In this video segment from Cyberchase, Inez estimates whether she has enough jelly beans in her large container to decorate all of the cookies in her batch.

A patient discusses diabetes and how he manages his carbohydrate intake in this video segment from TV 411.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Students explore the effects of wind on a plane's time and distance and represent these situations using algebraic expressions and equations. They use terms with positive, negative, and zero coefficients.Key ConceptsIn this lesson, students show what they remember from Grade 6 about writing expressions and solving one-step equations. They use what they learned earlier in Grade 7 about adding and subtracting integers. They extend these concepts to write and interpret an expression with a negative coefficient.Goals and Learning ObjectivesReview addition and subtraction of integers.Review the relationship between distance, time, and speed.Write an algebraic expression for distance in terms of time, t.Write a term with a negative coefficient.Review solving a one-step equation using the multiplication property of equality.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

In this interactive activity adapted for grades 3–5 from Annenberg Learner’s Teaching Math Grades 6–8, use virtual Cuisenaire® Rods to represent fractions and to perform operations with fractions.

In this lesson designed to enhance literacy skills, students examine how to multiply fractions by whole numbers in the context of a recipe.

(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 2, los estudiantes aplican patrones del sistema Base Ten a las estrategias mentales y un estudio secuencial de multiplicación a través de diagramas de área y la propiedad distributiva que conduce a la fluidez con el algoritmo estándar. Los estudiantes se mueven de números enteros a multiplicación con decimales, nuevamente utilizando el valor del lugar como guía para la razón y hacer estimaciones sobre los productos. La multiplicación se explora como un método para expresar medidas equivalentes tanto en el número entero como en las formas decimales. Una secuencia similar para la división comienza concretamente con discos numéricos como una introducción a la división con divisores de múltiples dígitos y lleva al estudiante a dividir los dividendos de número entero y decimales de múltiples dígitos por divisores de dos dígitos utilizando un método escrito vertical. Además, los estudiantes evalúan y escriben expresiones, registrando sus cálculos utilizando la propiedad asociativa y los paréntesis. Los estudiantes aplican el trabajo del módulo para resolver problemas de palabras de varios pasos utilizando multiplicación y división de múltiples dígitos con incógnitas que representan el tamaño del grupo o el número de grupos. El énfasis en la razonabilidad de los productos y los cocientes, la interpretación de los restos y el razonamiento sobre la colocación de decimales se basa en las habilidades aprendidas en todo el módulo, incluido el conocimiento del valor del lugar, el redondeo y la estimación.

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

English Description:
In Module 2 students apply patterns of the base ten system  to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm.  Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms.  A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method.  In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses.  Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups.  An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation.

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.)

El módulo 5 es la culminación del trabajo de los niños con el número en el año previo a K. A lo largo de los módulos 1 y 3, tuvieron extensas experiencias de conteo con los números 0-10. En el módulo 4, examinaron las relaciones entre los números 1-5 hasta la comparación. En el módulo 5, los niños hacen la transición del concepto comparativo de más (4 manzanas es más de 1 manzana) al concepto de adición (3 manzanas y 1 más manzanas hacen 4 manzanas). Están listos para comenzar a trabajar con operaciones, centrándose en las historias de suma y sustracción con los números 1 a 5. Los estudiantes también aprenderán a escribir números 0-5 y explorar patrones en este módulo final.

English Description:
Module 5 is the culmination of children's work with number in the Pre-K year.  Throughout Modules 1 and 3, they had extensive counting experiences with numbers 0-10.  In Module 4, they examined the relationships between numbers 1-5 through comparison.  In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples).  They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5.  Students will also learn to write numerals 0-5 and explore patterns in this final module.

Whole numbers are no better than any others! Practice plotting values on the number line as a passionate activist rises up and demands equity for all numbers, including fractions and decimals.

This course will address operations strategy by building on the concepts of:

Reengineering and process design developed by Dr. Michael Hammer.
Manufacturing strategy as developed in the literature, primarily by people at HBS.
Supply chain design and 3-D concurrent engineering literature as developed in Charles Fine’s book, Clockspeed: Winning Industry Control in the Age of Temporary Advantage. Perseus Books, 1999.

The concepts there emphasize the necessity of integrating product strategy, manufacturing strategy, and supply chain strategy. As a result, each of these will be touched upon in the course.

Two besotted rulers must embrace proportional units in order to unite their lands. It takes mathematical reasoning to identify the problem, and solution, when engineers from Queentopia and Kingopolis build a bridge to meet in the middle of the river.

Module 5 is the culmination of children's work with number in the Pre-K year.  Throughout Modules 1 and 3, they had extensive counting experiences with numbers 0-10.  In Module 4, they examined the relationships between numbers 1-5 through comparison.  In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples).  They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5.  Students will also learn to write numerals 0-5 and explore patterns in this final module.

This course introduces dynamic processes and the engineering tasks of process operations and control. Subject covers modeling the static and dynamic behavior of processes; control strategies; design of feedback, feedforward, and other control structures; and applications to process equipment.
Dedication
In preparing this material, the author has recalled with pleasure his own introduction, many years ago, to Process Control. This OCW course is dedicated with gratitude, to Prof. W. C. Clements of the University of Alabama.

This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.

The evil Scaleo has escaped from prison and is transforming the length, width, and height of objects until they become useless – or dangerous.
Who can put things right? Superheroine Scale Ella uses the power of scale factor to foil the villain.

The CyberSquad must divide 35 candies evenly among seven gargoyles in this video segment from Cyberchase.

In this video segment from Cyberchase, Jackie shows Buzz, Delete and Harold how to deal out rounds (or sets) of objects to solve a problem.

This lesson features a comparison of different travel options from New York City to six other cities. Students compare walking, biking, driving, taking the bus, riding the train, and flying. Students conduct research and calculate the CO2e for each travel option.

Step 1 - Inquire: Students watch a short video on the climate crisis. In groups, students explore and discuss emissions from the transportation sector.

Step 2 - Investigate: Students are assigned one route between New York City and another city in the Northeast. Students calculate miles, cost, time, and CO2e for each travel option for their route.

Step 3 - Inspire: Students participate in a group discussion about the results and explore different ways to decarbonize our transportation system.