Students represent and solve percent increase problems.Key ConceptsWhen there is a percent increase between a starting amount and a final amount, the relationship can be represented by an equation of the form y = kx where y is the final amount, x is the starting amount, and k is the constant of proportionality, which is equal to 1 plus the percent change, p, represented as a decimal: k = 1 + p, so y = (1 + p)x.The constant of proportionality k has the value it does—a number greater than 1—because of the way the distributive property can be used to simplify the expression for the starting amount increased by a percent of the starting amount: x + x(p) = x(1 + p).Goals and Learning ObjectivesDetermine the unknown amount—either the starting amount, the percent change, or the final amount—in a percent increase situation when given the other two amounts.Make a table to represent a percent increase problem.Write and solve an equation to represent a percent increase problem.

Students continue to explore the three relationships from the previous lessons: Comparing Dimensions, Driving to the Amusement Park, and Temperatures at the Amusement Park. They graph the three situations and realize that the two proportional relationships form a straight line, but the time and temperature relationship does not.Key ConceptsA table of values that represent equivalent ratios can be graphed in the coordinate plane. The graph represents a proportional relationship in the form of a straight line that passes through the origin (0, 0). The unit rate is the slope of the line.Goals and Learning ObjectivesRepresent relationships shown in a table of values as a graph.Recognize that a proportional relationship is shown on a graph as a straight line that passes through the origin (0, 0).

Students watch a video showing three different ways to solve a problem involving a proportional relationship, and then they use each method to solve a similar problem. Students describe each approach, including the mathematical terms associated with each.Key ConceptsThree methods for solving problems involving proportional relationships include:Setting up a proportion and solving for the missing valueFinding the unit rate and multiplyingWriting and solving a formula using the constant of proportionalityGoals and Learning ObjectivesSolve a problem involving a proportional relationship in three different ways: set up a proportion and solve for a missing value, use a unit rate, and use the constant of proportionality to write and solve a formula.

In Part l of this two-part lesson, students use an interactive to place percent increase and percent decrease signs between monetary amounts to indicate the correct increase or decrease between the amounts of money. They must also place the correct decimal multiplier  between the two amounts to show what decimal to multiply the original amount by to get the final amount.Key ConceptsStudents apply understanding of percent change situations to systematize and generalize patterns in relating two amounts by multiplication.Goals and Learning ObjectivesIdentify the percent increase or percent decrease between two amounts.Identify the decimal multiplier that when multiplied by the original amount results in the final amount.Reason abstractly and quantitatively.

Students further explore scale, taking a scale drawing floor plan and redrawing it at a different scale.Key ConceptsStudents explore change from one scale to another, focusing on the ratios. Students will draw a scale model of a house.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.

Students will explore scale and use it to find measurements in scale drawings.Key ConceptsScale drawings are drawn proportionally so that there is a ratio between a given length on the drawing and the actual length. This ratio is used to set up a proportion to find other measurements.GoalsUnderstand that scale drawings are proportional.Use scale to find actual measurements.ELL: Define these terms in the context of the discussion:scalescale drawingscaled to fitproportionalAllow ELLs to use the dictionary if they wish.

This lesson teaches about Rates, Ratios, and Unit Rates, using visually appealing art and real-life examples that will engage teenagers.

The lesson refers to: The circle, its circumference, its areaPi and Fi numberPolygons and the sum of their interior and exterior anglesThe Golden RatioFibonacci’s Sequence and Spiral                                  

Middle School Water Quality Curriculum SynopsisDesign your own wetland science field trip or have WREN staff visit your classroom.Programs address Oregon State Science Standards and Common Core State Learning Standards. Purpose of the Water Quality Curriculum: •    For students to model the scientific method, engineering, math, and social studies practices. •    To explore and solve problems along the Long Tom River Watershed. •    To use tools and technology to collect data and use that data to answer questions.•    To engineer solutions to real-life problems and learn how to resolve water quality disputes in real-life scenarios.  Each lesson can be integrated into our 2-hour tour of the West Eugene Wetlands (WEW). How much time is required for the lesson, the best season, and where the lesson is best experienced is indicated next to the lesson tile._______________________________________________________________________________________________What is a Watershed? Activity/ 50 minutes (Class or WEW):It’s recommended that all classes begin their wetland field study with this fun and interactive, whole-body activity that investigates how vegetation affects the movement of water over land surfaces and identifies best management practices to reduce erosion. Science Standards: MS-ESS2; MS-ESS2-4.    Earth’s Systems: Develop a model to describe cycling of water through earth’s systems driven by energy from the sun and force of gravity._______________________________________________________________________________________________Wetland Soil Study/ 90 minutes (WEW- Fall or Spring):Students will learn the history behind the unique composition of soil in the southern Willamette Valley, discover how wetland soils have an important role in filtering and cleaning the water that runs through them, explore and record the physical characteristics of wetland soil using a Munsell Chart, measure the hydric capacity of different types of soil, and make the connection between soils and water in a wet prairie. Science Standards: MS-ESS2-2.    Earth’s Systems: Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales.Common Core Standards:Mathematics7.EE.B.4.     Use variables to represent quantities in a real-world of mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about quantities.______________________________________________________________________________________________           Water Quality of Amazon Creek/ 90 minutes (WEW- Fall and Spring):Through experimentation and a simulation, students will learn how increases in water acidity have endangered the quality of life for water-based organisms in parts of Eugene. Students will model water molecules under different circumstances, test water samples from Amazon creek for dissolved oxygen, PH, and temperature and learn how these variables impact the quality of life in our waterways.  Science Standards: MS-PS1-1.          Matter and Its Interactions: Develop models to describe the atomic composition of simple molecules  and extended structures.Common Core Standards:Mathematics 6.SP.B.4.            Display numerical data in plots on a number line, including dot plots, histograms, and box plots.7.EE.3.               Solve multiple real-life & mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of operations to calculate with numbers in any form. _______________________________________________________________________________________________Flood-Plan Engineering Design/ 90 minutes (WEW or Class- Fall, Winter, Spring):Students will learn about historic floods in the Willamette Valley, and explore flood dynamics by building models of riverbeds and testing their holding capacity. Students will use engineering to design systems that will help prevent flood damage and learn about how human modifications to a river or wetland can alter the floodplain.Science Standards:MS-ESS3-3.     Earth’s & Human Activity: Apply Scientific principles to design a method for monitoring and minimizing a human impact on the environment.MS-ESS3-2.    Earth’s & Human Activity: Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their efforts.MS-ETS1-1; 1-4. Engineering Design: Develop a model to generate data for iterative testing and modification of a  proposed object, tool, or process such that an optimal design can be achieved.  Common Core Standards:MathematicsMP.2.        Reason abstractly and quantitatively._______________________________________________________________________________________________Water Quality Debate/ 60 minutes (Class- Fall, Winter, Spring):Students will demonstrate how disputes regarding water quality and quantity can be settled through mediation by playing character roles in a mock Town Hall Meeting. They will develop and engage in an evidence supporting argument surrounding a local water-related issue, evaluate arguments presented by others of different viewpoints, and decide on a resolution.Science Standards:MS-LS2-5.    Ecosystems: Interactions, Energy and Dynamics: Evaluate competing design solutions for maintaining biodiversity and ecosystem servicesCommon Core Standards:ELA/LiteracyMS-LS-2-2.    Engage effectively in a range of collaborative discussions (one on one, in groups, and teacher led) with diverse partners on grade 8 topics, texts, and issues, building on other’s ideas and expressing their own clearly. MS-LS2-2.    Present claims or findings, emphasizing salient points in a focused coherent manner with relevant evidence, sound valid reasoning and adequate well-chosen details, use appropriate eye contact, adequate volume, and other pronunciation. 

Students will breed fruit flies through several generations and record their data using mathematical models in order to demonstrate the inheritance of trait variations.

(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 3, la comprensión de los estudiantes de la adición y la resta de las fracciones se extiende desde el trabajo anterior con equivalencia de fracción y decimales. Este módulo marca un cambio significativo lejos de la centralidad de los grados elementales de las diez unidades de base al estudio y el uso del conjunto completo de unidades fraccionarias desde el avance de grado 5, especialmente como se aplica al álgebra.

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

English Description:
In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

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 el módulo 8, el módulo final del año, los estudiantes amplían su comprensión de las relaciones completas a través de la lente de la geometría. A medida que los estudiantes componen y descomponen formas, comienzan a desarrollar una comprensión de las fracciones unitarias como partes iguales de un todo.

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

English Description:
In Module 8, the final module of the year, students extend their understanding of part–whole relationships through the lens of geometry.  As students compose and decompose shapes, they begin to develop an understanding of unit fractions as equal parts of a whole.

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 de 40 días, los estudiantes se basan en su trabajo de grado 3 con fracciones unitarias mientras exploran la equivalencia de fracción y extienden esta comprensión a números mixtos. Esto lleva a la comparación de fracciones y números mixtos y a la representación de ambos en una variedad de modelos. Las fracciones de referencia juegan un papel importante en la capacidad de los estudiantes para generalizar y razonar sobre la fracción relativa y los tamaños de números mixtos. Luego, los estudiantes tienen la oportunidad de aplicar lo que saben para ser cierto para las operaciones de números enteros a los nuevos conceptos de fracción y operaciones de números mixtos.

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

English Description:
In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers.  This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models.  Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes.  Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.

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.)

Este módulo de 20 días brinda a los estudiantes su primera oportunidad de explorar los números decimales a través de su relación con las fracciones decimales, expresando una cantidad dada tanto en la fracción como en las formas decimales. Utilizando la comprensión de las fracciones desarrolladas en todo el Módulo 5, los estudiantes aplican el mismo razonamiento a los números decimales, construyendo una base sólida para el trabajo de grado 5 con operaciones decimales.

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

English Description:
This 20-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms.  Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations.

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.)

Módulo 4 de grado 5 extiende la comprensión del estudiante de las operaciones de fracción a la multiplicación y la división de fracciones y fracciones decimales. El trabajo procede de la interpretación de los gráficos de línea que incluyen mediciones fraccionales para interpretar las fracciones como división y razonamiento sobre la búsqueda de fracciones de conjuntos a través de la fracción por multiplicación de números enteros. El módulo procede a la fracción por multiplicación de fracción en formas de fracción y decimal. Una comprensión de la multiplicación como escala y multiplicación por N/N como multiplicación por 1 permite a los estudiantes razonar sobre productos y convertir fracciones en decimales y viceversa. Los estudiantes son presentados al trabajo de división con fracciones y fracciones decimales. Los casos de división se limitan a la división de números enteros por fracciones unitarias y fracciones unitarias por números enteros. Se introducen divisores de fracción decimal y la fracción equivalente y el pensamiento del valor del lugar permiten al alumno razonar sobre el tamaño de los cocientes, calcular los cocientes y colocar decimales con sensatez en los cocientes. A lo largo del módulo, se les pide a los estudiantes que razonen sobre estos conceptos importantes interpretando expresiones numéricas que incluyen operaciones de fracción y decimales y perseverar en la resolución de problemas de varios pasos en el mundo real que incluyen todas las operaciones de fracción compatibles con el uso de diagramas de cintas.

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

English Description:
Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

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 de 35 días de grado 3, los estudiantes extienden y profundizan la práctica de segundo grado con "acciones iguales" para comprender las fracciones como particiones iguales de un todo. Su conocimiento se vuelve más formal a medida que trabajan con los modelos de área y la línea numérica.

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

English Description:
In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.

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

Numberstring.com describes number strings as "a set of related math problems, crafted to support students to construct big ideas about mathematics and build their own strategies."

This number string builds students understanding and strategies related to percent, particularly exploring questions such as, "3 is 25% of what number?"

SWBAT articulate strategies for determining a whole when given a part and the percentage it represents.

This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

Christine Munafo's Flipped Classroom-4th grade STEM. This video gives instruction and examples to fourth grade students on how to order fractions.