Este curso permite a los estudiantes ampliar su comprensión de las relaciones y extender su resolución de problemas y habilidades algebraicas a través de la investigación, el uso eficaz de la tecnología y el razonamiento abstracto. Los alumnos explorarán las relaciones cuadráticas y sus aplicaciones; resolverán y aplicarán sistemas lineales; verificarán propiedades de figuras geométricas utilizando geometría analítica; e investigarán la trigonometría de triángulos rectángulos y agudos. Los alumnos razonarán matemáticamente y comunicarán su pensamiento al resolver problemas de varios pasos.
Al final de este curso, los estudiantes desarrollan las siguientes habilidades en estas diferentes áreas:
| 1. Quadratics in Standard Form | |
| 1.1 | Determine the basic properties of quadratic relations |
| 1.2 | Relate transformations of the graph of y=x² to the algebraic representation y=a(x-h)² +k |
| 1.3 | Solve quadratic equations and interpret the solutions with respect to the corresponding relations |
| 1.4 | Solve problems involving quadratic relations |
| 2. Analytic Geometry | |
| 2.1 | Model and solve problems involving the intersection of two straight lines |
| 2.2 | Solve problems using analytic geometry involving properties of lines and line segments |
| 2.3 | Verify geometric properties of quadrilaterals and triangles, using analytic geometry |
| 3. Trigonometry | |
| 3.1 | Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity |
| 3.2 | Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem |
| 3.3 | Solve problems involving acute triangles, using the sine law and cosine law |
| Tiempo asignado | Componente en línea/fuera de línea | |
|---|---|---|
| 1. Unit 1: Linear Systems | ||
Students will review the concepts of linear equations and models developed in grade 9. They will explore the different forms of linear equations and learn to solve for an unknown in linear equations. Students will demonstrate an ability to represent and solve linear systems, graphically and algebraically and apply these skills to familiar applications. | 15 horas | Online: 10 hours |
| 2. Unit 2: Analytic Geometry | ||
The skills acquired in Unit 1 will be applied to explore geometric shapes and properties.Students will develop logical and mathematical methods to determine the length and midpoint of a line segment, as well as the median, altitude and perpendicular bisector of a triangle. They will explore the properties and equations of circles and gain an appreciation for the useful applications of analytic geometry. | 15 horas | Online: 10 hours |
| 3. Unit 3: Graphs of Quadratic Equations | ||
Quadratic functions are introduced as students use technology to explore the properties of parabolas. While investigating the graphs of quadratic functions, students will explore the application of quadratic functions as mathematical models for real life situations. Students will identify and apply the relationship between the roots of a quadratic equation and its graph. They will demonstrate the ability to convert a polynomial function from factored form into standard form. | 15 horas | Online: 10 hours |
| 4. Unit 4: Factoring Algebraic Expressions | ||
Having explored quadratic functions graphically, students will now focus on the algebra of quadratic functions. Students will demonstrate an ability to use various factoring techniques to factor quadratics and other polynomials, while considering the relationship between these skills and the concepts of Unit 3. | 16 hours | Online: 10 hours |
| 5. Unit 5: Applying Quadratic Models | ||
This unit will focus on vertex form and the transformations of quadratic functions. The relationship between standard and vertex forms of quadratic will be explored. Students will represent transformations graphically, algebraically and through verbal descriptions. They will also apply vertex form and transformations of quadratics to solve application problems. | 14 hours | Online: 9 hours |
| 6. Unit 6: Quadratic Equations | ||
Students will learn to solve quadratic equations of different forms. The quadratic formula will be introduced as a method for solving quadratic equations. Students will investigate the relationship between standard, vertex and factored form of quadratic function and convert between the different forms. The algebraic method of completing the square will be used to convert the standard form of a quadratic into vertex form. The skills obtained in the previous units will be consolidated and applied to solving quadratic applications. | 15 horas | Online: 10 hours |
| 7. Unit 7: Similar Triangles and Trigonometry | ||
Students will be introduced to trigonometry and its importance in understanding many phenomena of the world around us. They will demonstrate an ability to determine congruence and similarity in triangles and solve problems involving similar triangles. Pythagorean Theorem will be reviewed and the primary trigonometric ratios will be introduced enabling students to solve right triangles. The Sine Law and Cosine Law will be explored and applied to solving problems involving acute triangles. | 14 hours | Online: 10 hours |
| 8. Final Evaluation | ||
Independent Study Unit | 3 horas | Online: 1 hours |
| 9. | ||
Examen final | 3 horas | En línea: 3 horas |
| Total | 110 horas | |
This course is organized into a semester format. Lessons and activities will be presented to students via the internet. Synchronous lessons will be provided though live online teaching and student to student discussion forums.
Se utilizarán diversas estrategias para impartir este curso en línea. Instrucción
Las estrategias incluirán, entre otras cosas
● Clases dirigidas por el profesor
● Student-led lessons
● Guided Lectures
● Aprendizaje cooperativo
● Investigación independiente
● Aprendizaje entre iguales
● Multimedia presentations
Los objetivos de aprendizaje se discutirán al principio de cada lección y se proporcionarán criterios de éxito a los estudiantes. Los criterios de éxito se utilizan para desarrollar las herramientas de evaluación en este curso, incluyendo rúbricas y listas de control.
The overriding aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly. A wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented.
Problem Solving: Course scaffolds learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing concepts related to numeracy) and build off of this knowledge to acquire new skills. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems.
Selecting Tools and Computational Strategies: Course models the use of graphing software to familiarize students with available software and resources which will allow them to explore graphs of equations and to analyze scatter plots
Connecting: The course makes connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)
Representing: Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development – concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.
Self-Assessment: Through the use of interactive activities (e.g. whiteboard group work, check-in quizzes and drag and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.
Se requiere una variedad de métodos, estrategias e instrumentos de valoración y evaluación adecuados a la expectativa evaluada. Estos incluyen el diagnóstico, formativo y sumativo dentro del curso y dentro de cada unidad. Seguimos estrictamente el documento Growing Success del Ministerio de Educación.
La evaluación PARA EL APRENDIZAJE y la evaluación COMO APRENDIZAJE se obtienen a través de diversos medios, entre los que se incluyen los siguientes:
● Ongoing descriptive feedback
● Autoevaluación
● Evaluación entre iguales
● Conferencias alumno-profesor de forma periódica para:
o verbalizar las observaciones
o hacer preguntas
o aclarar la comprensión
Las pruebas de los logros de los alumnos (evaluación DEL aprendizaje) se recogen a través de observaciones continuas del trabajo más consistente, teniendo en cuenta el trabajo más reciente de diversas fuentes.
La evaluación en este curso se basará en las expectativas del plan de estudios provincial de Ontario. Los estudiantes dispondrán de numerosas y variadas oportunidades para demostrar todo el alcance de sus logros. Las categorías de evaluación y los desgloses son los siguientes:
● Conocimiento 30%
● Thinking 25%
● Aplicación 25%
● Comunicación 20%
La nota final se determinará de la siguiente manera:
● Trabajo trimestral 70%
○ Tests 60%
○ Assignments 30%
○ Quizzes 10%
● Final Evaluation 30%
○ Proctored Final Exam 20%
○ Independent Study Unit 10%
A los estudiantes con necesidades especiales y a los que aprenden inglés se les proporcionará alojamiento, incluyendo tiempo adicional, tecnología de asistencia y escriba cuando esté disponible.
Teachers who are planning a program in this subject make an effort to take into account considerations for program planning that align with the Ontario Ministry of Education policy and initiatives in a number of important areas.
Las Capacidades de Aprendizaje que se enumeran a continuación son fundamentales para el éxito de los alumnos. Las Habilidades de Aprendizaje se evalúan independientemente de los logros y se determinan a través de la observación y la participación. Se utilizará una lista de comprobación y una conferencia del alumno para determinar el nivel en cada categoría.
1. Responsabilidad
2. Organización
3. Trabajo independiente
4. Colaboración
5. Iniciativa
6. Autorregulación
● Calculadora
● Graph paper, ruler, protractor
● Acceso a Internet
● Folletos y notas en PowerPoint
● Online readings and resources
● Videos
USD $549.00
