A collection of relevant lessons to supplement your units in Algebra I/II. Mix these lessons into your course to show students the algebraic reasoning behind social issues, public health, the environment, business, sports, and more.
This task is intended for instruction and to motivate "Building a general quadratic function.''
This word problem requires students to create expressions to calculate gas milage for a vehicle.
This lesson unit is intended to help teachers assess how well students are able to: model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions; and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
The purpose of this problem is to have students compose functions using tables of values only.
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 task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.
This interactive lesson covers the Mathematics Vision Projects lesson Composing and Decomposing. It helps develop an understanding of composing functions.Materials remixed from the Mathematics Vision Project.
Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascals Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)
Los estudiantes vuelven a visitar el teorema fundamental del álgebra mientras exploran raíces complejas de funciones polinomiales. Utilizan identidades polinomiales, el teorema binomial y el triángulo de Pascal para encontrar raíces de polinomios y raíces de la unidad. Los estudiantes comparan y crean diferentes representaciones de funciones mientras estudian composición de funciones, gráficos de funciones y encuentran funciones inversas.
Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.
English Description:
Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascals Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
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).
These unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).