This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. The task lends itself to an extended discussion comparing the differences that students have found and relating them back to the equation and the graph of the two functions.

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, tables, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view. Instead of giving a starting value and asking for subsequent values, it gives an end value and asks about what happened in the past. The simple first question can generate a surprisingly lively discussion as students often think that the algae will grow linearly.

The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

If you've been looking to learn how to code, we can help you get started. Here are 4.5 lessons on the basics and extra resources to keep you going. Lesson 1: Variables and Basic Data Types. Lesson 2: Working with Variables. Lesson 3: Arrays and Logic Statements. Lesson 4: Understanding Functions and Making a Guessing Game

This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).

The goal of this task is to have students appreciate how the different constants (P0, K, and r) influence the shape of the graph.

This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.

In this lesson for grades 3, 4 and 5, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. The focus of this lesson is determining the position necessary to balance uneven objects and the effect on balance of moving the fulcrum. Printable activity sheets, ideas for implementation and extension are included.

This task addresses the first part of standard F-BF.3: ŇIdentify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).Ó Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.

First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

(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 el primer tema de este módulo de 15 días, los estudiantes aprenden el concepto de una función y por qué las funciones son necesarias para describir conceptos geométricos y ocurrencias en la vida cotidiana. Una vez que se proporciona una definición formal de una función, los estudiantes consideran funciones de tarifas discretas y continuas y comprenden la diferencia entre los dos. Los estudiantes aplican su conocimiento de las ecuaciones lineales y sus gráficos del módulo 4 a los gráficos de funciones lineales. Los estudiantes inspeccionan la tasa de cambio de funciones lineales y concluyen que la tasa de cambio es la pendiente de la gráfica de una línea. Aprenden a interpretar la ecuación y = mx+b como definir una función lineal cuyo gráfico es una línea. Los estudiantes comparan funciones lineales y sus gráficos y también obtienen experiencia con funciones no lineales. En el segundo y último tema de este módulo, los estudiantes extienden lo que aprendieron en el grado 7 sobre cómo resolver los problemas del mundo real y las matemáticas relacionadas con el volumen de sólidos simples para incluir problemas que requieren las fórmulas para conos, cilindros y esferas.

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

English Description:
In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life.  Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two.  Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions.  Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line.  They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line.  Students compare linear functions and their graphs and gain experience with non-linear functions as well.  In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.

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 los grados 6 y 7, los estudiantes trabajaron con datos que involucraban una sola variable. El módulo 6 presenta a los estudiantes a bivariando datos. Los estudiantes se introducen a una función como una regla que asigna exactamente un valor a cada entrada. En este módulo, los estudiantes usan su comprensión de las funciones para modelar las posibles relaciones de datos bivariados. Este módulo es importante para establecer una base para los estudiantes que trabajan en álgebra en el grado 9.

English Description:
In Grades 6 and 7, students worked with data involving a single variable.  Module 6 introduces students to bivariate data.  Students are introduced to a function as a rule that assigns exactly one value to each input.  In this module, students use their understanding of functions to model the possible relationships of bivariate data.  This module is important in setting a foundation for students’ work in algebra in Grade 9.

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

The primary purpose of this task is to illustrate that the domain of a function is a property of the function in a specific context and not a property of the formula that represents the function. Similarly, the range of a function arises from the domain by applying the function rule to the input values in the domain. A second purpose would be to illicit and clarify a common misconception, that the domain and range are properties of the formula that represent a function.

This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.

The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.