In Module 5, students consider part–whole relationships through a geometric lens. The module opens with students identifying the defining parts, or attributes, of two- and three-dimensional shapes, building on their kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects. Students combine shapes to create a new whole: a composite shape. They also relate geometric figures to equal parts and name the parts as halves and fourths. The module closes with students applying their understanding of halves to tell time to the hour and half hour.

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.

Explains the use of the correct case of pronoun when used in comparisons.

This tutorial teaches writing students how to share convincing in well-written sentences that are connected from one to the other--that is, they exhibit transition. W.9-10.1c cohesion/clarity/reason, W.9-10.2c cohesion/clarity/trans

Here is a run-down of several basic patterns of organization to use when writing. An example is given for each pattern, as well as an explanation.

A guide to support parents as they work with their students in place value, comparison, addition and subtraction to 100.

A guide to support parents as they work with their students in place value, comparison, addition and subtraction to 40.

This QuickTime movie gives examples of writing ratios. As you watch and listen to the teacher and students interact it helps clarify the thinking behind applying this concept.

This QuickTime movie explains what ratios are and models how to solve a ratio problem. As you watch and listen to the teacher and students interact it helps clarify the thinking behind applying this concept. Click the start button to access the video. [4:36]

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.

This multimedia Learn Alberta math resource focuses on graphing data. In the video portion, students will see how math is involved in the display of merchandise in stores. The accompanying interactive component provides an exploration and comparison of a variety of graph types, namely line graphs, bar graphs, and circle graphs. Students will need to assess whether different graphs represent the same data. Be sure to follow the link to the printable activity included to reinforce target skills.

This animated video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to use fractions to compare the spring weight of a hedgehog with its weight just before hibernation. In the accompanying classroom activity, students use visual models to work through the challenge problem presented at the end of the video, which also involves the division of fractions and comparison.

This video [2:31] illustrates a word problem involving the multiplication of fractions that requires students to find an unknown product based on a comparison of two quantities. One of the world's largest insects, the Goliath beetle, is known for its strength as well as its size. The animation shows a beetle lifting many times its own weight and then models how to determine the number of pounds that the beetle is lifting. In the accompanying classroom activity, students watch the video, reproduce the visualization modeled in the video, and solve a problem using a visual model. Includes teacher and student materials.

(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 5, los estudiantes consideran parte de las relaciones completas a través de una lente geométrica. El módulo se abre con estudiantes que identifican las partes definidas, o atributos, de formas dos y tridimensionales, basándose en sus experiencias de jardín de infantes de clasificación, análisis, comparación y creación de varias formas y objetos de dos y tridimensionales. Los estudiantes combinan formas para crear un nuevo todo: una forma compuesta. También relacionan las figuras geométricas con partes iguales y nombran las partes como mitades y cuartos. El módulo se cierra con estudiantes que aplican su comprensión de las mitades para decir tiempo a la hora y media hora.

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

English Description:
In Module 5, students consider part–whole relationships through a geometric lens. The module opens with students identifying the defining parts, or attributes, of two- and three-dimensional shapes, building on their kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects. Students combine shapes to create a new whole: a composite shape. They also relate geometric figures to equal parts and name the parts as halves and fourths. The module closes with students applying their understanding of halves to tell time to the hour and half hour.

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 3 comienza extendiendo las experiencias de jardín de infantes de los estudiantes con una comparación de longitud directa con la comparación indirecta por la cual la longitud de un objeto se usa para comparar las longitudes de otros dos objetos. Más largo que y más corto que se llevan a un nuevo nivel de precisión al introducir la idea de una unidad de longitud. Luego, los estudiantes exploran la utilidad de medir con unidades similares. El módulo se cierra con estudiantes que representan e interpretan datos.

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

English Description:
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.