This lesson unit is intended to help teachers assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help teachers identify and help students who have the following difficulties: understanding how the factored form of the function can identify a graphŐs roots; understanding how the completed square form of the function can identify a graphŐs maximum or minimum point; and understanding how the standard form of the function can identify a graphŐs intercept.

This is a booklet containing 37 space science mathematical problems, several of which use authentic science data. The problems involve math skills such as unit conversions, geometry, trigonometry, algebra, graph analysis, vectors, scientific notation, and many others. Learners will use mathematics to explore science topics related to Earth's magnetic field, space weather, the Sun, and other related concepts. This booklet can be found on the Space Math@NASA website.

This seminar will show you how to graph a linear inequality in two variables on a Cartesian Coordinate Plane. You will learn when and why to use dashed lines and solid lines. You will also learn why it is necessary to shade a half-plane, as well as how to determine which half-plane to shade.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

This seminar will help you to identify a linear equation written in slope-intercept form.  It will also help you to write and graph slope-intercept equations when you are given different pieces of information.  You will be able to make connections between algebraic equations written in slope-intercept form and the real-life situations that they represent.  StandardsCC.2.2.HS.D.10  Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.

This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

This seminar will explore how to solve systems of equations using elimination. You will discover the most efficient methods of preparing a system to be solved using elimination and how to identify the best variable to eliminate.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Many students are motivated by real world applications of mathematics, and most students are familiar with the term CGI from watching movies and playing video games. This particular activity ties matrix multiplication to CGI (Computer Generated Imagery). It has been used successfully with high school students in an Algebra II course who had just learned how to do matrix multiplication, middle school and high school students (some of whom were seeing matrix multiplication for the first time) attending a special Math Day on a university campus, and with College Algebra students (during a unit about matrices).

This seminar will introduce you to the concept of linear inequalities.  You will learn how to solve and graph inequalities in one variable, and you will learn when and why you must consider the direction of the inequality symbol when solving the problem.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

This lesson unit is intended to help teachers assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest problems.

This task asks students to consider the linear and quadratic functions appearing on a coordinate plane.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.

This seminar will explore how to solve a system of linear equations using substitution. It will also describe what it means for a system of equations to have no solution or infinitely many solutions.  Applications of systems of equations will also be explored.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials. In particular, it aims to identify and help students who have difficulties in: switching between visual and algebraic representations of polynomial expressions; and performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier.

Course Objective: This course is an introduction to basic algebra; elements of probability and statistics; and basic concepts of Euclidean geometry, including congruence, similarity, measurements, areas, and volumes.

This seminar will show you how to identify, solve, and graph compound inequalities.  You will learn the difference between the union and intersection of solutions, and you will also learn the importance of distinguishing between “and” and “or” when constructing compound inequalities.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

This seminar will teach you about the Pythagorean Theorem. It will also teach you how to use the converse of the theorem and how to identify Pythagorean triples. You will have to apply the techniques you have learned to simplify radicals, and you will learn how to apply exponential properties. You will be shown visual demonstrations of the Pythagorean Theorem and be asked to connect them to the algebraic models of the Theorem.StandardsCC.2.3.8.A.3.Understand and apply the Pythagorean Theorem to solve problems.

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.