar contract between an employee and an employer. Application of the concept of geometric progression to social cause activism is addressed. 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.

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever _AXB is a right angle.

This course introduces quantitative approaches to understanding brain and cognitive functions. Topics include mathematical description of neurons, the response of neurons to sensory stimuli, simple neuronal networks, statistical inference and decision making. It also covers foundational quantitative tools of data analysis in neuroscience: correlation, convolution, spectral analysis, principal components analysis, and mathematical concepts including simple differential equations and linear algebra.

An interactive applet and associated web page that calculate the area of a triangle using the formula method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's area is recalculated from the vertex coordinates using the formula. The grid and coordinates can be turned on and off. The area calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area using the formula method, a worked example and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page showing how to find the area and perimeter of a square from the coordinates of its vertices. The square can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. 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.

"How has the War on Drugs impacted the lives of people in my community?" Students will attack this question from a socio-emotional perspective in the context of U.S. History and then through a statistical lens in Algebra.

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.