In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

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 calificaciones anteriores, los estudiantes definen, evalúan y comparan las funciones y las usan para modelar las relaciones entre las cantidades. En este módulo, los estudiantes extienden su estudio de funciones para incluir la notación de la función y los conceptos de dominio y rango. Exploran muchos ejemplos de funciones y sus gráficos, centrándose en el contraste entre las funciones lineales y exponenciales. Interpretan funciones dadas gráfica, numérica, simbólica y verbalmente; traducir entre representaciones; y comprender las limitaciones de varias representaciones.

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

English Description:
In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

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

Students will compare data for two states using comparison symbols and both rounded and unrounded (exact) numbers. Students will then write their own question to compare the data.

Engineering analysis distinguishes true engineering design from "tinkering." In this activity, students are guided through an example engineering analysis scenario for a scooter. Then they perform a similar analysis on the design solutions they brainstormed in the previous activity in this unit. At activity conclusion, students should be able to defend one most-promising possible solution to their design challenge. (Note: Conduct this activity in the context of a design project that students are working on; this activity is Step 4 in a series of six that guide students through the engineering design loop.)

The 11th grade learning experience consists of 7 mostly month-long units aligned to the Common Core State Standards, with available course material for teachers and students easily accessible online. Over the course of the year there is a steady progression in text complexity levels, sophistication of writing tasks, speaking and listening activities, and increased opportunities for independent and collaborative work. Rubrics and student models accompany many writing assignments.Throughout the 11th grade year, in addition to the Common Read texts that the whole class reads together, students each select an Independent Reading book and engage with peers in group Book Talks. Students move from learning the class rituals and routines and genre features of argument writing in Unit 11.1 to learning about narrative and informational genres in Unit 11.2: The American Short Story. Teacher resources provide additional materials to support each unit.

In this short unit, students will spend three lessons exploring the importance of themes and main ideas in fiction and informational texts.  Now would be a good time to have them take an assessment of their reading and writing skills. They'll explore theme through O. Henry's classic short story  "The Gift of the Magi" and consider how this piece compares to the main idea in the article "The Proven Power of Giving, Not Getting."

In this lesson, students will read a famous short story by the author O. Henry and consider how gift giving affects both the giver and the receiver. They’ll learn about aphorisms and create their own bumper sticker.

Module 3 begins by extending students’ kindergarten experiences with direct length comparison to indirect comparison whereby the length of one object is used to compare the lengths of two other objects.  Longer than and shorter than are taken to a new level of precision by introducing the idea of a length unit.  Students then explore the usefulness of measuring with similar units. The module closes with students representing and interpreting data.

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

Module 4 builds upon Module 2’s work with place value within 20, now focusing on the role of place value in the addition and subtraction of numbers to 40.  Students study, organize, and manipulate numbers within 40.  They compare quantities and begin using the symbols for greater than (>) and less than (<).  Addition and subtraction of tens is another focus of this module as is the use of familiar strategies to add two-digit and single-digit numbers within 40.  Near the end of the module, the focus moves to new ways to represent larger quantities and adding like place value units as students add two-digit numbers.

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

After students observed, analyzed, and classified objects by shape into pre-determined categories in Module 2, they now compare and analyze length, weight, volume, and, finally, number in Module 3. The module supports students’ understanding of amounts and their developing number sense. The module culminates in a three-day exploration, one day devoted to each attribute: length, weight, and volume.

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

Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.

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

Using guided notes, students will learn what comparison shopping is, how it can help consumers, and when it makes sense to comparison shop

The primary purpose of this seminar is to enable students to craft approaches to so-called “First World”/ “Third World” city comparisons that are theoretically sophisticated, methodologically rigorous, contextually grounded, and significantly beneficial. Since there exists very little literature and very few projects which compare “First World” and “Third World” cities in a sophisticated and genuinely useful manner, the seminar is structured around a series of readings, case studies, and discussions to assist students in becoming mindful of the potential and pitfalls of comparative analysis, the types of data, the methods of analysis, and the urban issues or sectors which may benefit the most from such approaches. The course is designed to be interdisciplinary and interactive, and is geared towards masters and doctoral students.

Students will research different colleges they would potentially be interested in and then complete a college comparison worksheet.

Ratios

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Calculate with whole numbers up to 100 using all four operations.
Understand fraction notation and percents and translate among fractions, decimal numbers, and percents.
Interpret and use a number line.
Use tables to solve problems.
Use tape diagrams to solve problems.
Sketch and interpret graphs.
Write and interpret equations.

Lesson Flow

The first part of the unit begins with an exploration activity that focuses on a ratio as a way to compare the amount of egg and the amount of flour in a mixture. The context motivates a specific understanding of the use of, and need for, ratios as a way of making comparisons between quantities. Following this lesson, the usefulness of ratios in comparing quantities is developed in more detail, including a contrast to using subtraction to find differences. Students learn to interpret and express ratios as fractions, as decimal numbers, in a:b form, in words, and as data; they also learn to identify equivalent ratios.

The focus of the middle part of the unit is on the tools used to represent ratio relationships and on simplifying and comparing ratios. Students learn to use tape diagrams first, then double number lines, and finally ratio tables and graphs. As these tools are introduced, students use them in problem-solving contexts to solve ratio problems, including an investigation of glide ratios. Students are asked to make connections and distinctions among these forms of representation throughout these lessons. Students also choose a ratio project in this part of the unit (Lesson 8).

The third and last part of the unit covers understanding percents, including those greater than 100%.

Students have ample opportunities to check, deepen, and apply their understanding of ratios, including percents, with the selection of problems in the Gallery.

This lesson formally introduces and defines a ratio as a way of comparing numbers to one another.Key ConceptsA ratio is defined by the following characteristics:A ratio is a pair of numbers (a:b).Ratios are used to compare two numbers.The value of a ratio a:b is the quotient a ÷ b, or the result of dividing a by b.Other important features of ratios include the following:A ratio does not always tell you the values of quantities being compared.The order of values in a ratio matters.Goals and Learning ObjectivesIntroduce a formal definition of ratio.Use the definition of ratio to solve problems related to comparing quantities.Understand that ratios do not always tell you the values of the quantities being compared.Understand that the order of values in a ratio matters.

Students work with a set of cards showing different ways of expressing ratios numerically. They group the cards showing equivalent ratios and then order the groups from least to greatest value.Key ConceptsIt can be hard to compare the values of ratios represented in different forms (e.g., a:b, decimal, fraction, a to b). Simplifying ratios makes it easier to compare and order their values.Goals and Learning ObjectivesIdentify ratios that are equivalent but expressed differently.Simplify ratios in order to group and order cards efficiently and successfully.

Students use percents greater than 100% to solve problems about rainfall, revenue, snowfall, and school attendance.Key ConceptsPercents greater than 100% are useful in making comparisons between the values of a single quantity at two points in time. When a later value is more than 100% of an earlier value, it means the quantity has increased over time. This percent comparison can be used to find unknown values, whether the earlier or later value is unknown.Goals and Learning ObjectivesUnderstand the meaning of a percent greater than 100% in real-world situations.Use percents greater than 100% to interpret situations and solve problems.