CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

My school uses a series of "Gateway" quizzes to evaluate a baseline level of learning for students in my Algebra I course. These are not to be confused with Mastery quizzes; instead, they are meant as a bare-minimum level of achievement. These 17 quizzes consititute the base level of learning a student needs to achieve to earn at least a 60% (D-) grade in my class.

Teachers could use these quizzes as described above, or simply as periodic assessments if they happen to be on a given topic.

Again, I do NOT consider these topics to be sufficient to compromise a standard Algebra I course, simply as a bare-minimum to be prepared for the next school year.

*note: for each of the 17 quizzes, I included a pdf, and also a file created in the original software, Kuta Software. Downloading the Kuta software (sadly, only available on Windows) will allow you to regenerate multiple versions of each quiz.

Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages.

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

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.

"Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

"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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics."

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

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 conectan la aritmética polinomial con los cálculos con números enteros e enteros. Los estudiantes aprenden que la aritmética de las expresiones racionales se rige por las mismas reglas que la aritmética de los números racionales. Esta unidad ayuda a los estudiantes a ver conexiones entre soluciones a ecuaciones polinomiales, ceros de polinomiales,, y gráficos de funciones polinómicas. Las ecuaciones polinomiales se resuelven sobre el conjunto de números complejos, lo que lleva a una comprensión inicial del teorema fundamental del álgebra. Los problemas de aplicación y modelado conectan múltiples representaciones e incluyen situaciones de mundo real y puramente matemáticas.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
"Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

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.)

"En este módulo, los estudiantes sintetizan y generalizan lo que han aprendido sobre una variedad de familias de funciones. Extienden el dominio de las funciones exponenciales a toda la línea real (n-rn.a.1) y luego extienden su trabajo con estas funciones a incluir la resolución de ecuaciones exponenciales con logaritmos (F-le.a.4). Exploran (con herramientas apropiadas) los efectos de las transformaciones en gráficos de funciones exponenciales y logarítmicas. Notan que las transformaciones en un gráfico de una función logarítmica se relacionan con el Propiedades logarítmicas (F-BF.B.3). Los estudiantes identifican tipos apropiados de funciones para modelar una situación. Ajustan los parámetros para mejorar el modelo y comparan los modelos analizando la idoneidad del ajuste y las juicios sobre el dominio sobre el cual un modelo es un buen ajuste. La descripción del modelado como, el proceso de elegir y usar matemáticas y estadísticas para analizar situaciones empíricas, comprenderlas mejor y tomar decisiones, está en el corazón de este módulo. En particular, a través de oportunidades repetidas para trabajar a través del ciclo de modelado (consulte la página 61 del CCLS), los estudiantes adquieren la idea de que la misma estructura matemática o estadística a veces puede modelar situaciones aparentemente diferentes.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics ".

English Description:
"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.

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 crean una comprensión formal de la probabilidad, considerando eventos complejos como sindicatos, intersecciones y complementos, así como el concepto de independencia y probabilidad condicional. La idea de usar una curva suave para modelar una distribución de datos se introduce junto con el uso de tablas y tecnología para encontrar áreas bajo una curva normal. Los estudiantes hacen inferencias y justifican conclusiones de encuestas de muestra, experimentos y estudios de observación. Los datos se usan de muestras aleatorias para estimar una media o proporción de población. Los estudiantes calculan el margen de error y lo interpretan en contexto. Dados los datos de un experimento estadístico, los estudiantes usan la simulación para crear una distribución de aleatorización y lo usan para determinar si hay una diferencia significativa entre dos tratamientos.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Algebra II is the second semester of a year-long introduction to modern algebra. The course focuses on group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
These notes, which were created by students in a recent on-campus 18.702 Algebra II class, are offered here to supplement the materials included in OCW’s version of 18.702. They have not been checked for accuracy by the instructors of that class or by other MIT faculty members.

National Board Certified teacher Marlo Warburton introduces a fresh approach to teaching the notoriously difficult "mixture" word problems for Algebra I. Using an in-class demonstration and incorporating basic physics principles of weight and distance, Ms. Warburton helps her students visualize, solve -- and even enjoy! -- these challenging problems.

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.