This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The slope between two points is calculated by finding the change in $y$-values and dividing by the change in $x$-values. For example, the slope between...

This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear equations.

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d 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 lesson unit is intended to help teachers assess how well students are able to: estimate lengths of everyday objects; convert between decimal and scientific notation; and make comparisons of the size of numbers expressed in both decimal and scientific notation.

This task helps students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

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.

In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.  Students understand the connections between proportional relationships, lines, and linear equations in this module.  Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.

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

In this lesson designed to enhance literacy skills, students learn how to read and interpret a distance–time graph.

My goal is to merge New York State standards with Common Core Standards and Integrated Algebra Regent Standards for our 8th grade curriculum.

This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

(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 módulo 4, los estudiantes extienden lo que ya saben sobre las tarifas unitarias y las relaciones proporcionales con ecuaciones lineales y sus gráficos. Los estudiantes entienden las conexiones entre relaciones proporcionales, líneas y ecuaciones lineales en este módulo. Los estudiantes aprenden a aplicar las habilidades que adquirieron en los grados 6 y 7, con respecto a la notación simbólica y las propiedades de la igualdad para transcribir y resolver ecuaciones en una variable y luego en dos variables.

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

English Description:
In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.  Students understand the connections between proportional relationships, lines, and linear equations in this module.  Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.

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

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This lesson unit is intended to help teachers assess how well students are able to: translate between decimal and fraction notation, particularly when the decimals are repeating; create and solve simple linear equations to find the fractional equivalent of a repeating decimal; and understand the effect of multiplying a decimal by a power of 10.

This lesson unit is intended to help teachers assess how well students are able to: solve linear equations in one variable with rational number coefficients; collect like terms; expand expressions using the distributive property; and categorize linear equations in one variable as having one, none, or infinitely many solutions. It also aims to encourage discussion on some common misconceptions about algebra.

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the break-even point, checking it for confirmation; and communicate their reasoning clearly.