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Sumar números de varios dígitos: 48,029+233,930

Suma 48,029+233,930 mediante el algoritmo estándar.

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Trovare i fattori di un numero

Sal trova i fattori di 120.

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Sumar curvas de demanda

Cómo añadir curvas de demanda

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Nado de aproximação

Neste vídeo você vai aprender o nado de aproximação, técnica para manter a observação na zona de arrebentação do surf.

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 Nado de aproximação Saber nadar nas ondas sem a prancha é fundamental para um aprendizado completo do surf, especialmente caso você perca a prancha na água. Neste vídeo você vai aprender o nado de aproximação, uma técnica que favorece a observação do entorno enquanto você se move pela zona de arrebentação. Pratique essa técnica em piscina antes de cair no mar. Para complementar esse treino você pode assistir aos vídeos do nosso programa de Natação, como o Nado Crawl. A técnica do nado de aproximação consiste em cinco etapas: a propulsão, a recuperação e o deslize, que compõem a braçada, a pernada e a posição da cabeça. A propulsão consiste em puxar a água ao longo do corpo, buscando o apoio necessário para acelerar o corpo à frente. Nesta fase você tem de aumentar o apoio com uma leve mudança de direção no momento de puxar a água: para trás e para fora; para trás e para dentro; para trás novamente, até a completa extensão do cotovelo. Para iniciar a recuperação da braçada traga o cotovelo por sobre a água no eixo do ombro. Na segunda metade desse giro você pode deixar o braço cair à frente, de modo que o polegar seja o primeiro dedo da mão a entrar na água. Para deslizar, estique ao máximo o membro superior que voltou para a água aproveitando a energia do seu deslocamento e mantendo a posição por um instante antes de iniciar o próximo ciclo de braçada. Durante esse movimento, a parte superior das costas vai criar um movimento que chega até o quadril. Os ciclos de pernada são feitos entre esses movimentos: uma pernada forte quando você mudar o sentido da rotação do quadril seguida de duas pernadas mais suaves. Elas estabilizam e preparam o corpo para a próxima inversão. Ao longo do movimento mantenha sua cabeça erguida, com o olhar fixo no objetivo do seu deslocamento. É importante encaixar o tempo certo da pernada principal para aumentar a sustentação enquanto nada. Encontre um ponto de apoio ao final de cada deslize de braçada.

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Sikana Education

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geometry-m3-topic-a-overview.pdf

geometry-m3-topic-a-overview.pdf

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Estándares Comunes del Estado de Nueva York Plan de estudios de matemáticas GEOMETRÍA • MÓDULO 3 Tema A: Área G-GMD.A.1 Estándar del enfoque: G-GMD.A.1 Días de enseñanza: 4 Proporciona un argumento informal para las fórmulas para la circunferencia de un círculo, área de un círculo, volumen de un cilindro, pirámide y cono. Usar argumentos de disección, principio de Cavalieri y argumentos de límites informales. Lección 1: ¿Qué es área? (E) 1 Lección 2: Propiedades del área (E) Lección 3: El principio de escala para el área (E) Lección 4: Comprobar el área de un disco (S) El tema del área se debe reexaminar para poder tener una conversación sobre las figuras en tres dimensiones; primero tenemos la discusión necesaria sobre el área. El área se introdujo en el Grado 3, pero solo se toman en consideración las figuras que son fáciles de “llenar” con unidades. En el Grado 5, se entiende la necesidad de usar partes de cuadrados unitarios para algunas figuras y se aplica en el Grado 6. En el Grado 7, los estudiantes se dan cuenta que una figura puede tener un área aun si, al igual que el disco, no se puede descomponer en un número finito de cuadrados unitarios, pero (debidamente) esto se trata a nivel intuitivo. A medida que progresan los grados, se elabora el vínculo entre el área como una cantidad geométrica medible y el área representada por números para cálculos. La culminación es un método universal para medir las áreas, aun cuando no sean uniones finitas de cuadrados unitarios o partes simples de cuadrados unitarios. Los matemáticos se refieren a esto como la medida de Jordan. Aunque pueda parecer que es una idea intimidante introducirla en este nivel, se puede pensar como simplemente las propiedades bien conocidas del área con las que los estudiantes ya están familiarizados. Esto no solo es un enfoque del área aceptable intuitivamente, sino es completamente riguroso a nivel universitario. El concepto forma un puente importante para cálculo, pues la medida de Jordan es la idea empleada al definir la integral de Riemann. 1 Clave de la estructura de la lección: P: Lección de conjuntos de problemas, M: Lección del ciclo de elaboración de modelos, E: Lección de exploración, S: Lección socrática Topic A: Date: Area 8/31/15 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 6 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. PLAN DE ESTUDIOS DE MATEMÁTICAS DE LOS ESTÁNDARES COMUNES DEL ESTADO DE NUEVA YORK Tema A M3 GEOMETRÍA En este tema, la Lección 1 muestra cómo encontrar el área de una figura curvada se puede aproximar por rectángulos y triángulos. Al refinar el tamaño de los rectángulos y triángulos, la aproximación del área se acerca al área real. Los estudiantes experimentan un proceso de aproximación similar en el Grado 8 (Módulo 7, Lección 14) para poder calcular 𝜋𝜋. El argumento informal de límite prepara a los estudiantes para el desarrollo de las fórmulas de volumen para conos y cilindros, y anuncia ideas que los estudiantes explorarán formalmente en cálculo. Este proceso de aproximación es importante para desarrollar la fórmula de volumen de conos y cilindros. En la Lección 2, los estudiantes estudian las propiedades básicas del área utilizando la notación de conjuntos; en el Tema B podrán ver cómo las propiedades son análogas a aquellas del volumen. En la Lección 3, los estudiantes estudian el principio de escala, que afirma que si una región de planos está graduada por los factores 𝑎𝑎 y 𝑏𝑏 en dos direcciones perpendiculares, entonces su área se multiplica por un factor de 𝑎𝑎 × 𝑏𝑏. De nuevo, estudiamos esto en dos dimensiones para establecer la base para tres dimensiones cuando se escala a sólidos. Finalmente, en la Lección 4 los estudiantes desarrollan la fórmula para el área de un disco y al igual que en la Lección 1, incorporan un proceso de aproximación. Los estudiantes aproximan el área del disco, o un círculo, al inscribir un polígono dentro del círculo, y consideran cómo el área de la región poligonal cambia a medida que aumenta el número de lados y el polígono se mira más y más como el disco en el que está inscrito. Topic A: Date: Area 8/31/15 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 7 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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Engage NY

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5.12E: Regulation of the Calvin Cycle

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LEARNING OBJECTIVES Outline the three major phases of the Calvin cycle: carbon fixation, reduction, and regeneration of ribulose The Calvin cycle (https://bio.libretexts.org/Bookshelves/Biochemistry/Book%3A_Biochemistry_Free_and_Easy_(Ahern_and_Rajagopal)/07%3A_Metabolism_II/7.03%3A_Calvin_Cycle) is a process utilized to ensure carbon dioxide fixation. In this process, carbon dioxide and water are converted into organic compounds that are necessary for metabolic and cellular processes. There are various organisms that utilize the Calvin cycle for production of organic compounds including cyanobacteria and purple and green bacteria. The Calvin cycle requires various enzymes to ensure proper regulation occurs and can be divided into three major phases: carbon fixation, reduction, and regeneration of ribulose. Each of these phases are tightly regulated and require unique and specific enzymes. Figure \(\PageIndex{1}\): Overview of the Calvin cycle. An overview of the Calvin cycle and the three major phases. Image used with permission (CC SA-BY 3.0; Mike Jones (https://commons.wikimedia.org/wiki/User:Adenosine)). During the first phase of the Calvin cycle, carbon fixation occurs. The carbon dioxide is combined with ribulose 1,5-bisphosphate to form two 3-phosphoglycerate molecules (3-PG). The enzyme that catalyzes this specific reaction is ribulose bisphosphate carboxylase (RuBisCO). RuBisCO is identified as the most abundant enzyme on earth, to date. RuBisCO is the first enzyme utilized in the process of carbon fixation and its enzymatic activity is highly regulated. RuBisCO is only active during the day as its substrate, ribulose 1,5-bisphosphate, is not generated in the dark. RuBisCO enzymatic activity is regulated by numerous factors including: ions, RuBisCO activase, ATP /ADP and reduction/oxidation states, phosphate and carbon dioxide. The various factors influencing RuBisCO activity directly affect phase 1 of the Calvin cycle. During the second phase of the Calvin cycle, reduction occurs. The 3-PG molecules synthesized in phase 1 are reduced to glyceraldehyde-3-phosphate (G3P). This reducing process is mediated by both ATP and NADPH. One of the two G3P molecules formed are further converted to dihydroxyacetone phosphate (DHAP) and the enzyme aldolase is used to combine G3P and DHAP to form fructose-1,6-bisphosphate. The enzyme aldolase is typically characterized as a glycolytic enzyme with the ability to split fructose 1,6-bisphosphate into DHAP and G3P. However, in this specific phase of the Calvin cycle, it is used in reverse. Therefore, aldolase is said to regulate a reverse reaction in the Calvin cycle. Additionally, aldolase can be utilized to promote a reverse reaction in gluconeogenesis as well. The fructose-1,6-bisphosphate formed in phase 2 is then converted into fructose-6-phosphate. During the third phase of the Calvin cycle, regeneration of RuBisCO occurs. This specific phase involves a series of reactions in which there are a variety of enzymes required to ensure proper regulation. This phase is characterized by the conversion of G3P, which was produced in earlier phase, back to ribulose 1,5-bisphosphate. This process requires ATP and specific enzymes. The enzymes involved in this process include: triose phosphate isomerase, aldolase, fructose-1,6-bisphosphatase, transketolase, sedoheptulase-1,7-bisphosphatase, phosphopentose isomerase, phosphopentose epimerase, and phosphoribulokinase. The following is a brief summary of each enzyme and its role in the regeneration of ribulose 1,5-bisphosphate in the order it appears in this specific phase. Triose phosphate isomerase: converts all G3P molecules into DHAP Aldolase and fructose-1,6-bisphosphatase: converts G3P and DHAP into fructose 6-phosphate Transketolase: removes two carbon molecules in fructose 6-phosphate to produce erythrose 4-phosphate (E4P); the two removed carbons are added to G3P to produce xylulose-5-phosphate (Xu5P) Aldolase: converts E4P and a DHAP to sedoheptulose-1,7-bisphosphate Sedoheptulase-1,7-bisphosphatase: cleaves the sedohetpulose-1,7-bisphosphate into sedoheptulase-7-phosphate (S7P) Transketolase: removes two carbons from S7P and two carbons are transferred to one of the G3P molecules producing ribose-5-phosphate (R5P)and another Xu5P Phosphopentose isomerase: converts the R5P into ribulose-5-phosphate (Ru5P) Phosphopentose epimerase: converts the Xu5P into Ru5P Phosphoribulokinase: phosphorylates Ru5P into ribulose-1,5-bisphosphate After this final enzyme performs this conversion, the Calvin cycle is considered complete. The regulation of the Calvin cycle requires many key enzymes to ensure proper carbon fixation. Key Points In this process, carbon dioxide and water are converted into organic compounds that are necessary for metabolic and cellular processes. The three phases of the Calvin cycle, fixation, reduction, and regeneration require specific enzymes to ensure proper regulation. The last phase of the Calvin cycle, regeneration, is considered the most complex and regulated phase of the cycle. Key Terms calvin cycle: A series of biochemical reactions that take place in the stroma of chloroplasts in photosynthetic organisms. gluconeogenesis: A metabolic process which glucose is formed from non-carbohydrate precursors. ribulose: A ketopentose whose phosphate derivatives participate in photosynthesis.

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Reflexionemos sobre lo que vemos y escuchamos

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Lección 7 Reflexionemos sobre lo que vemos y escuchamos En esta lección conoceré contenidos relacionados con los distintos programas de televisión. Realizaremos un conversatorio acerca de la programación que trasmiten las cadenas televisivas. Seguiré leyendo relatos e identificaré su secuencia (cómo empiezan, qué pasó luego y cómo terminan). También, ejercitaré el uso adecuado de las letras mayúsculas. Me expreso con claridad acb Aprendo más La televisión es un medio de comunicación audiovisual en el que se transmiten distintos tipos de programaciones. La primera transmisión de televisión se efectuó en inglaterra en el año 1927. 189 Converso con mis compañeras y compañeros sobre el texto Cuidado con la televisión. Contesto las preguntas de forma oral y expreso mi opinión según las experiencias vividas. • ¿Cuándo y dónde ocurre el acontecimiento narrado en el relato? • ¿Quiénes son los personajes del relato y cuáles son las características principales? • ¿Cuál es el problema o situación que enfrentan los personajes? • ¿Cómo se soluciona? • ¿El programa de televisión que miraban los hermanos, ¿era adecuado para su edad?, ¿por qué? • ¿Todos los programas que presenta la televisión, ¿son educativos?, ¿por qué? Reflexionemos sobre lo que vemos y escuchamos Hablo con cortesía Converso con mis compañeras y compañeros acerca de los distintos programas de televisión (noticieros, educativos, infantiles, películas, telenovelas, entre otros. Observo las siguientes imágenes y las comento con mis compañeras y compañeros. Recuerdo Debemos ver y escuchar programas adecuados para nuestra edad. Vamos a leer Comprendo lo que leo Escribo en el cuaderno el cuadro. Leo las oraciones y marco con una X, la opción que considero acertada. Oraciones Acuerdo Desacuerdo El lenguaje de los programas infantiles debe ser adecuado para los niños. Todos los programas de televisión tienen mensajes positivos para los niños. Es conveniente que los niños vean televisión antes de hacer las tareas. Glosario Acuerdo: decisión tomada por una o por varias personas. Desacuerdo: falta de acuerdo entre ideas, acciones, personas, etc. Comento y valoro Leo con atención el texto, discuto con mis compañeras y compañeros su contenido. Los medios están en todas partes Vivimos en un mundo en el que tenemos información y diversiones a nuestro alcance inmediato. Existe una amplia variedad de medios de comunicación entre ellos el cine, la radio, los periódicos, la televisión, el internet entre otros, y se hallan en todas partes. Tal como lo muestran la televisión, la radio, los libros, las computadoras y toda una serie de otros medios comienzan instantáneamente a formar parte del mundo de las personas desde que nacemos. 190 Libro de actividades Vamos a escribir Redacto Enumero dos programas de televisión; identifico algunas de sus características. Programas/ Aspectos Nombre del Programa 1 Nombre del Programa 2 Mensaje Vocabulario Imágenes Sabía que En la actualidad debido a la facilidad que ofrece el internet, los mensajes se envían y reciben con mayor rapidez. Vamos a leer Reconozco Relaciono el medio de comunicación con el sentido que se utiliza para recibir los mensajes. Medio de comunicación La televisión La radio El periódico La internet Sentido que se utiliza Vista Oído vista y oído Me expreso con claridad Converso con mis compañeras y compañeros sobre los relatos y su estructura. 191 Reflexionemos sobre lo que vemos y escuchamos Vamos a leer Reconozco • Leo el relato. El sapo y la flor En un jardín vivía una bella flor, un día vino al jardín un sapo que cuando pasó y la vio quedó admirado de su belleza y dijo --¡eres la más bella de todas las flores! ella respondió --¡si lo soy!, pero tú eres un sapo muy feo, -- vete del jardín, y el sapo muy triste se fue. Pasaron los días y cayó una tormenta muy fuerte, la flor perdió su belleza a causa de la lluvia y los insectos se comieron sus pétalos, pasado un tiempo el sapo volvió, y al ver a la flor tan fea le expresó somos importantes y necesitamos del otro no importa la apariencia, si me permites quedarme en el jardín los insectos nunca más te molestarán y serás siempre bella, la flor muy arrepentida le respondió--puedes quedarte a cuidar el jardín ya no me burlaré de ti. Desde ese día el sapo y la flor fueron los mejores amigos del jardín. Sabía que Los sapos son parte del ecosistema, sin ellos no existiría un equilibrio en el control de las plagas. • Nos organizamos en equipo. cada uno de nosotros relatará un evento y lo ordenamos así: 1. Primero 2. Luego 3. Después 4. Finalmente 192 Libro de actividades Vamos a escribir Genero ideas acb Aprendo más Los relatos tienen la siguiente estructura: introducción, desarrollo y desenlace. Hay palabras que indican una secuencia: primero, inicialmente, luego, segundo, finalmente, para concluir. Escribo algunas ideas para crear un relato. Redacto Trabajo en el cuaderno. Elijo uno de los temas, escritos anteriormente y escribo un relato 1. ¿Cómo empieza? 2. ¿Qué pasó luego? 3. ¿Cómo termina? Escribo correctamente • Escribo nuevamente el relato, ahora con las correcciones realizadas. 1. ¿Cómo empieza? 2. ¿Qué pasó luego? 3. ¿Cómo termina? • Ilustro el relato que escribí. Me expreso con claridad • Elijo un tema y lo relato con mis compañeras y compañeros. • No olvido que debo explicar qué pasó primero, qué paso luego, qué pasó después y qué pasó finalmente. a. Una aventura con mis amigos. b. Algo extraño que me sucedió. c. Un día de terror. 193 Reflexionemos sobre lo que vemos y escuchamos Vamos a leer Amplío mi vicabulario • Observo las imágenes • Elijo un nombre para el perro • Identifico el país que representa el mapa. • Comento si los nombres de animales y países se escriben con letra inicial mayúscula. Recuerdo Al escribir un texto siempre comienzo con letra inicial mayúscula. También después de punto y seguido. Aprendo más • En el cuaderno escribo una lista de nombres de países y de animales y los escribo correctamente con letra inicial mayúscula. • Escribo un relato, utilizo correctamente las letras mayúsculas. bca Se escriben con letra mayúscula los nombres propios de personas, lugares, de animales entre otros. ¿Qué aprendí? Escribo entre los paréntesis una V si la oración es verdadera o una F si es falsa. • La televisión es uno de los medios de comunicación más utilizado por las personas.............................................................................................................( • Un desacuerdo, es una situación donde todas las personas piensan y consideran las mismas ideas..................................................................................( • Todo relato posee la siguiente secuencia; cómo empieza en qué termina qué pasó luego.......................................................................................................( • Se escribe con letra mayúscula los nombres comunes..........................................( • La primera transmisión televisiva se dió en Inglaterra en el año 1927.....................( ) ) ) ) ) 194

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Publicado por el Lic. Edelberto Andino(edelberto.andino.ea@gmail.com) para ser utilizado con fines educativos únicamente, no debe ser utilizado con fines lucrativos de ninguna índole.

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अंग्रेजी ओके प्लीज 1.2

source_url=http://www.prathamopenschool.org/CourseContent/videos/AOK_1.2.mp4

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4.E: Genomes and Chromosomes (Exercises)

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4.3 (BPA) Answer the following questions with reference to the figure below. Figure for 4.3 Reassociation of nucleic acids, sheared to 500-nucleotide fragments, from various sources [Derived fom R. J. Britten and D. Kohne, Science, 161,529 (1968).] How many of these DNA preparations contain more than one frequency class of sequences? Explain your answer. If the genome size of E. coliis taken to be 4.5 x 106 nucleotide pairs, what is the genome size of T4? What is the complexity of mouse satellite DNA? Mouse satellite DNA represents 10% of the mouse genome. What is the repetition number for mouse satellite sequences, given that the haploid genome size is 3.2 x 109 nucleotide pairs? The calf genome is the same size as the mouse genome. What fraction of the calf genome is composed of unique sequences? 4.4 Let’s imagine that you obtained a DNA sample from an armadillo and measured the kinetics of renaturation of the genomic DNA. A standard of bacterial DNA (N= 3 x 106 bp) was also renatured under identical conditions. Three kinetic components were seen in the armadillo DNA C0t curve, renaturing fast, medium or slow. The fraction of the genome occupied by each component (f) and the C0tvalue for half-renaturation (Cot1/2(measured)) are as follows: -------------------------------------- | Component | f | Cot1/2(measured) | | fast | 0.2 | \(10^{-4}\) | | medium | 0.4 | \(10^{-1}\) | | slow | 0.4 | \(10^{4}\) | -------------------------------------- Use the information provided to calculate the Cot1/2(pure), the complexity (N), and the repetition frequency (R) for each component. Assume that the slowly renaturing component is single copy. Calculate the genome size (G) of the armadillo under the assumption that the slowly renaturing component is single copy. Which of the following sequences could be a member of the fast renaturing component? GACTCAGACTCAGACTCA ATATATATATATATATAT ACTGCCACGGGATACTGC GCGCGC

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La banca 12: los bonos del tesoro (deuda pública)

Introducción a la deuda y los fondos públicos. Qué significa cuando decimos que los pagarés de la Reserva Federal son emitidos por el banco de la reserva, pero son una obligación del gobierno.

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9.3: Van Der Waals Forces between Atoms

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Introduction The perfect gas equation of state \(PV=NkT\) is manifestly incapable of describing actual gases at low temperatures, since they undergo a discontinuous change of volume and become liquids. In the 1870’s, the Dutch physicist Van der Waals came up with an improvement: a gas law that recognized the molecules interacted with each other. He put in two parameters to mimic this interaction. The first, an attractive intermolecular force at long distances, helps draw the gas together and therefore reduces the necessary outside pressure to contain the gas in a given volume—the gas is a little thinner near the walls. The attractive long range force can be represented by a negative potential \(-aN/V\) on going away from the walls—the molecules near the walls are attracted inwards, those in the bulk are attracted equally in all directions, so effectively the long range attraction is equivalent to a potential well extending throughout the volume, ending close to the walls. Consequently, the gas density \(N/V\) near the walls is decreased by a factor \(e^{-E/kT}=e^{-aN/VkT}\cong 1-aN/VkT\). Therefore, the pressure measured at the containing wall is from slightly diluted gas, so \(P=(N/V)kT\) becomes \(P=(N/V)(1-aN/VkT)kT\), or \((P+a(N/V)^2)V=NkT\). The second parameter van der Waals added was to take account of the finite molecular volume. A real gas cannot be compressed indefinitely—it becomes a liquid, for all practical purposes incompressible. He represented this by replacing the volume \(V\) with \(V-Nb\),  \(Nb\) is referred to as the “excluded volume”, roughly speaking the volume of the molecules. Putting in these two terms gives his famous equation \[ \left[ P+a\left(\frac{N}{V}\right)^2\right] (V-Nb)=NkT. \label{9.3.1}\] This rather crude approximation does in fact give sets of isotherms representing the basic physics of a phase transition quite well. (For further details, and an enlightening discussion, see for example Appendix D of Thermal Physics, by R. Baierlein.) Ground State Hydrogen Atoms Our interest here is in understanding the van der Waals long-range attractive force between electrically neutral atoms and molecules in quantum mechanical terms. We begin with the simplest possible example, two hydrogen atoms, both in the ground state: We label the atoms \(A\) and \(B\), the vectors from the protons to the electron position are denoted by \(\vec{r_A}\) and \(\vec{r_B}\) respectively, and \(\vec{R}\) is the vector from proton \(A\) to proton \(B\). Then the Hamiltonian \(H=H^0+V\), where \[ H^0=-\frac{\hbar^2}{2m}(\nabla^2_A+\nabla^2_B)-\frac{e^2}{r_A}-\frac{e^2}{r_B} \label{9.3.2}\] and the electrostatic interaction between the two atoms \[ V=\frac{e^2}{R}+\frac{e^2}{|\vec{R}+\vec{r_B}-\vec{r_A}|}-\frac{e^2}{|\vec{R}+\vec{r_B}|}-\frac{e^2}{|\vec{R}-\vec{r_A}|} \label{9.3.3}\] The ground state of \(H^0\) is just the product of the ground states of the atoms \(A,B\), that is, \[ |0\rangle =|100\rangle_A\otimes |100\rangle_B. \label{9.3.4}\] Assuming now that the distance between the two atoms is much greater than their size, we can expand the interaction \(V\) in the small parameters \(r_A/R,\;  r_B/R\). As one might suspect from the diagram above, the leading order terms in the electrostatic energy are just those of a dipole-dipole interaction: \[ V=-e^2(\vec{r_A}\cdot \vec{\nabla})(\vec{r_B}\cdot \vec{\nabla})\frac{1}{R}=e^2\left[ \frac{\vec{r_A}\cdot \vec{r_B}}{R^3}-\frac{3(\vec{r_A}\cdot \vec{R})(\vec{r_B}\cdot \vec{R})}{R^5}\right] \label{9.3.5}\] Taking now the z- axis in the direction \(\vec{R}\), this interaction energy is \[ V=\frac{e^2}{R^3}(x_Ax_B+y_Ay_B-2z_AZ_B) \label{9.3.6}\] Now the first-order correction to the ground state energy of the two-atom system from this interaction is \(E^1_n=\langle n^0|H^1|n^0\rangle\) , where here \(H^1=V\) and \(|n^0\rangle =|100\rangle_A\otimes |100\rangle_B\). Beginning with the first term \(x_Ax_B\) in \(V\) \[ (_A\langle 100|\otimes_B\langle 100|)(x_Ax_B)(|100\rangle_A\otimes |100\rangle_B)=(_A\langle 100|x_A|100\rangle_A)(_B\langle 100|x_B|100\rangle_B) \label{9.3.7}\] is clearly zero since the ground states are spherically symmetric. Similarly, the other terms in \(V\) are zero to first order. Recall that the second-order energy correction is \(E^2_n=\sum_{m\neq n} \frac{|\langle m0|H^1|n^0\rangle |^2}{E^0_n-E^0_m} \). That is, \[ E^{(2)}=\sum_{\begin{matrix}n,l,m\\ n′,l′,m′ \end{matrix}} \frac{|(_A\langle nlm|\otimes_B\langle n′l′m′|)V(|100\rangle_A\otimes |100\rangle_B)|^2}{2E_1-E_n-E_{n′}}. \label{9.3.8}\] A typical term here is \[ (_A\langle nlm|\otimes_B\langle n′l′m′|)(x_Ax_B)(|100\rangle_A\otimes |100\rangle_B)=(_A\langle nlm|x_A|100\rangle_A)(_B\langle n′l′m′|x_B|100\rangle_B), \label{9.3.9}\] so the single-atom matrix elements are exactly those we discussed for the Stark effect (as we would expect—this is an electrostatic interaction!). As before, only \(l=1,\;\;  l′=1\) contribute. To make a rough estimate of the size of \(E^{(2)}\), we can use the same trick used for the quadratic Stark effect: replace the denominators by the constant \(2E_1\) (the other terms are a lot smaller for the bound states, and continuum states have small overlap terms in the numerator). The sum over intermediate states \(n,l,m,n′,l′,m′\) can then be taken to be completely unrestricted, including even the ground state, giving \[ \sum_{\begin{matrix}n,l,m\\ n′,l′,m′ \end{matrix}} (|nlm\rangle_A\otimes |n′l′m′\rangle_B)(_A\langle nlm|\otimes_B\langle n′l′m′|)=I, \label{9.3.10}\] the identity operator. In this approximation, then, just as for the Stark effect, \[ E^{(2)}\simeq \frac{e^4}{R^6}\frac{1}{2E_1}(_A\langle 100|\otimes_B\langle 100|)(x_Ax_B+y_Ay_B-2z_AZ_B)^2(|100\rangle_A\otimes |100\rangle_B) \label{9.3.11}\] where \(E_1=-1\) Ryd., so this is a lowering of energy. In multiplying out \((x_Ax_B+y_Ay_B-2z_AZ_B)^2\), the cross terms will have expectation values of zero. The ground state wave function is symmetrical, so all we need is \(\langle 100|x^2|100\rangle =a^2_0\), where \(a_0\) is the Bohr radius. This gives \[ E^{(2)}\simeq \frac{e^4}{R^6}\frac{1}{2E_1}6a^4_0\simeq -6\frac{e^2}{R}\left( \frac{a_0}{R}\right)^5 \label{9.3.12}\] using \(E_1=-e^2/2a_0\). Bear in mind that this is an approximation, but a pretty good one—a more accurate calculation replaces the 6 by 6.5. Forces between a 1s Hydrogen Atom and a 2p Hydrogen Atom With one atom in the \(|100\rangle\) and the other in \(|210\rangle\) , say, a typical leading order term would be \[ (_A\langle 100|\otimes_B\langle 210|)(x_Ax_B)(|100\rangle_A\otimes |100\rangle_B)=(_A\langle 100|x_A|100\rangle_A)(_B\langle 210|x_B|100\rangle_B), \label{9.3.13}\] and this is certainly zero, as are all the other leading terms. Baym (Lectures on Quantum Mechanics) concluded from this that there is no leading order energy correction between two hydrogen atoms if one of them is in the ground state. This is incorrect: the first excited state of the two-atom system (without interaction) is degenerate, so, exactly as for the 2-D simple harmonic oscillator treated in the previous lecture, we must diagonalize the perturbation in the subspace of these degenerate first excited states. (For this section, we follow fairly closely the excellent treatment in Quantum Mechanics, by C. Cohen-Tannoudji et al.) The space of the degenerate first excited states of the two noninteracting atoms is spanned by the product-space kets: \[ \begin{matrix} (|100\rangle_A\otimes |200\rangle_B), &(|200\rangle_A\otimes |100\rangle_B),&(|100\rangle_A\otimes |211\rangle_B),&(|211\rangle_A\otimes |100\rangle_B),\\ (|100\rangle_A\otimes |210\rangle_B),&(|210\rangle_A\otimes |100\rangle_B),&(|100\rangle_A\otimes |21-1\rangle_B),&(|21-1\rangle_A\otimes |100\rangle_B). \end{matrix} \label{9.3.14}\] The task, then, is to diagonalize \(V=\frac{e^2}{R^3}(x_Ax_B+y_Ay_B-2z_AZ_B)\) in this eight-dimensional subspace. We begin by representing \(V\) as an \(8\times 8\) matrix using these states as the basis. First, note that all the diagonal elements of the matrix are zero—in all of them, we’re finding the average of x,y or z for one of the atoms in the ground state. Second, writing \(V=\frac{e^2}{R^3}(\vec{r_A}\cdot \vec{r_B}-3z_AZ_B)\), it is evident that \(V\) is unchanged if the system is rotated around the z- axis (the line joining the two protons). This means that the commutator \([V,L_z]=0\), where \(L_z\) is the total angular momentum component in the z- direction, so \(V\) will only have nonzero matrix elements between states having the same total \(L_z\). Third, from parity (or Wigner-Eckart) all matrix elements in the subspace spanned by \((|100\rangle_A\otimes |200\rangle_B),\; (|200\rangle_A\otimes |100\rangle_B)\) must be zero. This reduces the nonzero part of the \(8\times 8\) matrix to a direct product of three \(2\times 2\) matrices, corresponding to the three values of \(L_z=m\). For example, the \(m=0\) subspace is spanned by \((|100\rangle_A\otimes |210\rangle_B),\; (|210\rangle_A\otimes |100\rangle_B)\). The diagonal elements of the \(2\times 2\) matrix are zero, the off-diagonal elements are equal to \(-2\frac{e^2}{R^3}(_A\langle 100|z_A|210\rangle_A)(_B\langle 210|Z_B|100\rangle_B)\), where we have kept the unnecessary labels \(A,B\) to make clear where this term comes from. (The \(x_A\) and \(y_A\) terms will not contribute for \(m=0\). ) This is now a straightforward integral over hydrogen wave functions. The three \(2\times 2\) matrices have the form \[ \begin{pmatrix} 0&k_m/R^3\\ k_m/R^3 &0 \end{pmatrix} \label{9.3.15}\] (following the notation of Cohen-Tannoudji) where \(k_m\sim e^2a^2_0\), and the energy eigenvalues are \(\pm k_m/R^3\), with corresponding eigenkets \( (1/\sqrt{2})[(|100\rangle_A\otimes |210\rangle_B)\pm (|210\rangle_A\otimes |100\rangle_B)]\). So for two hydrogen atoms, one in the ground state and one in the first excited state, the van der Waal interaction energy goes as \(1/R^3\), much more important than the \(1/R^6\) energy for two hydrogen atoms in the ground state. Notice also that the \(1/R^3\) can be positive or negative, depending on whether the atoms are in an even or an odd state—so the atoms sometimes repel each other. Finally, if two atoms are initially in a state \((|100\rangle_A\otimes |210\rangle_B)\), note that this is not an eigenstate of the Hamiltonian when the interaction is included. Writing the state as a sum of the even and odd states, which have slightly different phase frequencies from the energy difference, we find the excitation moves back and forth between the two atoms with a period \(hR^3/2k_{m=0}\). Contributors Michael Fowler (http://galileo.phys.virginia.edu/~mf1i/home.html) (Beams Professor, Department of Physics (http://www.phys.virginia.edu/), University of Virginia) (http://www.virginia.edu/)

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CSU and Merlot

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Compare multi-digit numbers

Use your place value skills to practice comparing whole numbers.

exercise

en

c_0005765779c8

Ендомембранна система

Преглед на мембранните структури, които образуват ендомембранната система в еукариотните клетки.

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В това видео ще разгледаме ендомембранната система на еукариотните клетки. Ендомембранната система. На много общо ниво - ендомембранната система включва всички мембрани, които си взаимодействат в клетката. За кои мембрани става дума? Мога да започна със самата клетъчна мембрана. Всички тези мембрани имат двоен слой от фосфолипиди. Понякога мозъкът ми дава накъсо и ги наричам билипидни слоеве, но това е двоен липиден слой. Ако се фокусираме ето тук и увеличим тази част, ще видим, че тази линия всъщност е двоен липиден слой. Ще изглежда ето така. Имаме хидрофилни глави, които сочат навън и хидрофобни опашки, които сочат навътре. Хидрофилните глави сочат навън, хидрофобните опашки сочат навътре и така слоят продължава. Ако мислим за него от ляво надясно имаме двоен слой от фосфлипиди. Това ще е вярно за клетъчната мембрана, ще бъде вярно и за външната ядрена мембрана ето тук. Рисували сме тази мембрана във видеото за ендоплазмената мрежа. Ето тук виждаш тези две мембрани. Може да си кажеш, "Добре, това двоен слой ли е?" Не, това всъщност са два двойни слоя. Тази мембрана тук има двоен фосфолипиден слой и тази мембрана тук също има двоен фосфолипиден слой. Ще използвам друг цвят. Това, което започвам да очертавам в маджента е външната мембрана от ядрената обвивка. Тя е свързана с мембраната на ендоплазмената мрежа. Започвам да очертавам и нея. Това, което очертавам в лилаво е вътрешната мембрана от ядрената обвивка. Всичко това е част от ендомембранната система. Вече започнах да говоря за ендоплазмената мрежа. Обяснихме някои от детайлите за нея във видеото за ендоплазмената мрежа и за апаратът на Голджи, но тя също е част от ендомембранната система. Едноплазмената мрежа може да представлява 50% или повече от фосфолипидните мебрани в клетката. Вече сме говорили за това, което се случва в лумена на ендоплазмената мрежа. Тази зона тук -- Говорили сме за това, което се случва там. Синтезират се белтъци. Всъщност там могат да се синтезират и други молекули, като липиди. След това те могат да се транспортират до гладката ендоплазмена мрежа, а мястото, където могат да напуснат гладката ендоплазмена мрежа, видяхме как се откъсват във видеото за ендоплазмената мрежа. Често наричаме тази зона преходна ендоплазмена мрежа. Тази зона тук можем да наречем преходна ендоплазмена мрежа. Преходна ендоплазмена мрежа е тази част, в която белтъците се откъсват, обвити във везикули (секреторни мехурчета). Това е преходната ендоплазмена мрежа. Секреторните мехурчета са тези малки отделения, които са оградени от мембрана и могат да транспортират неща като белтъци. Не искам да хабя енергия на вятъра, но всички тези линии, които рисувам, въпреки че са нарисувани като единична линия, са двойни слоеве от фосфолипиди. Мембраната може да е различна, двойният фосфолипиден слой може да е различен между различните части на мембраната, но всички имат еднакво общо устройство, имат двоен фосфолипиден слой. Като преговор: тези белтъци могат да напуснат ендоплазмената мрежа през преходната ендоплазмена мрежа и да се отправят към апарата на Голджи. Вече сме говорили за това как протеините "узряват" в апарата на Голджи. Когато казвам "узряват", иска да кажа, че има ензими, ензими на Голджи, които могат да променят белтъците по най-различни начини, могат да ги обозначат, да добавят захариди към тях, за да станат гликопротеини. Могат да ги обозначат като белтъци, които трябва да се използват в клетъчната мембрана или извън клетъчната мембрана, или в други части на клетката. Например този протеин тук се откъсва в секреторно мехурче и се отправя към апарата на Голджи, двете мембрани могат да се слеят и протеина да попадне в апарата на Голджи. Там белтъкът може да бъде модифициран. Може да се превърне в гликопротеин например, кой знае? След това може отново да се откъсне и сега този белтък, които е откъснат в секреторно мехурче може да бъде поставен в клетъчната мембрана. Белтъкът може да бъде отделен извън клетката или да отиде към други части на клетката. Всички тези мембрани, за които говорих, не са единствените части на едномембранната система. Има и неща като вакуоли, които са мембранни органели в клетката. В растителните клетки вакуолата се използва за съхранение на вещества или за поддържане на клетъчната форма и структура. Вакуолите могат да са доста големи и да дадат структура на цялото растение. В животинските клетки има лизозоми. Лизозомите са мембранни структури, в които се изпращат неща, които са за рециклиране или за разрушаване. Например нещо може да се пакетира на друго място. Ще използвам друг цвят. Нарисувах това мехурче прекалено голямо. Но да кажем, че това вътре трябва да се разруши. Следователно тази мембрана се слива с тази мембрана и съдържанието на мехурчето се озовава в лизозомата. В лизозомите има ниско pH, благодарение на това нещата, които попаднат в лизозомите се смилат и рециклират до съставните им части. Всичко това е част от едномембранната система. Още веднъж ще повторя, че рядко хората осъзнават колко сложни са клетките и колко красиви могат да бъдат.

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Khan Academy

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સમક્ષિતિજ પ્રક્ષિપ્ત માટે શુદ્ધ ગતિવિજ્ઞાનના સમીકરણને ઉકેલવું

જયારે સદિશના સમક્ષિતિજ અને શિરોલંબ ઘટક આપેલા હોય, ત્યારે બે પરિમાણીય પ્રક્ષિપ્ત ગતિના પ્રશ્નને ઉકેલવાનો મહાવરો (ત્રિકોણમિતિ નથી).

exercise

gu

c_00068709797c

Kuhesabu vizio mraba kutafuta kanuni ya eneo

Sal anatumia kizio mraba kuona kwa nini kuzidisha pande za mstatili unaweza kupata eneo la mistatili

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Nina mistatili mitatu hapa, na pia nina vipimo vyake. Nina urefu wake na upana wake. Hii hapa ina urefu na upana sawa, kwa hiyo, huu ni mraba. Tuangalie ni ukubwa gani wa eneo limechukua katika ubao. Sababu tunatumiamita kwa kila kitu , na vipimo vyote ni mita, Tutapima eneo kwa kutumia mita za miraba. Tutazame ni mita ngapi za mraba zitaenea kwenye mstatili wa njano bila kuwa nje ya mipaka na bila kuingiliana. Kwa hiyo, tunaweka mita moja ya mraba. Kumbuka,mita mraba ni mraba ambao urefu ni mita moja na upana ni mita moja. Kwa hiyo mita moja ya mraba2,3,4, au 5, na 6 kwa hiyo , tunaona eneo ni mita 6 za mraba. Eneo ni sawa na mita sita za mraba. Kuna kitu unaweza kukifanya . Unahitaji kweli kukaa na kuhesabu 1,2,3,4,5,6 ? Unaweza ukawa umegundua unaweza kufanya makundi mawili ya tatu. Niwaeleweshe vizuri. Kwa mfano,ungeona kundi moja la tatu na lingine la tatu. Sasa, utapataje makundi ya tatu? Sababu upana una mita tatu. Nitaweka mita tatu za mirabakila upande. Na jinsi gani nitapata makundimbili? hapa tuna urefu wa mita mbili. Njia nyingine kimsingi ya kuhesabu hivi vitu sita ningesema, Tazama,nina urefu wa mita mbili. nitakuwa na makundi mawili ya tatu. Kwa hiyo, nitazidisha mbili mara tatu,mbili ya makundi ya tatu, ni sawa na 6. unaweza kushangaa kuwa hii imetokea kwa bahati, kama ukichukua urefu na kuzidisha na upana, kwamba utapata jibu linalofanana na eneo? Hapa, siyo,kama utachukua urefu, kimsingi ukasema,una safu ngapi? Na ukizidisha na upana, unatakuwa na mita za miraba ngapi zitakazo enea safu? Kwa hiyo, hii ni njia rahisi ya kuhesabu idadi ya mita za miraba uliyonayo. Mita mbili kuzidisha mita tatu ni sawa sawa na mita sita za miraba. Unaweza ukafikiri hii haitumiki Tuone kama itatumika kwenye mistatili mingine hapa Kama tunavyoona,Tuchukue urefu , mita nne , na kuzidisha na upana, na kuzidisha mita mbili. Sasa, nne mara mbili ni nane. K wa hiyo, wanatakiwa kutupa mita nane za miraba. Tuone kama ni sahihi. kwa hiyo, 1,2,3,4,5,-na unaona inaenda mwelekeo sahihi- 6,7, na 8. Kwa hiyo, eneo la mstatili huu,ni mita nane za miraba. Na hii ukiangalia ni makundi manne ya mbili. kwa usahihi kabisa ni makundi manne ya mbili. Ambapo nne mara mbili ilikotokea. unaweza sema ni makundi manne ya mbili au makundi mawili ya nne. Kwa hiyo,kundi moja la nne hapa. ambalo ni mbili mara nne, na makundi mawili ya nne. tuoneshe mchoro ukae vizuri. Sasa, unaweza kukokotoa eneo la mstatili . ambalo ni mraba,sababu una urefusawa sawa naupana. Tunazidisha urefu ,mita tatu, mara upana, mara mita tatu, kupata tatu mara tatu ni tisa- mita tisa za miraba. Tuakikishe Zidisha vipimo vya mstatili. kwa hiyo tuna 1, 2, 3, 4, 5, 6, 7, 8, na 9. Kwa hiyo ime wiana. Tunahitaji mita za miraba ngapi ili kuweza kuenea pote, bilakuingiliana , bila kuvuka mipaka. Tuna pata sawa kabisa kama tunge zidishatatu mara tatu, kama tuta zidiasha urefu mara upana katika mita.

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Khan Academy

CC BY-NC-SA

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आधे और चौथाई

Practice dividing shapes into 2 or 4 equal sections.

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hi

c_0006ec4d828a

बहुपदों को जोड़ना

exercise

hi

c_0006f51dc8e7

Lección 13

Objetivo: multiplicar factores numéricos mixtos y relacionarlos con la propiedad distributiva y el modelo de área.

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Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Objective: Multiply mixed number factors, and relate to the distributive property and the area model. Suggested Lesson Structure Fluency Practice  Application Problem  Concept Development  Student Debrief  Total Time (10 minutes) (7 minutes) (33 minutes) (10 minutes) (60 minutes) Fluency Practice (10 minutes)  Multiplying Fractions 5.NF.4 (4 minutes)  Find the Volume 5.MD.C (6 minutes) Multiplying Fractions (4 minutes) Materials: (S) Personal white board Note: This fluency activity prepares students for today’s lesson. T: S: T: S: T: S: 1 3 1 1 1 × = . 3 5 15 2 (Write × 3 2 2 4 × = . 3 5 15 3 (Write 4 × 1 5 (Write × = 2 5 .) Say the complete multiplication number sentence.. = .) Say the complete multiplication number sentence. 2 3 = . Beneath it, write = .) On your personal white board, write the complete multiplication sentence. Then, simplify the fraction. 3 2 6 1 (Write 4 × 3 = 12. Beneath it, write = 2.) Continue with the following possible sequence: Lesson 13: 1 2 3 2 3 3 4 5 3 3 5 × 4, 3 × 5, 4 × 5, 6 × 4, and 5 × 6. Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 177 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM Find the Volume (6 minutes) Materials: (S) Personal white board Note: This fluency activity reviews volume concepts and formulas. T: S: T: S: T: S: T: S: T: S: T: S: T: S: (Project a prism 4 units × 2 units × 3 units. Write V = ____ units × ____ units × ____ units.) Find the volume. (Write 4 units × 2 units × 3 units = 24 units3.) How many layers of 6 cubes are in the prism? 4 layers. (Write 4 × 6 units3.) Four copies of 6 cubic units is…? 24 cubic units. How many layers of 8 cubes are there? 3 layers. (Write 3 × 8 units3.) Three copies of 8 cubic units is…? 24 cubic units. How many layers of 12 cubes are there? 2 layers. Write a multiplication equation to find the volume of the prism, starting with the number of layers. (Write 2 × 12 units3 = 24 units3.) Repeat the process for the prisms pictured. Application Problem (7 minutes) 1 The Colliers want to put new flooring in a 6 2-foot by 1 7 3-foot bathroom. The tiles they want come in 12-inch squares. What is the area of the bathroom floor? If the tiles cost $3.25 per square foot, how much will they spend on the flooring? Note: This type of tiling applies the work from Lessons 10–12 and bridges to today’s lesson on the distributive property. Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 178 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM Concept Development (33 minutes) Materials: (S) Personal white board In this lesson, students reason about the most efficient strategy to use for multiplying mixed numbers: distributing with the area model or multiplying improper fractions and canceling to simplify. Problem 1 1 3 Find the area of a rectangle 1 3 inches × 3 4 inches, and discuss strategies for solving. T: S: T: S: T: S: T: MP.4 S: T: (Project Rectangle 1.) How is this rectangle different from the rectangles we have been working with? We know the dimensions of this one.  The side lengths are given to us, so we don’t need to tile or measure. Find the area of this rectangle. Use an area model to show your thinking. (Find the area using a model.) What is the area of this rectangle? 5 inches squared. 1 𝟏 𝟑 in 𝟑 3 in 𝟒 We have used the area model many times in Grade 5 to help us multiply numbers with mixed units. How are these side lengths like multi-digit numbers? Turn and talk. A two-digit number has two different size units in it. The ones are the smaller units, and the tens are the bigger units. These mixed numbers are like that. The ones are the bigger units, and the fractions are the smaller units.  Mixed numbers are another way to write decimals. Decimals have ones and fractions, and so do these. (Point to the model and calculations.) When we add partial products, what property of multiplication are we using? S: The distributive property. T: Let’s find the area of this rectangle again. This time, let’s use a single unit to express each of the side lengths. 1 What is 1 expressed in thirds? 3 S: 4 thirds. T: (Record on the rectangle.) Express 3 using only fourths. S: 15 fourths. 3 4 Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 179 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM T: S: T: S: T: S: T: S: T: (Record on the rectangle.) Multiply these fractions to find the area. NOTES ON MULTIPLE MEANS (Multiply to find the area.) OF ENGAGEMENT: What is the area? 2 Some students may need a quick 5 in . refresher on changing mixed numbers Which strategy did you find to be more efficient? Why? to improper fractions or vice versa. I like the strategy of expressing the dimensions as a Students should be reminded that a fraction greater than one. This way was a lot faster for mixed number is an addition sentence. So, when converting to an improper me!  These fractions were easy to simplify before I fraction, the whole number can be multiplied, so there were fewer calculations to do to expressed in the unit of the fractional find the area. part and then both like fractions Do you think it will always be true that multiplying the added. fractions will be the most efficient? Why or why not? This seems easier because it’s multiplying whole numbers.  I like the distributive property better because the numbers stay smaller doing one part at a time.  I’m not sure—some larger mixed numbers might be a lot more challenging. There are lots of different viewpoints here. Let’s try another example to test these strategies again. Problem 2 Determine when the distributive property or the multiplication of fractions is more efficient to solve for area. T: 1 (Draw a rectangle with side lengths 16 2 inches and 1 S: 4 inches.) Which strategy do you think might be 4 more efficient to find the area of this rectangle? Turn and talk. The fractions are pretty easy, so I think the distributive property will be quicker.  The numerators will be big. I think distributing will be easier.  I like to simplify fractions, so I think it would be easier to work with improper fractions. T: Work with a partner to find the area of this rectangle. Partner A, use the distributive property with an area model. Partner B, express the sides using fractions greater than 1. (Allow students time to work.) T: S: What is the area? Which strategy was more efficient? The improper fractions were messy. When I converted to improper fractions, the numerators were 561 2 33 and 17, and there weren’t any common factors to help me simplify. The area is in , which is 1 8 right, but it’s weird. I had to use long division to figure out that the area was 70 8 square inches.  The distributive property was much easier on this one. The partial products were all easy to do in 1 my head. I just added the sums of the rows and got 70 8 square inches. Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 180 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM T: S: Does the method that you choose matter? Why or why not? Turn and talk. Either way, we got the right answer.  Depending on the numbers, sometimes distributing is easier, and sometimes just multiplying the improper fractions is easier. 2 Repeat the process to find the area of a square with side length 3 3 m. T: S: When should you use each strategy? Talk to your partner. If the numbers are small, fraction multiplication might be better, especially if some factors can be simplified.  For large mixed numbers, I think the area model is easier, especially if some of the partial products are whole numbers or have common denominators.  You can always start with one strategy and change to the other if it gets too hard. 𝟑 𝟒 Problem 3 in T: S: T: T: S: 10 in An 8-inch by 10-inch picture is resting on a mat. Three-fourths inch of the mat shows around the entire edge of the picture. Find the area of the mat not covered by the picture. Compare this problem to others we have done. Turn and talk. There are two rectangles to think about here.  We have to think about how to get just the part that is the mat—not the area of the whole thing.  It is a little bit of a mystery rectangle because they 8 in are asking about the mat. They gave us the measurements of the picture and only what we see of the mat. Work with your partner, and use RDW to solve. (Allow students time to work.) What did you think about to solve this problem? I started by imagining the mat without the picture on top. I added the extra part of the mat 1 (1 2 inches) to the picture to find the length and width of the mat. Then, I multiplied and found the area of the mat. I subtracted the picture’s area from the mat and got the answer.  I started to use improper fractions, but the numbers were really large, so I used the area model.  I used the area model for the mat’s area because I saw the measurements were going to have fractions. Then, I just multiplied 8 × 10 to find the area of the picture.  After I figured out the area of the mat, I drew a tape diagram to show the part I knew and the part I needed to find.  I visualized 4 rectangles and then added their areas. Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 181 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students should solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Multiply mixed number factors, and relate to the distributive property and the area model. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. Any combination of the questions below may be used to lead the discussion.     What are the strategies that we have used to find the area of a rectangle? Which one do you find the easiest? The most difficult? How do you decide which strategy you will use for a given problem? What kinds of things do you think about when deciding? In the Problem Set, when did you use the distributive property, and when did you multiply improper fractions? Why did you make those choices? How did you solve Problem 3? What are some situations in real life where finding the area of something would be needed or useful? Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 182 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 5 NYS COMMON CORE MATHEMATICS CURRICULUM Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with assessing students’ understanding of the concepts that were presented in today’s lesson and planning more effectively for future lessons. The questions may be read aloud to the students. Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 183 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 Problem Set 5 NYS COMMON CORE MATHEMATICS CURRICULUM Name 1. 2. Date Find the area of the following rectangles. Draw an area model if it helps you. a. 5 4 c. 4 yd × 5 yd km × 1 3 1 1 12 km 5 b. 16 2 m × 4 5 m 2 3 d. 7 8 1 3 mi × 4 mi 3 2 Julie is cutting rectangles out of fabric to make a quilt. If the rectangles are 2 inches wide and 3 inches 5 3 long, what is the area of four such rectangles? Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 184 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 Problem Set 5 NYS COMMON CORE MATHEMATICS CURRICULUM 3. Mr. Howard’s pool is connected to his pool house by a sidewalk as shown. He wants to buy sod for the lawn, shown in gray. How much sod does he need to buy? 1 24 yd 2 Pool 3 yd 1 yd 1 7 yd 2 1 24 yd 2 12 yd 2 Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 185 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 Exit Ticket 5 NYS COMMON CORE MATHEMATICS CURRICULUM Name Date Find the area of the following rectangles. Draw an area model if it helps you. 1. 7 2 mm × 14 5 7 mm 2. 5 8 km × Lesson 13: 18 4 km Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 186 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 Homework 5 NYS COMMON CORE MATHEMATICS CURRICULUM Name 1. 2. Date Find the area of the following rectangles. Draw an area model if it helps you. a. 8 3 c. 5 6 in × 4 5 in cm × 4 24 cm 4 3 b. 32 ft 5 d. 5 7 3 × 3 8 ft 3 5 m×6 m 1 3 Chris is making a tabletop from some leftover tiles. He has 9 tiles that measure 3 8 inches long and 2 4 inches wide. What is the greatest area he can cover with these tiles? Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 187 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 13 Homework 5 NYS COMMON CORE MATHEMATICS CURRICULUM 3. A hotel is recarpeting a section of the lobby. Carpet covers the part of the floor as shown below in gray. How many square feet of carpeting will be needed? 1 19 ft 2 3 13 ft 5 3 11 ft 7 4 31 ft 8 3 3 ft 4 12 ft 1 2 ft 2 17 ft Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model. This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org This file derived from G5-M5-TE-1.3.0-08.2015 188 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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Engage NY

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Tangents of circles problem (example 2)

Sal finds a missing angle using the property that tangents are perpendicular to the radius.

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Angle A is a circumscribed angle on circle O. So this is angle A right over here. Then when they say it's a circumscribed angle, that means that the two sides of the angle are tangent to the circle. So AC is tangent to the circle at point C. AB is tangent to the circle at point B. What is the measure of angle A? Now, I encourage you to pause the video now and to try this out on your own. And I'll give you a hint. It will leverage the fact that this is a circumscribed angle as you could imagine. So I'm assuming you've given a go at it. So the other piece of information they give us is that angle D, which is an inscribed angle, is 48 degrees and it intercepts the same arc-- so this is the arc that it intercepts, arc CB I guess you could call it-- it intercepts this arc right over here. It's the inscribed angle. The central angle that intersects that same arc is going to be twice the inscribed angle. So this is going to be 96 degrees. I could put three markers here just because we've already used the double marker. Notice, they both intercept arc CB so some people would say the measure of arc CB is 96 degrees, the central angle is 96 degrees, the inscribed angle is going to be half of that, 48 degrees. So how does this help us? Well, a key clue is that angle is a circumscribed angle. So that means AC and AB are each tangent to the circle. Well, a line that is tangent to the circle is going to be perpendicular to the radius of the circle that intersects the circle at the same point. So this right over here is going to be a 90-degree angle, and this right over here is going to be a 90-degree angle. OC is perpendicular to CA. OB, which is a radius, is perpendicular to BA, which is a tangent line, and they both intersect right over here at B. Now, this might jump out at you. We have a quadrilateral going on here. ABOC is a quadrilateral, so its sides are going to add up to 360 degrees. So we could know, we could write it this way. We could write the measure of angle A plus 90 degrees plus another 90 degrees plus 96 degrees is going to be equal to 360 degrees. Or another way of thinking about it, if we subtract 180 from both sides, if we subtract that from both sides, we get the measure of angle A plus 96 degrees is going to be equal to 180 degrees. Or another way of thinking about it is the measure of angle A or that angle A and angle O right over here-- you could call it angle COB-- that these are going to be supplementary angles if they add up to 180 degrees. So if we subtract 96 degrees from both sides, we get the measure of angle A is equal to-- I don't want to make that look like a less than symbol, let make it-- measure of angle-- this one actually looks more like a-- measure of angle A is equal to 180 minus 96. Let's see, 180 minus 90 would be 90, and then we subtract another 6 gets us to 84 degrees.

en

Khan Academy

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c_0007d37600f3

Momento dipolar

Prevendo o momento de dipolo baseado na geometria molecular.

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pt

c_0007dcb52752

Fuentes de la Contaminación del Agua

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c_0007f60e1887

Lección 11

La evaluación a pedido de hoy les pide que vuelvan a su Evaluación de Mid-Unit 3: First Draft (sobre su país experto) y la revisen en función de las habilidades de edición que han estado practicando. Se debe alentar a los estudiantes a buscar la ortografía y el significado de las palabras en el diccionario.

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Grade 3: Module 2B: Unit 3: Lesson 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Exempt third-party content is indicated by the footer: © (name of copyright holder). Used by permission and not subject to Creative Commons license. GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Long-Term Targets Addressed (Based on NYSP12 ELA CCLS) I can write informative/explanatory texts that convey ideas and information clearly. (W.3.2) With support from adults, I can produce writing that is appropriate to task and purpose. (W.3.4) With support from peers and adults, I can use the writing process to plan, revise, and edit my writing. (W.3.5) I can use grammar conventions to send a clear message to a reader or listener. (L.3.1) I can use conventions to send a clear message to my reader. (L.3.2) I can express ideas using carefully chosen words. (L.3.3) Supporting Learning Targets Ongoing Assessment • I can revise and edit a first draft of my research-based letter to Mary Pope Osborne. • Mid-Unit 3 Assessment: Writing a First Draft about Expert Country (with annotations for revising and editing) • I can use feedback from peers to improve my writing. Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 1 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Agenda Teaching Notes 1. Opening • For the past several lessons, they have practiced editing and revising (with support from peers) their letters to Mary Pope Osborne about Japan. They focused on correct spelling, punctuation, and capitalization. Today’s on-demand assessment asks them to return to their Mid-Unit 3 Assessment: First Draft (about their expert country), and revise it based on the editing skills they have been practicing. This task addresses NYSP12 ELA CCLS W.3.2, W.3.4, W.3.5, L.3.1, L.3.2, and L.3.3. A. Engaging the Writer (2 minutes) B. Unpacking the Learning Targets (5 minutes) 2. Work Time A. Identifying Three Things to Revise and Edit (15 minutes) • Students will need a variety of papers and materials for the End of Unit 3 Assessment. Take time to help them get organized with these materials before beginning the assessment. B. Making Edits/Revisions and Completing a Second Draft (30 minutes) • Consider allowing students to use a dictionary to look up the correct spelling and meaning of words. 3. Closing and Assessment A. Letter Share (8 minutes) 4. Homework A. Continue reading your independent reading book for this unit. • After the completion of this lesson, students will have a letter that is ready for publication. The final lesson in the module focuses on publishing and celebrating the completion of the letters. • Use the NYS 4 point rubric to score students’ End of Unit 3 Assessments. In the mid-unit 3 Assessment, students were formally assessed on Content and Analysis, Command of Evidence, and Coherence, Organization, and Style. For the End of Unit 3 assessment, formally assess them on the Control of Conventions criterion. • In advance: – Post the learning targets. Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 2 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Lesson Vocabulary Materials revise, edit • Mid-Unit 3 Assessment: First Draft (from Lesson 7; one per student) • End of Unit 3 Assessment: Using the Writing Process: Revising and Editing the Letter to Mary Pope Osborne about Expert Country (one per student) • Editing checklist (one per student) • Markers (one green, one blue, one purple per student) • Things I Need to Remember for Writing recording form (from Lesson 5; one per student) • Document camera • Dictionary (optional; one per couple of students) • New York State Grade 3 Expository Writing Evaluation Rubric (from Lesson 7; see Teaching Notes) Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 3 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Opening Meeting Students’ Needs A. Engaging the Writer (2 minutes) • Tell students that in today’s lesson, they are going to apply the editing skills they have been honing over the past few lessons, as well as the feedback they have received from their writing partners. They are going to use these skills and feedback to make revisions to their Mid-Unit 3 Assessment: First Draft. They will also have the opportunity to celebrate their hard work by sharing their letters to Mary Pope Osborne with a classmate. B. Unpacking the Learning Targets (5 minutes) • Direct students’ attention to the learning targets and read them aloud: * “I can revise and edit a first draft of my researched based letter to Mary Pope Osborne.” * “I can use feedback from peers to improve my writing.” • Students should be familiar with the language of the targets from previous lessons in this unit. • Invite students to turn and talk: * “What does it mean to be able to revise and edit your drafts? What will you need to do as a writer today?” • Circulate as students talk. Address any questions or misconceptions whole group. Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 4 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Work Time Meeting Students’ Needs A. Identifying Three Things to Revise and Edit (15 minutes) • Introduce the End of Unit 3 Assessment by saying something like: * “You have been working hard as writers to learn how to make a high-quality research-based letter effective and engaging. You have also been working hard to use the writing process to make your writing stronger. We have done this as a class, and you have practiced with partners and by yourself. Today, you are going to show what you know by revising and editing on your own.” • Tell students that you are going to help them prepare for the assessment by helping them get the necessary materials ready. • Distribute: – Mid-Unit 3 Assessment: First Drafts – End of Unit 3 Assessment: Using the Writing Process: Revising and Editing the Letter to Mary Pope Osborne about Expert Country – Editing checklist – Markers • Ask students to take out: – Things I Need to Remember for Writing recording form. • Use a document camera to display the end of unit assessment. Ask students to follow along as you read the assessment directions aloud. • Clarify these points: – “You must identify at least three areas in your writing that you will revise. Write above your original writing.” – “Then, edit your letter using the editing checklist. Color-code the edits you made. Use a green marker for spelling corrections, a blue marker for punctuation corrections, and a purple marker for capitalization corrections.” – “Be sure you can explain how you used feedback from your peers to revise and improve your writing.” • Check for understanding: * “Give a thumbs-up if you understand and have an idea what you will revise and edit in your letter.” Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 5 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit Assessment: On-Demand Revising and Editing Research-Based Letter to Mary Pope Osborne about Expert Country Work Time (continued) Meeting Students’ Needs • Note students who are unsure about what they will revise. Direct them to stay in the circle and provide a quick example and answer clarifying questions. • Ask students to read through their first drafts and identify at least three areas they will revise. Encourage them to refer to their Things I Need to Remember for Writing recording forms and the editing checklist for guidance. This means that they shouldn’t be writing anything at this point, only reading and thinking. B. Making Edits/Revisions and Completing a Second Draft (30 minutes) • Answer any clarifying questions and invite students to begin working on Steps 2 and 3 of the End of Unit 3 Assessment. • Circulate and prompt them to insert a caret above original writing for insertions. Remind them of the color-coding guidelines: Use a green marker for spelling corrections, a blue marker for punctuation corrections, and a purple marker for capitalization corrections. • Be sure to collect the End of Unit 3 Assessments after the Closing and Assessment. Closing and Assessment Meeting Students’ Needs A. Letter Share (8 minutes) • Celebrate the completion of this on-demand assessment by having students share about their letters with others. They can work in pairs or in small groups to share what they wrote to Ms. Osborne. They can also share the kinds of revisions they decided to make. • Circulate as students share. • Refocus them whole group and ask for volunteers to share about their letters. • Collect the End of Unit 3 Assessments. Homework Meeting Students’ Needs • Continue reading your independent reading book for this unit. Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 •June 2014 • 6 Grade 3: Module 2B: Unit 3: Lesson 11 Supporting Materials This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Exempt third-party content is indicated by the footer: © (name of copyright holder). Used by permission and not subject to Creative Commons license. GRADE 3: MODULE 2B: UNIT 3: LESSON 11 End of Unit 3 Assessment: Using the Writing Process: Revising and Editing the Letter to Mary Pope Osborne about Expert Country Name: Date: Directions: Revise and edit the first draft of your letter to Mary Pope Osborne about the country you researched in Unit 2. Be sure to do the following: 1. You must identify at least three areas in your writing that you will revise. Use the Things I Need to Remember for Writing recording form to help you make your choices. 2. Write above your original writing. 3. Edit your letter using the editing checklist. Use a green marker for spelling corrections, a blue marker for punctuation corrections, and a purple marker for capitalization corrections. 4. Be sure you can explain how you used feedback from your peers to revise and improve your writing. Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 • June 2014 • 8 GRADE 3: MODULE 2B: UNIT 3: LESSON 11 Editing Checklist Name: Date: Target Not Yet Almost There Excellent! Teacher Comments I can capitalize appropriate words, such as character names and titles. I can use simple and compound sentences in my writing. I can use resources to check and correct my spelling. I can use correct beginning and end punctuation in my writing. (Note: Target not explicitly taught in this unit, but previously taught/assessed in Module 1.) I can spell gradeappropriate words correctly. (Note: Target not explicitly taught in this unit, but previously taught/assessed in Module 1.) Copyright © 2013 by Expeditionary Learning, New York, NY. All Rights Reserved. NYS Common Core ELA Curriculum • G3:M2B:U3:L11 • June 2014 • 9

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Engage NY

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Resumen: Los cinco sentidos

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Reflexión y Refracción de la Luz

Explora la curvatura de la luz entre dos medios con distintos índices de refracción. Ve cómo el cambiar de aire a agua y a vidrio cambia el ángulo de flexión. Juega con prismas de diferentes formas y

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¿Qué es la democracia? (infografia)

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3.er y 4.° grado | Educación Física Presentación Tomamos acuerdos en familia para cuidar nuestra salud ¡Hola! Bienvenida/o a esta primera experiencia de aprendizaje. Iniciamos esta experiencia observando la siguiente imagen: DIRECCIÓN DE EDUCACIÓN FÍSICA Y DEPORTE 3.er y 4.° grado | Primaria Educación Física Presentación Luego de observar la imagen, responde las siguientes preguntas: • ¿Quiénes participan en la limpieza del hogar? • ¿Cómo se han organizado? • En tu hogar, ¿apoyas con las actividades? • ¿Qué otras actividades realizas en tu casa? Durante esta pandemia, muchas familias se han organizado para apoyar en las distintas actividades de la casa y superar diversos problemas. Esto ha permitido fortalecer las relaciones entre las y los integrantess de la familia respetando las decisiones y los acuerdos asumidos con responsabilidad para el cuidado de la salud. Es necesario mantener la armonía en el hogar y continuar con una buena organización. A lo largo del desarrollo de esta experiencia de aprendizaje, aprenderás a organizarte en familia y a tomar acuerdos para adaptar o modificar los juegos, e identificar tu frecuencia cardiaca para regular tu esfuerzo durante la práctica, contribuyendo así al bienestar de tu salud. Para ello, te planteamos el siguiente reto: ¿cómo se pueden adaptar o modificar juegos para que se ajusten a las posibilidades de todas y todos los integrantes de la familia, de tal manera que ayude a mejorar la salud de todas y todos? Al finalizar la experiencia de aprendizaje, habrás elaborado un cronograma donde organices juegos que permitan la participación de toda la familia y ejecutarlo. No olvides que las evidencias de las actividades serán las fotos, dibujos o los videos que muestres al finalizar cada una. Para elaborar el cronograma, considera lo siguiente: • Adaptas o modificas los juegos para la participación de toda tu familia. • Organizas diversos juegos para la práctica saludable de todas y todos los integrantes de tu familia. • Realizas mediciones de las frecuencias cardiaca y respiratoria al realizar los juegos. • Consideras ejercicios de activación y relajación antes y después de desarrollar los juegos. 2 3.er y 4.° grado | Primaria Educación Física Presentación Para lograr el reto que hemos planteado, durante las siguientes tres semanas desarrollarán una serie de actividades que les señalamos a continuación: • Actividad 1: Reconocemos nuestra frecuencia cardiaca y respiratoria al jugar en familia • Actividad 2: Identificamos los juegos que se practican en mi comunidad • Actividad 3: Adaptamos o modificamos los juegos • Actividad 4: Organizamos los juegos para la semana • Actividad 5: Jugamos y nos divertimos en familia • Actividad 6: Examinamos nuestros aprendizajes Estas actividades las puedes organizar de acuerdo al tiempo disponible que tengas en la semana. Asimismo, distribuye las actividades en tres semanas; es decir, realiza dos actividades por semana. Te mostramos un ejemplo de cómo puedes organizarte: Plan Semanal Semana 1 Día Hora Actividad Lunes 8:30 a. m. - 9:15 a. m. Actividad 1: Reconocemos nuestra frecuencia cardiaca y respiratoria al jugar en familia Jueves 8:30 a. m. - 9:15 a. m. Actividad 2: Identificamos los juegos que se practican en mi comunidad Semana 2 Día Hora Actividad Lunes 8:30 a. m. - 9:15 a. m. Actividad 3: Adaptamos o modificamos los juegos Jueves 8:30 a. m. - 9:15 a. m. Actividad 4: Organizamos los juegos para la semana Semana 3 Día Hora Actividad Lunes 8:30 a. m. - 9:15 a. m. Actividad 5: Jugamos y nos divertimos en familia Jueves 8:30 a. m. - 9:15 a. m. Actividad 6: Examinamos nuestros aprendizajes 3 3.er y 4.° grado | Primaria Educación Física Presentación Recuerda Para la realización de todas las actividades… • Considera siempre y prioritariamente tu seguridad. Los espacios donde desarrolles la actividad física deben estar libres de cualquier objeto que te pueda dañar, y los materiales a utilizar no deben afectar tu salud. • Busca el espacio y el tiempo adecuados para realizar la actividad. • Ten en cuenta que cualquier actividad física debe realizarse antes de ingerir alimentos o mínimo dos horas después de consumirlos. • Si presentas problemas de salud, no desarrolles la actividad física hasta que te encuentres en buen estado. • Siempre empieza la actividad física con una activación corporal (calentamiento); por ejemplo, movimientos articulares, pequeños saltos o trotes sobre el mismo sitio y estiramientos en general. Además, siempre realiza la recuperación al concluir tu rutina o práctica de actividad física. • Ten una botella de agua para que puedas hidratarte durante la actividad. • Realiza tu aseo personal al concluir cada práctica. El contenido del presente documento tiene fines exclusivamente pedagógicos y forma parte de la estrategia de educación a distancia gratuita que imparte el Ministerio de Educación. 4

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Public Domain

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Разработен пример за идентифициране на проучване с извадка

Разработен пример за идентифициране на проучване с извадка

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Нека разгледаме някои статистически проучвания и да видим дали можем да разберем какъв вид са. Първото: "Roy's Toys получили пратка от 100 000 гумени патета от фабриката. Фабриката не можела да обещае, че всички гумени патета са в перфектна форма, но обещали, че процентът на дефектни играчки няма да надвиши 5%." Нека подчертая това. "Те обещали, че процентът на дефектни играчки няма да надвиши 5%." "Рой искал да направи изчисление на процента дефектни играчки и, след като не можел да провери всички 100 000 патета, взел случайна извадка от 10 патета. Открил, че 10% от тях били дефектни." Какво става тук? Рой получава доставка. В доставката има 100 000 патета. Той иска да открие какъв процент от тях са дефектни. Не може да провери всички 100 000 патета, не е практично, затова взима извадка от 10 от тях. Едно, две, три, четири, пет, шест, седем, осем, девет, 10. И открива, че едно от тези 10, е дефектно, 10% от 10. Първо, това очевидно е проучване с извадка. Това е проучване с извадка. Откъде знаем това? Той взима извадка от по-широка генерална съвкупност, за да изчисли един параметър и параметърът е процентът от тези 100 000 патета, които са дефектни. Следващият въпрос е: "Какъв вид заключение може да направи той?" Рой, след като той е получил доставката и е направил извадка, и е открил, че 10% от тази извадка били дефектни, може би ще си каже: "Тази доставка на играчки от фабриката, те нарушиха това обещание, че процентът на дефектни играчки няма да надвиши 5%, понеже направих извадка от 10 играчки и 10% от тези 10 играчки бяха дефектни." Но това не е логично заключение, понеже това е малка извадка. Това е малка извадка. Помисли. Можел е да направи извадка от пет патета и, ако се случеше така, че да получи едно от дефектните, би си казал: "Може би 20% са дефектни." Той трябва да направи по-голяма извадка и, отново, на каквото и да правиш извадка, винаги съществува вероятност, че изчислението ти няма да е близо или определено няма да е същото като параметъра за генералната съвкупност. Но, колкото по-голяма е извадката ти, толкова по-висока е вероятността, че изчислението ти ще е близо до реалния параметър за генералната съвкупност, като 10 от това е твърде малко. В бъдещи видеа ще говорим за това как можеш да изчислиш вероятността или как можеш да разбереш дали извадката ти е била достатъчна. Но сега, за това, което Рой е направил, не мисля, че 10 патета са достатъчни. Ако беше направил извадка от, може би, 100 патета или повече от това, и беше открил, че 10% от тях са дефектни, това изглежда по-малко вероятно да се случи просто случайно. Нека направим още няколко от тези и, всъщност, ще ги направя в следващите видеа.

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Khan Academy

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المفردات والتراكيب

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ما معنى "حطّت" في جملة: "حَطَّتِ الطّائِرَةُ لِبِضْعِ ساعاتٍ"؟ - هبطت - وضعت - طارت - أقلعت ما معنى "البهو" في جملة: "فَأَسْرَعْتُ مُتَّجِهًا نَحْوَ البَهْوِ الواسِعِ، ثُمَّ خَرَجْتُ..."؟ - مكان مخصّص للنّوم - مكان مخصّص للأكل - مكان مخصّص للاستقبال ما العلاقة بين الكلمتيْن "أعرق" وأعظم" في الجملة الآتية: "لَفَتَني غِنى تِلْكَ المَدينَةِ بِالمَعالِمِ السّياحيَّةِ، فَفيها أَعْرَقُ المَطاعِمِ...وأَعظَمُ الفَنادِقِ..."؟ - علاقة ترادف - علاقة تضادّ ما المقصود بكلمة "استئناف" في الجملة الآتية: "أَنْ يَحينَ مَوعِدُ إِقْلاعِ الطّائِرَةِ وَاسْتِئْنافِ الرِّحْلَة."؟ - إلغاء الرّحلة نهائيًّا - مواصلة الرّحلة - إعادة النّظر بالرّحلة

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Kamkalima

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Intermediate Circulatory System Quiz

Intermediate Circulatory System Quiz

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النوم سلطان | النوم | صحة

في الفيديو ده هتعرف إيه هو النوم وإيه مراحله وأنواعه وفوائد النوم الكافي وأضرار قلة النوم. اتفرج علي الفيديو و اعرف ايه هو التفسير العلمي للنوم و ايه هي فوائد النوم الكافي و ايه هي اضراره.

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Lateral Inhibition

Which is in control, your eye or your brain?

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.field-slideshow-caption { margin-top:10px; margin-left:5px; } .item-list { margin-top:25px; } .item-list ul li{ margin:0 10px 10px 0; opacity: 0.6; filter: alpha(opacity=60); /* For IE8 and earlier */ } .item-list ul .activeSlide{ opacity: 1; filter: alpha(opacity=100); /* For IE8 and earlier */ } Lateral Inhibition Which is in control, your eye or your brain? Do receptors in our eyes act independently, or do they influence each other? Look through some simple paper tubes and explore how your eyes work. Subjects: Keywords: Biology Neuroscience Perception Light, Color & Seeing Physics Light eye paper Tools and Materials Two sheets of 8 12/ x 11-inch (or A4) white paper Transparent tape A well-lit white screen, wall, or sheet of paper Scissors Assembly Take a full sheet of paper and roll it lengthwise into a tube that is about 1/2 inch (13 millimeters) in diameter. (If you are using 8 1/2 x 11-inch paper, the tube length will be 11 inches; if you are using A4 paper, it will be about 30 centimeters.) Use tape to keep the tube from unrolling. Take the other sheet of paper and cut a lengthwise strip that’s about 2 1/2 inches (6.4 cm) wide (if you are using 8 1/2 x 11-inch paper, the tube length will be 11 inches; if you are using A4 paper, it will measure about 30 cm). Roll this strip lengthwise into a tube that’s also about 1/2 inch (13 mm) in diameter and tape it as well. To Do and Notice With both eyes open, look at the white screen, wall, or paper through the tube you made from a full sheet of paper (the wall of this tube will be thicker than the other tube). Notice that the spot of light you see through the tube appears brighter than the wall of the tube. Now do the same thing using the tube you made from the narrow strip of paper. Notice that the spot you see through the tube appears darker than the wall of the tube. What’s Going On? When light hits your eyes, receptors in your eyes send a signal to your brain. Receptors that receive light also send signals to neighboring receptors that tell them to turn down, or inhibit, their sensitivity to light. When you look at the white wall without a tube, you see a uniform field of brightness because all the receptors are equally inhibited. When you look through the tube that you made from a full sheet of paper, the spot of light is surrounded by the dark ring of the tube. The spot appears brighter because the receptors in the center of your retina are not inhibited by signals from the surrounding dark ring. In contrast, light shines through the walls of the tube that you made from the thin strip of paper. When you look through this thin-walled tube, the spot appears darker because light comes through the wall of the tube, causing the receptors at the center of your retina to be inhibited. This is known as lateral inhibition .

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Exploratorium Teacher Institute

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Translations

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TI-AIE: Conjecturing and generalising in mathematics: introducing algebra

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निरपेक्ष मान उदाहरण

5, -10 और 12 का निरपेक्ष मान ज्ञात करना सीखें।

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Primeros auxilios : Quemadura leve

En este vídeo te enseñamos cómo actuar en caso de quemadura leve. Este vídeo ha sido traducido por Elena Nicolau y doblado por Claudia Olvera. Si, como ellas, tú también quieres participar en la creación de nuestros vídeos, ¡únete a nuestra comunidad de voluntarios aquí!

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Este vídeo ha sido realizado en colaboración con: Primeros auxilios. Quemadura leve En este vídeo te enseñamos qué gestos debes realizar en caso de quemadura leve. Una quemadura es leve cuando su superficie es inferior a la mitad de la palma de la mano de la víctima. Pasos a seguir: 1- Eliminar la fuente de la quemadura Si es posible, elimina el agente responsable de la quemadura. 2 - Mojar la zona afectada Aplica agua fría inmediatamente - nunca congelada -sobre la quemadura, hasta que desaparezca el dolor. Retira la ropa en contacto con la quemadura, salvo si se pega a la piel. Si tienes dudas sobre la gravedad de la quemadura, llama a un médico o al servicio de emergencias para pedir consejo. 3 - Apósito estéril Si no es posible, haz un vendaje con compresas estériles. 4 - Vigilancia Vigila la evolución: si la quemadura se pone roja, caliente o duele, consulta a un médico. No explotes nunca una ampolla ya que, una vez abierta, se convierte en la puerta de entrada a numerosos microbios que causarían infección. 5 - ¿Vacuna contra el tétanos? Aségurate de que la víctima tiene al día la vacuna contra el tétanos. En caso de duda, consulta con su médico.

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Sikana Education

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બેચરાજી-મોઢેરા અને જોટાણા

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Grade 6 Mathematics Module 2, Topic D, Lesson 18: Student Version

Examples 1, 3; Exercise 1

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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 6•2 Lesson 18: Least Common Multiple and Greatest Common Factor Classwork Opening The greatest common factor of two whole numbers (not both zero) is the greatest whole number that is a factor of each number. The greatest common factor of two whole numbers 𝑎 and 𝑏 is denoted by GCF (𝑎, 𝑏). The least common multiple of two whole numbers is the smallest whole number greater than zero that is a multiple of each number. The least common multiple of two whole numbers 𝑎 and 𝑏 is denoted by LCM (𝑎, 𝑏). Example 1: Greatest Common Factor Find the greatest common factor of 12 and 18.  Listing these factor pairs in order helps ensure that no common factors are missed. Start with 1 multiplied by the number.  Circle all factors that appear on both lists.  Place a triangle around the greatest of these common factors. GCF (12, 18) 12 18 Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.85 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 6•2 Example 2: Least Common Multiple Find the least common multiple of 12 and 18. LCM (12, 18) Write the first 10 multiples of 12. Write the first 10 multiples of 18. Circle the multiples that appear on both lists. Put a rectangle around the least of these common multiples. Exercises Station 1: Factors and GCF Choose one of these problems that has not yet been solved. Solve it together on your student page. Then, use your marker to copy your work neatly on the chart paper. Use your marker to cross out your choice so that the next group solves a different problem. GCF (30, 50) GCF (30, 45) GCF (45, 60) GCF (42, 70) GCF (96, 144) Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.86 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 6•2 Next, choose one of these problems that has not yet been solved: a. There are 18 girls and 24 boys who want to participate in a Trivia Challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter? Find how many boys and girls each team would have. b. Ski Club members are preparing identical welcome kits for new skiers. The Ski Club has 60 hand-warmer packets and 48 foot-warmer packets. Find the greatest number of identical kits they can prepare using all of the hand-warmer and foot-warmer packets. How many hand-warmer packets and foot-warmer packets would each welcome kit have? c. There are 435 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress if we want the largest groups possible? How many representatives and senators would be in each group? d. Is the GCF of a pair of numbers ever equal to one of the numbers? Explain with an example. e. Is the GCF of a pair of numbers ever greater than both numbers? Explain with an example. Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.87 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 6•2 Station 2: Multiples and LCM Choose one of these problems that has not yet been solved. Solve it together on your student page. Then, use your marker to copy your work neatly on the chart paper. Use your marker to cross out your choice so that the next group solves a different problem. LCM (9, 12) LCM (8, 18) LCM (4, 30) LCM (12, 30) LCM (20, 50) Next, choose one of these problems that has not yet been solved. Solve it together on your student page. Then, use your marker to copy your work neatly on this chart paper and to cross out your choice so that the next group solves a different problem. a. Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic with none left over, what is the least amount of each we need to buy? How many packages of each item would we have to buy? b. Starting at 6:00 a.m., a bus stops at my street corner every 15 minutes. Also starting at 6:00 a.m., a taxi cab comes by every 12 minutes. What is the next time both a bus and a taxi are at the corner at the same time? c. Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has 24 teeth, and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again? Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.88 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 18 NYS COMMON CORE MATHEMATICS CURRICULUM d. Is the LCM of a pair of numbers ever equal to one of the numbers? Explain with an example. e. Is the LCM of a pair of numbers ever less than both numbers? Explain with an example. 6•2 Station 3: Using Prime Factors to Determine GCF Choose one of these problems that has not yet been solved. Solve it together on your student page. Then, use your marker to copy your work neatly on the chart paper and to cross out your choice so that the next group solves a different problem. GCF (30, 50) GCF (30, 45) GCF (45, 60) GCF (42, 70) GCF (96, 144) Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.89 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 18 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Next, choose one of these problems that has not yet been solved: a. Would you rather find all the factors of a number or find all the prime factors of a number? Why? b. Find the GCF of your original pair of numbers. c. Is the product of your LCM and GCF less than, greater than, or equal to the product of your numbers? d. Glenn’s favorite number is very special because it reminds him of the day his daughter, Sarah, was born. The factors of this number do not repeat, and all the prime numbers are less than 12. What is Glenn’s number? When was Sarah born? Station 4: Applying Factors to the Distributive Property Choose one of these problems that has not yet been solved. Solve it together on your student page. Then, use your marker to copy your work neatly on the chart paper and to cross out your choice so that the next group solves a different problem. Find the GCF from the two numbers, and rewrite the sum using the distributive property. 1. 12 + 18 = 2. 42 + 14 = 3. 36 + 27 = 4. 16 + 72 = 5. 44 + 33 = Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.90 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 6•2 Next, add another example to one of these two statements applying factors to the distributive property. Choose any numbers for 𝑛, 𝑎, and 𝑏. 𝑛(𝑎) + 𝑛(𝑏) = 𝑛(𝑎 + 𝑏) 𝑛(𝑎) − 𝑛(𝑏) = 𝑛(𝑎 − 𝑏) Problem Set Complete the remaining stations from class. Lesson 18: Least Common Multiple and Greatest Common Factor This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M2-TE-1.3.0-08.2015 S.91 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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Engage NY

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বিয়োগের কথার সমস্যা: বাস্কেটবল

ভিডিওতে "তুলনামূলক কম" এর সাথে সম্পর্কিত কথার সমস্যার সমাধান দেখানো হয়েছে।

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Los estados del agua

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NCLEX-RN questions on chronic bronchitis 2

Questions related to chronic bronchitis

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Understanding place value

Sal discusses how a digit in one place represents ten times what it represents in the place to its right.

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The 4 in the number 5,634 is blank times blank than the 4 in the number 12,749. So let's think about what they're saying. So the 4 in the number 5,634, that's literally in the ones place. It literally just represents 4. Now, the 4 in the number 12,749, that 4 is in the tens place. It represents 40. So this 4, it's a 10 times smaller value than this 4. Or this 4, I should say. This 4 right over here represents 4, while this represents 40. So it is 10 times smaller than the 4 in 12,749. 4 by itself is 10 times smaller than 40. Make sure I got the right answer. Let's do another one. In the number 3,779,264, how many times less is the value of the second 7 than the value of the first 7? How many times less is the value of the second 7 than the value of the first 7? So the second 7 right over here, that's in the ten thousands place. It literally represents 70,000, 7 ten thousands, or 70,000, while this represents 700 thousands, or 700,000. So the second 7 is 1/10 the value of the first 7. Or another way of thinking, it's 10 times less. This is 70,000, and this is 700,000. So the value of the second 7 is 10 times less than the value of the first 7. Let's do one more. This is fun. Fill in the following blanks to complete the relationships between 25,430 and 2,543. All right, so 25,430 is 10 times larger than 2,543. Literally, you take this, you multiply it by 10, you're going to get 25,430. The digits in 25,430 are one place to the blank of the digits in the number 2,543. Well, let's think about it. Here you have a 2 in the thousands place. Here you have a 2 in the ten thousands place. Here you have a 5 in the hundreds place. Here you have a 5 in the thousands place. And we could keep going. But what we see is a corresponding digit. In 25,430, they're one place to the left of the digits right over here. Now, finally, we're going to take 25,430 and divide it by 2,543. Well, we already know that the first number is 10 times larger than this number right over here. So literally, if you divide the smaller number into the larger one, you're going to get 10. This right over here is 10 times larger than this. So that was the first part of the question, and we are done.

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Khan Academy

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Graham's Law

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Understanding Instructions With AND-OR - WorkSheet

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Understanding Instructions With AND-OR Work Sheet:​ ​03-ALG-18-WS 1. Into which basket will the following go – A, B, C or D? Can you write the conditionals? Orange – Watermelon – Spinach – Corn – [veggies] Ladies finger – Chili powder – Wheat – Cinnamon powder – [spices] Banana – Turmeric powder – Rice – Cabbage – [fruits] [grains] 2. Here are the marks of 4 children. Can you find out their grade by following the rules below? Keerti Pranav Anubhav Ravi Suman Bharat Amita Sara Ganesh Maths marks 80 78 88 47 62 20 91 84 70 Grade?? Rules: a) IF (marks > 85) Grade is A b) IF (marks < 50) Grade is F c) IF (marks are from 50 to 65) Grade is D d) IF (marks are from 66 to 75) Grade is C e) IF (marks are from 76 to 85) Grade is B Name: Class: 1 Div: Roll. No: Understanding Instructions With AND-OR Work Sheet:​ ​03-ALG-18-WS 3. There are many chits in a box. Each chit has a number written on it. Teacher takes chits from the box one by one. Depending on the number written on the chit, one of the teams gets points! IF ​number is even and less than 100 Team A gets 10 points ELSE IF ​number is odd and less than 100 Team B gets 15 points ELSE IF ​number is odd and more than 100 Team A gets 15 points ELSE Team B gets 10 points Teacher pulls the following numbers: write down the points and find out which team’s total is more and who wins!! Number 10 433 560 25 108 77 265 1000 Team A Team B Name: Class: 2 Div: Roll. No: Understanding Instructions With AND-OR Work Sheet:​ ​03-ALG-18-WS 4. Look at the conditionals below and write the output for the given input. IF (number is even) Output number X 100 ELSE IF (number is odd) AND (number < 25) Output number + 100 ELSE Output number X 2 Input 8 13 42 11 37 21 50 49 Output Name: Class: 3 Div: Roll. No:

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ACM India

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Comentários

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Comentários Tipo: lectura Formato: self-paced Duración: 15min Objetivos de Aprendizajem Aprender o que são os comentários e sua utilidade. Comentários Muitas vezes, não importa quão descritivo você escreva seu código, é necessário oferecer mais informação para que outras pessoas possam entender facilmente como funciona o seu programa. Para adicionar essa informação sem afetar o fluxo do seu código, existem os comentários. Eles são assim: // Isto é um comentário de uma linha /* Isto é um comentário de múltiplas linhas */ O computador ignora os comentários completamente. Os comentários no JavaScript começam com //. Tudo o que segue às barras comuns (na mesma linha) é ignorado pelo interpretador do JavaScript. Os comentários de múltiplas linhas começam com /* e acabam com */. Tudo o que fica entre isso é ignorado pelo programa. Dessa forma, os comentários não têm efeito algum em como se executa o programa. Só estão aí para prover contexto. É uma boa prática incluir comentários no código para melhorar sua legibilidade. Comentários como sugestões ou instruções Muitos dos exercícios e questionários neste curso vão incluir os comentários para oferecer sugestões ou instruções. Por exemplo, é normal ver algo tipo: const firstName = // seu código aqui console.log(/* seu código aqui */); A ideia é que você apague o comentário e utilize esse espaço para escrever seu código. Não se preocupe em apagar os comentários. Aliás, não apague outras partes do programa. Se você faz isso, é muito provável que não funcione muito bem. Agora sim, continue com os exercícios e questionários desta lição. Boa sorte!

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Laboratoria

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الدرس الثالث شرح مستودع PECL

"هنالك ثلاث انواع الموديول الخاص بلغة البي اتش بي وتم ذكر موقع مستودع PECL الذي يوجد فيه هذا النوع من الموديول وايضا تم التطرق لطريقة استخدام هذا الموقع والوصول للموديول الذي تريده "

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‫الدرس الثالث شرح مستودع ‪PECL‬‬

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Public Domain

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Sistemas cuadráticos: ambas variables están al cuadrado

Resolvemos el sistema y=0.5x y 2x^2-y^2=7.

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c_0018cad41a6e

5. Evaluación final (218-221)

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¿Qué aprendí? Evaluación final A continuación, te proponemos preguntas que tendrás que desarrollar considerando lo que has aprendido en esta unidad. Sectores y segmentos circulares 1. Determina qué parte del círculo son los siguientes sectores circulares. (1 punto cada uno) a. b. C 60° c. 270° E G 120° 2. En la siguiente circunferencia se destacan segmentos y sectores circulares. (1 punto cada uno) A a. ¿Cuál es el área del sector circular pintado? 8 cm b. ¿Cuál es el perímetro del sector circular pintado? c. ¿Cuál es el área del segmento circular marcado? O 2 cm B d. ¿Cuál es el perímetro del segmento circular marcado? Área y volumen del cono 3. Los envases de cabritas que se muestran en la imagen están hechos de cartón y tiene igual forma. a. ¿Qué forma tienen los envases de las cabritas? (1 punto) b. ¿Cuánta capacidad tiene cada envase de cabritas, suponiendo que el grosor del cartón es despreciable? (2 puntos) c. ¿Cuánto cartón se usó en cada envase? (2 puntos) 8 cm 15 cm d. Si los envases tuvieran tapa, ¿cambia su capacidad? Justifica tu respuesta. (1 punto) e. Si los envases tuvieran tapa, ¿cambia su superficie? Justifica tu respuesta. (1 punto) 4. Resuelve los siguientes problemas. (3 puntos cada uno) a. Andrés va a una tienda a comprar una copa con forma cónica. El vendedor le dice que tiene una de 4 cm de diámetro y 15 cm de altura y otra de 6 cm de diámetro y 7 cm de altura. Si Andrés escoge la que tiene mayor capacidad, ¿cuál elige? b. Andrea debe construir 200 conos de cartulina para usarlos como envases de papas fritas que venderán en la fiesta de la escuela. Si cada envase debe tener 5 cm de radio, 12 cm de altura y el precio de una cartulina de 70 cm de ancho y 100 cm de largo es de $ 150, ¿cuánto gastará? 218 Unidad 3 • Geometría Lib_Mat_1M_2019.indb 218 20-08-19 14:41 Unidad 3 Homotecia y teorema de Tales 5. Con la información que aparece en la imagen, responde. (3 puntos) L3 a L2 L1 b c C D a. Nombra tres proporciones entre las medidas de segmentos definidos por las rectas paralelas sobre las transversales. d A e B F L1 // L2 // L3 6. En cada caso, calcula el valor de x. E (3 puntos cada uno) a. b. L1 2 cm x 3,5 cm y A L2 L3 20 cm x 10 m B 14 cm C 4m L1 // L2 // L3 BC // DE 5m D E 7. Mide y determina el valor de razón de homotecia en cada caso. (1 punto cada uno) a. b. c. B A A' B' C' A C C D D' E' C' D B' F E' A' E B O A E C' B' D' C B D A' 8. Determina si las siguientes afirmaciones son verdaderas (V) o falsas (F). Justifica las falsas. (1 punto cada uno) a. 1 La imagen de una figura al aplicarle una homotecia es siempre congruente con la figura original. b. 1 Si el valor de la razón en una homotecia es menor que 1 y mayor que 0, siempre es una reducción de la figura original. c. 1 Vectorialmente, una homotecia es una transformación que pondera cada uno de los vectores por una razón dada. Unidad 3 • Geometría Mat_1M_U3_2019.indd 219 219 04-09-19 13:18 ¿Qué aprendí? Evaluación final Semejanza 2 cm 7 cm 9. El siguiente plano tiene una escala de 1 : 100. Responde las siguientes preguntas. a. En el mapa, ¿cuáles son las medidas del comedor? (1 punto) 3 cm 5 cm 4 cm b. En la realidad, ¿cuáles serían las medidas del comedor? (1 punto) c. ¿Cuál es el área real del comedor en metros cuadrados? (2 puntos) 4 cm d. Se quiere poner cerámica en la cocina, cuyo metro cuadrado cuesta $ 1 500, ¿cuánto dinero se necesita, aproximadamente? (2 puntos) 3 cm 5 cm 1 cm 10. Observa la imagen y responde. a. ¿Por qué el triángulo ABC es semejante al ACD? ¿Y al triángulo CBD? (1 punto) C b. ¿Qué proporciones se cumplen entre las medidas de los lados de los triángulos ABC y ACD? (2 puntos) A c. Usa lo anterior para demostrar que b2 = q • c. (3 puntos) a b h q D c p B Verifica tus respuestas en el solucionario y con ayuda de tu profesor o profesora completa la tabla. Ítems Conocimientos y habilidades 1y2 Calcular el área y el perímetro de sectores y segmentos circulares. 3y4 Calcular el área y el volumen de conos. 5, 6, 7 y 8 Comprender el concepto de homotecia. Desarrollar y aplicar el teorema de Tales. 9 y 10 Tu puntaje Tu desempeño Logrado: 28 puntos o más. Medianamente logrado: 23 a 27 puntos. Aplicar y reconocer propiedades de semejanza en modelos a escala, triángulos y los teoremas de Euclides. Por lograr: 22 puntos o menos. Total 220 Unidad 3 • Geometría Lib_Mat_1M_2019.indb 220 20-08-19 14:41 Unidad 3 Actividad de cierre Completa el esquema con tus conocimientos antes de empezar la unidad y lo que has aprendido en ella. Tema 1 ¿Qué sabías antes de comenzar? Sectores y segmentos circulares Área y perímetro de una circunferencia. ¿Qué querías aprender al comienzo? ¿Qué aprendí al finalizar? Tema 2 Área y volumen del cono Calcular el área y el volumen de un cono. Tema 3 Homotecia y teorema de Tales Tema 4 Semejanza Reflexiona sobre tu trabajo • Las estrategias que planteaste, ya sea de forma individual o con tus compañeros al inicio de cada tema, ¿de que forma te ayudaron a desarrollar los aprendizajes para esta unidad? Explica. • ¿De qué manera crees que lo aprendido en esta unidad te ayuda a resolver desafíos matemáticos relacionados con la resolución de problemas reales? Explica. • ¿Cumpliste tu meta propuesta al iniciar la unidad? Explica. Unidad 3 • Geometría Lib_Mat_1M_2019.indb 221 221 20-08-19 14:41

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Public Domain

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PIB real direcionando preços

Pensando em como a alta utilização poderia direcionar o preço como outra justificativa para uma curva de oferta agregada de curto prazo de inclinação ascendente

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Muromachi to Momoyama period Negoro ware ewer

Negoro ware ewer, Negoro workshop, Muromachi period (1392-1573) to Momoyama period (1573-1615) second half of 16th century, lacquered wood, Wakayama prefecture, Japan (Portland Art Museum)

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- [Voiceover] I'm standing here in the galleries, the Japanese galleries at the Portland Art Museum. And we're looking at a recent acquisition. It is a ewer which is a particular kind of pitcher that comes to us from late 16th century Japan. - [Voiceover] The first thing that comes to mind is its material because when I first walked up to this I imagined in some way, probably because of the sides that it was metal. And when I came close to it I realized that it wasn't. It's wood, is that right? - [Voiceover] Yes it's wood. And what's interesting is that the body, and we often talk about pots in this anthropomorphic way. The body has a very slight, I mean it's almost a cylinder. But it tapers a little bit at the foot. So the body is sort of in the shape of a bucket. This isn't carved from a single block of wood but it's rather a strip of wood that was steamed and wrapped. Then we see these things that these ridges on it. Those are actually strips of bamboo that are sort of like little reinforcing girders that help hold that steamed wood in that wrapped cylindrical shape. - [Voiceover] So it's really a process of construction that's made in a way that is not dissimilar to the way that we might treat metal. - [Voiceover] If you think of a sheet of metal hammered and then bent, that's like that. And what is so interesting, if we think okay what are the normal ways that you handle wood? Well we think of carving wood. - [Voiceover] Yes exactly. - [Voiceover] That idea of making a vessel by wrapping a slab of wood into a cylinder and then putting a bottom on it, that is a technique in which Japanese wood makers excel. - [Voiceover] There's a kind of delicacy and a kind of I think that I get the sense of the thinness of the wall that seems to me only possible in metal. And I think that's why I jumped there. But I think that really speaks to the extraordinary sort of tradition out of which this is coming. And I see it as incredibly impressive. Can we talk a little bit about the way the wood is treated and the color which I find beautiful. It's got this almost gorgeous almost patina. - [Voiceover] Yes it does have a patina. This ware is an example of Japanese lacquer ware. So the wood turning, the wood bending, the wood shaping happens, and then it goes through a number of stages of being coated with lacquer. And lacquer is found really in much of Southeast Asia and East Asia. But in Japan, Japanese lacquer was so treasured by the Europeans when trade began that, analogous to the way that we use the word China to associate ceramics with China, Europeans used to call works that were lacquered Japaned. - [Voiceover] Oh is that right? - [Voiceover] It was so associated with Japan. And lacquer is the sap of a lac tree. It's a naturally occurring sap. So think of maple syrup. And think of it as something that trees ooze out at a particular season of the year. You have to go and tap it. And it's thick and viscous like maple syrup. Interestingly, it's also toxic. - [Voiceover] Oh really? - [Voiceover] It has the same chemicals in it that poison ivy does. So lacquer workers have to spend a lifetime building up resistance to this. So you have this lacquer and then you can, there's sort of traditional colors to dye it and in Japan, those two traditional colors were black, which you did essentially by mixing lamp black, a kind of soot with it. And the other was what you see here. This fantastic cinnabar red by mixing in cinnabar which is powdered mercury. - [Voiceover] So this was toxic on two levels. - [Voiceover] This is toxic on two levels, yes. - [Voiceover] I suppose one would save drinking water out of this, but it does sort of bring that to mind. - [Voiceover] Well, but by the time it dries, all that toxicity is gone. So what happens is lacquer has to be painted on in many many coats. But what lacquer does, and lacquer is used in East Asia from the fourth century BC onward, lacquer can make a wooden object like a high fired porcelain. It can make it perfectly impervious to leaks. It can hold hot water. It can hold cold water. So it can handle a variety of temperatures. It's perfect for containers like this. - [Voiceover] It's also gorgeous. The surface has almost a kind of translucence that's this kind of milky kind of beautiful. Is that original or is that a result of its age? - [Voiceover] Well both. Because it's many layers of lacquer. And the lacquer layers are very very thin and then they have to dry. And then it's polished. And another layer is put on and it's polished. And the secret of this particular ware, this comes from a monastic workshop in Japan. And it's called Negoro. That's the name of the monestary so we call this Negoro ware. First several layers are black. And then the last layers are red. And if you look at the handle you can see where it is touched the most often. The lacquer has worn a little bit thin. And a little bit of the black is coming through. And that is the secret of Negoro ware. It's seeing that suggestion of black underneath the red. - [Voiceover] It gives incredible dimension. - [Voiceover] It's like looking into this pool of red and then seeing the black underneath. But I think it really gives this depth. - [Voiceover] This is an object that comes from the 16th century, and yet it is so pristine. It is in such incredible condition. I mean it looks as if it was made just a few years ago. And it speaks to I think the resilience as you were saying of the lacquer. But is it also that these were because they were in a monastic enviroment that these were kept sort of out of everyday use? Why would this be in such good condition? Do we have any idea? - [Voiceover] Although Negoro ware is very very highly treasured today, and this particular shape and in this condition is extremely rare. We know of two similar pieces in American collections but that's all that I know of right now. Of this particular shape. This shape belongs to a particular moment in history. But it's not-- It would not have to its original uses or its original makers been a particularly a precious object. So we wouldn't think of it the way that Chinese would think of something like jade. - [Voiceover] So this was not safeguarded as a particularly special-- - [Voiceover] So it wouldn't have been hidden away. And in fact, that's great because look at the wonderful black that we can see in the handle. So it's not something that was brought out at Christmas. You know? It was something that would have been used. But you're quite right that because it was in a monestary and monasteries are likely to have the resources to have a big huge store house with a foot thick or two foot thick clay walls, that it would not be subject to the kind of frequent flyers that would happen to let's say an urban merchant's collection. That's one. And the other thing that's very important. Tea objects were treated with a special reverence. Now that's different than being precious, if you know what I mean. I mean I'm not talking about the preciousness of the material, but they were revered and taken care of very well. So the Japanese would make Paulownia boxes and they would keep it in the Paulownia box which keeps it from expanding and contracting in different weather and that stuff. So they take exceptionally good care of things. - [Voiceover] It is absolutely gorgeous and I have a totally new appreciation for it. Thank you so much. - [Voiceover] I'm glad you like it.

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Khan Academy

CC BY-NC-SA

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Volumes of cylinders

Practice applying the volume formulas for cylinders.

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c_001a5ae305c2

Calcolare il perimetro quando manca uno dei lati

Lindsay calcola il perimetro di una figura quando manca uno dei lati.

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Aplicación de las Raíces Cuadradas

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O modelo logístico de crescimento

A equação diferencial logística dN/dt=rN(1-N/K) descreve a situação em que uma população cresce proporcionalmente ao seu tamanho, mas para quando atinge o tamanho K.

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Finding average speed or rate

Using the formula for finding distance we can determine Usian Bolt's average speed, or rate, when he broke the world record in 2009 in the 100m. Watch.

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SALMAN KHAN: I have some footage here of one of the most exciting moments in sports history. And to make it even more exciting, the commentator is speaking in German. And I'm assuming that this is OK under fair use, because I'm really using it for a math problem. But I want you to watch this video, and then I'll ask you a question about it. [CHEERING] COMMENTATOR: [SPEAKING GERMAN] SALMAN KHAN: So you see, it's exciting in any language that you might watch it. But my question to you is, how fast was Usain Bolt going? What was his average speed when he ran that 100 meters right there? And I encourage you to watch the video as many times as you need to do it. And now I'll give you a little bit of time to think about it, and then we will solve it. So we needed to figure out how fast was Usain Bolt going over the 100 meters. So we're really thinking about, in the case of this problem, average speed or average rate. And you might already be familiar with the notion that distance is equal to rate or speed-- I'll just write rate-- times time. And I could write times like that, but once we start doing algebra, the traditional multiplication symbol can seem very confusing because it looks just like the variable x. So instead, I will write times like this. So distance is equal to rate times time. And hopefully, this makes some intuitive sense for you. If your rate or your speed were 10 meters per second-- just as an example. That's not necessarily how fast he went. But if you went 10 meters per second, and if you were to do that for two seconds, then it should hopefully make intuitive sense that you went 20 meters. You went 10 meters per second for two seconds. And it also works out mathematically. 10 times 2 is equal to 20. And then you have seconds in the denominator and seconds up here in the numerator. I just wrote seconds here with an s. I wrote it out there. But they also cancel out, and you're just left with the units of meters. So you're just left with 20 meters. So hopefully this makes intuitive sense. With that out of the way, let's actually think about the problem at hand. What information do we actually have? So do we have the distance? So what is the distance in the video we just did? And I'll give you a second or two to think about it. Well, this race was the 100 meters. So the distance was 100 meters. Now, what else do we know? Do we know-- well, we're trying to figure out the rate. That's what we're going to figure out. What else do we know out of this equation right over here? Well, do we know the time? Do we know the time? What was the time that it took Usain Bolt to run the 100 meters? And I'll give you another few seconds to think about that. Well luckily, they were timing the whole thing. And they also showed that it's a world record. But this right over here is in seconds. It's how long it took Usain Bolt to run the 100 meters. It was 9.58 seconds. And I'll just write s for seconds. So given this information here, what you need to attempt to do is now give us our rate in terms of meters per second. I want you to think if you could figure out the rate in terms of meters per second. We know the distance, and we know the time. Well, let's substitute these values into this equation right over here. We know the distance is 100 meters. And it's equal to-- we don't know the rate, so I'll just write rate right over here. And let me write it in that same color. It's equal to rate times-- and what's the time? We do know the time. It's 9.58 seconds. And we care about rate. We care about solving for rate. So how can we do that? Well, if you look at this right hand side of the equation, I have 9.58 seconds times rate. If I were able to divide this right hand side by 9.58 seconds, I'll just have rate on the right hand side. And that's what I want to solve for. So you say, well, why don't I just divide the right hand side by 9.58 seconds? Because if I did that, the units cancel out, if we're doing dimensional analysis. Don't worry too much if that word doesn't make sense to you. But the units cancel out, and the 9.58 cancels out. But I can't just divide one side of an equation by a number. When we started off, this is equal to this up here. If I divide the right side by 9.58, in order for the equality to still be true, I need to divide the left side by the same thing. So I can't just divide the right side. I have to divide the left side in order for the equality to still be true. If I said one thing is equal to another thing, and I divide the other thing by something, in order for them to still be equal, I have to divide the first thing by that same amount. So I divide by 9.58 seconds. So on our right hand side-- and this was the whole point-- these two cancel out. And then on the left hand side, I'm left with 100 divided by 9.58. And my units are meters per second, which are the exact units that I want for rate, or for speed. And so let's get the calculator out to divide 100 by 9.58. So I've got 100 meters divided by 9.58 seconds gives me 10 point-- this says we've got about three significant digits here-- so let's say 10.4. So this gives us 10.4. And I'll write it in the rate color. 10.4-- and the units are meters per second-- meters per second is equal to my rate. Now, the next question. So we got this in meters per second. But unfortunately, meters per second, they're not the-- when we drive a car, we don't see the speedometer in meters per second. We see either kilometers per hour or miles per hour. So the next task I have for you is to express this speed, or this rate-- and this is his average speed, or his average rate, over the 100 meters. But to think about this in terms of kilometers per hour. So try to figure out if you can rewrite this in kilometers per hour. Well, let's just take this step by step. So I'm going to write-- so let me just go down here, start over. So I started off with 10.4. And I'll write meters in blue, and seconds in magenta. Now, we want to get to kilometers per hour. Right now we're meters per second. So let's take baby steps. Let's first think about it in terms of kilometers per second. And I'll give you a second to think about what we would do this to turn this into kilometers per second. Well, the intuition here, if I'm going 10.4 meters per second, how many kilometers is 10.4 meters? Well, kilometers is a much larger unit of measurement. It's 1,000 times larger. So 10.4 meters will be a much smaller number of kilometers. And in particular, I'm going to divide by 1,000. Another way to think about it, if you want to focus on the units, we want to get rid of this in meters, and we want a kilometers. So we want a kilometers, and we want to get rid of these meters. So if we had meters in the numerator, we could divide by meters here. They would cancel out. But the intuitive way to think about it is we're going from a smaller unit, meters, to a larger unit, kilometers. So 10.4 meters are going to be a much smaller number of kilometers. But if we look at it this way, how many meters are in 1 kilometer? 1 kilometer is equal to 1,000 meters. This right over here, 1 kilometer over 1,000 meters, this is 1 over 1. We're not changing the fundamental value. We're essentially just multiplying it by one. But when we do this, what do we get? Well, the meters cancel out. We're left with kilometers and seconds. And the numbers, you get 10.4 divided by 1,000. 10.4 divided by 1,000 is going to give you-- so if you divide by 10, you're going to get 1.04. You divide by 100, you get 0.104. You divide by 1,000, you get 0.0104. So that's just 10.4 divided by 1,000. And then our units are kilometers per second. So that's the kilometers, and then I have my seconds right over here. So let me write the equal sign. Now, let's try to convert this to kilometers per hour. And I'll give you a little bit of time to think about that one. Well, hours, there's 3,600 seconds in an hour. So however many kilometers I do in a second, I'm going to do 3,600 times that in an hour. And the units will also work out. If I do this many in a second, so it's going to be times 3,600, there are 3,600 seconds in an hour. And another way to think about it is we want hours in the denominator. We had seconds. So if we multiply by seconds per hour, there are 3,600 seconds per hour, the seconds are going to cancel out, and we're going to be left with hours in the denominator. So seconds cancel out, and we're left with kilometers per hour. But now we have to multiply this number times 3,600. I'll get the calculator out for that. So we have 0.0104 times 3,600 gives us, I'll just say 37.4. So this is equal to 37.4 kilometers per hour. So that's his average speed in kilometers per hour. And now the last thing I want to do, for those of us in America, we'll convert into imperial units, or sometimes called English units, which are ironically not necessarily used in the UK. They tend to be used in America. So let's convert this into miles per hour. And the one thing I will tell you, just in case you don't know, is that 1.61 kilometers is equal to 1 mile. So I'll give you a little bit of time to convert this into miles per hour. Well, as you see from this, a mile is a slightly larger or reasonably larger unit than a kilometer. So if you're going 37.4 kilometers in a certain amount of time, you're going to go slightly smaller amount of miles in a certain amount of time. Or in particular, you're going to divide by 1.61. So let me rewrite it. If I have 37.4 kilometers per hour, we're going to a larger unit. We're going to miles. So we're going to divide by something larger than one. So we have one-- let me write it in blue-- 1 mile is equal to 1.61 kilometers. Or you could say there's one 1.61th mile per kilometer. It also, once again, works out with units. We want to get rid of the kilometers in the numerator. So we would want it in the denominator. We want a mile in the numerator. So that's why we have a mile in the numerator here. So let's once again multiply, or I guess in this case we're dividing by 1.61. And we get-- let's just divide our previous value by 1.61. And we get 23 point-- I'll just round up-- 23.3. This is equal to 23.3. And then we have miles per hour. Which is obviously very fast. He's the fastest human. But it's not maybe as fast as you might have imagined. In a car, 23.3 miles per hour doesn't seem so fast. And especially relative to the animal world, it's not particularly noteworthy. This is actually slightly slower than a charging elephant. Charging elephants have been clocked at 25 miles per hour.

en

Khan Academy

CC BY-NC-SA

c_001af7fb178a

El límite de una función trigonométrica por medio de la identidad pitagórica

En este video encontramos el límite de (1-cosθ)/(2sin²θ) en θ=0 al reescribir la expresión usando la identidad pitagórica.

video

es

c_001b2f6899e9

11.7.1: The Control Volume Analysis_Governing equations

html5

The momentum equation is written as the following The mass conservation is reduced to Figure 11.17 describes the flow of gas from the left to the right. The heat transfer up stream (or down stream) is assumed to be negligible. Hence, the energy equation can be written as the following: \[ \dfrac{d\, Q }{ \dot{m} } = c_p dT + d \dfrac{U^2 }{ 2} = c_p dT_{0} \label{isothermal:eq:CV} \] \[ -A\, dP - \tau_{w}\, dA_{\text{wetted area}} = \dot{m}\, dU \label{isothermal:eq:momentum} \] where \(A\) is the cross section area (it doesn't have to be a perfect circle; a close enough shape is sufficient.). The shear stress is the force per area that acts on the fluid by the tube wall. The \(A_{wetted\;\;area}\) is the area that shear stress acts on. The second law of thermodynamics reads \[ {s_2 - s_1 \over C_p} = \ln {T_2 \over T_1 } - {k -1 \over k} \ln {P_2 \over P_1} \label{isothermal:eq:2law} \] \[ \dot {m} = \text{constant} = \rho\, U\, A \label{isothermal:eq:mass} \] Again it is assumed that the gas is a perfect gas and therefore, equation of state is expressed as the following: \[ P = \rho\, R\, T \label{isothermal:eq:state} \] Contributors and Attributions Dr. Genick Bar-Meir (http://www.potto.org/genick.php). Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.

en

CSU and Merlot

CC BY-NC-SA

c_001b7af5bb15

01. Concepts and Principles

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An Alternative Approach A Gravitational Analogy Relating the Electric Field and the Electric Potential An Alternative Approach The electric field surrounding electric charges and the magnetic field surrounding moving electric charges can both be conceptualized as information embedded in space. In both cases, the information is embedded as vectors, detailing both the magnitude and direction of each field. Moreover, when this information is "read" by other moving electric charges, the result is a force acting on the charge. These forces can be calculated to allow us to determine the subsequent motion of the charge. Just as in mechanics, there is an alternative to this force-based approach to analyzing the behavior of electric charges. In this chapter I will define a new field, the electric potential, which surrounds every electric charge. This field differs from the electric field because it is a scalar field, meaning that this field has only a magnitude at every point in space and no associated direction. Moreover, the information in this field, when read by other electric charges, does not result in a force on the charge but rather determines the electric potential energy the charge possesses at that point in space. Understanding how to calculate this new field, how this field relates to energy, and how this field is related to the electric field will be the focus of this chapter. A Gravitational Analogy Rather than thinking in terms of the gravitional force and Newton's Second Law, an alternative way to examine mechanics scenarios is by using the concept of gravitational potential energy and the conservation of energy. In the force approach, we envision a vector field surrounding the earth, regardless of whether a second mass is nearby to interact with this field. If a mass is present, the mass interacts with this field and feels a gravitational force. This idea is captured in the equation: pic 1 In the energy approach, we can envision a scalar field, the gravitational potential, which is present regardless of whether a second mass is nearby to interact with this field. If a mass is present, the mass interacts with this field and has gravitational potential energy. Near the surface of the earth, the familiar expression for gravitational potential energy: pic 2 can be thought of as the product of the mass of the object and this pre-existing gravitational potential, VG: pic 3 if we define the gravitational potential by: pic 4 Although we didn't use the concept of gravitational potential while studying mechanics, it will prove to be a very useful concept in our study of electrical phenomenon. The general expression for gravitational potential, valid regardless of distance from a massive object, is: pic 5 In summary, just as a mass will interact with the vector gravitational field as a force, a mass will interact with the scalar gravitational potential field as potential energy. The situation is very similar for electrical phenomenon. We can envision a scalar field, the electric potential, which is present regardless of whether a second charge is nearby to interact with this field. If a charge is present, the charge interacts with this field and has electric potential energy. The electric potential, VE, is defined by the relationship: pic 6 where q is the source charge, the electric charge that creates the field, and r is the distance between the source charge and the point of interest. This leads to an expression for the electric potential energy of: pic 7 where q is the charge on the particle of interest, the charge that is interacting with the field, and VE is the net electric potential at the location of the particle of interest (created by all of the other charged particles in the universe). We will typically leave the subscript off the electric potential and electric potential energy unless the possibility of confusion with the gravitational potential and potential energy are present. Relating the Electric Field and the Electric Potential The electric field and the electric potential are not two, independent fields. They are two independent ways of conceptualizing the effect that an electric charge has on the space surrounding it. Just as problems in mechanics can be analyzed using a force-approach or an energy-approach, problems dealing with electrical phenomenon can be analyzed by focusing on the electric field or on the electric potential. Additionally, just as it is sometimes necessary in mechanics to transfer between force and energy representations, it is sometimes necessary to transfer between the electric field and electric potential representations. The relationship between two fields can be understood by examining the expression for work, which relates force to transfer of energy. Utilizing the dot product, the work donw in moving a particle from an initial point, i, to a final point, f, can be written as: pic 8 where (pic 9) is an infinitesimal portion of the path along which the particle moves. You may also recall that the difference in potential energy between initial and final locations is defined as the opposite of the work needed to move the particles between the two points: pic 10 Putting these two ideas together yields: pic 11 We can now use this result to relate the electric potential and the electric field. Substituting in expressions for potential energy and force in terms of the fields that convey them leads to: pic 12 In English, this final result states that the electric potential difference between any two points is defined as the negative of the integral of the electric field along a path connecting the two points. (I'm sure that doesn't seem like particularly clear English, but this idea will become more tangible once you get to work on some of the fun activities in this chapter.) The bottom line is that the electric potential can be determined by intergrating the electric field, and, conversely, the electric field can be determined by differentiating the electric potential. Paul D’Alessandris (http://www.monroecc.edu/etsdbs/staffdir.nsf/859a9527fb0e5236852569740064462a/8a9d551ad9d5ede98525663b0051abe3?OpenDocument) (Monroe Community College (http://www.monroecc.edu/))

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CSU and Merlot

CC BY-NC-SA

c_001b7c737a3a

55. تضمين الملفات بدالة require

video

ar

c_001bff5d9b68

Chapter 1: Getting started with TypeScript

Chapter 1 of the book on TypeScript.

document

Chapter 1: Getting started with TypeScript Version Release Date 2.8.3 2018-04-20 2.8 2018-03-28 2.8 RC 2018-03-16 2.7.2 2018-02-16 2.7.1 2018-02-01 2.7 beta 2018-01-18 2.6.1 2017-11-01 2.5.2 2017-09-01 2.4.1 2017-06-28 2.3.2 2017-04-28 2.3.1 2017-04-25 2.3.0 beta 2017-04-04 2.2.2 2017-03-13 2.2 2017-02-17 2.1.6 2017-02-07 2.2 beta 2017-02-02 2.1.5 2017-01-05 2.1.4 2016-12-05 2.0.8 2016-11-08 2.0.7 2016-11-03 2.0.6 2016-10-23 2.0.5 2016-09-22 2.0 Beta 2016-07-08 1.8.10 2016-04-09 1.8.9 2016-03-16 1.8.5 2016-03-02 1.8.2 2016-02-17 1.7.5 2015-12-14 1.7 2015-11-20 1.6 2015-09-11 1.5.4 2015-07-15 1.5 2015-07-15 1.4 2015-01-13 1.3 2014-10-28 1.1.0.1 2014-09-23 Section 1.1: Installation and setup Background TypeScript is a typed superset of JavaScript that compiles directly to JavaScript code. TypeScript files commonly use the .ts extension. Many IDEs support TypeScript without any other setup required, but TypeScript can also be compiled with the TypeScript Node.JS package from the command line. GoalKicker.com – TypeScript Notes for Professionals 2 IDEs Visual Studio Visual Studio 2015 includes TypeScript. Visual Studio 2013 Update 2 or later includes TypeScript, or you can download TypeScript for earlier versions. Visual Studio Code Visual Studio Code (vscode) provides contextual autocomplete as well as refactoring and debugging tools for TypeScript. vscode is itself implemented in TypeScript. Available for Mac OS X, Windows and Linux. WebStorm WebStorm 2016.2 comes with TypeScript and a built-in compiler. [WebStorm is not free] IntelliJ IDEA IntelliJ IDEA 2016.2 has support for TypeScript and a compiler via a plugin maintained by the JetBrains team. [IntelliJ is not free] Atom & atom-typescript Atom supports TypeScript with the atom-typescript package. Sublime Text Sublime Text supports TypeScript with the TypeScript package. Installing the command line interface Install Node.js Install the npm package globally You can install TypeScript globally to have access to it from any directory. npm install -g typescript or Install the npm package locally You can install TypeScript locally and save to package.json to restrict to a directory. npm install typescript --save-dev Installation channels You can install from: Stable channel: npm install typescript Beta channel: npm install typescript@beta Dev channel: npm install typescript@next Compiling TypeScript code The tsc compilation command comes with typescript, which can be used to compile code. tsc my-code.ts This creates a my-code.js file. Compile using tsconfig.json GoalKicker.com – TypeScript Notes for Professionals 3 You can also provide compilation options that travel with your code via a tsconfig.json file. To start a new TypeScript project, cd into your project's root directory in a terminal window and run tsc --init. This command will generate a tsconfig.json file with minimal configuration options, similar to below. { "compilerOptions": { "module": "commonjs", "target": "es5", "noImplicitAny": false, "sourceMap": false, "pretty": true }, "exclude": [ "node_modules" ] } With a tsconfig.json file placed at the root of your TypeScript project, you can use the tsc command to run the compilation. Section 1.2: Basic syntax TypeScript is a typed superset of JavaScript, which means that all JavaScript code is valid TypeScript code. TypeScript adds a lot of new features on top of that. TypeScript makes JavaScript more like a strongly-typed, object-oriented language akin to C# and Java. This means that TypeScript code tends to be easier to use for large projects and that code tends to be easier to understand and maintain. The strong typing also means that the language can (and is) precompiled and that variables cannot be assigned values that are out of their declared range. For instance, when a TypeScript variable is declared as a number, you cannot assign a text value to it. This strong typing and object orientation makes TypeScript easier to debug and maintain, and those were two of the weakest points of standard JavaScript. Type declarations You can add type declarations to variables, function parameters and function return types. The type is written after a colon following the variable name, like this: var num: number = 5; The compiler will then check the types (where possible) during compilation and report type errors. var num: number = 5; num = "this is a string"; // error: Type 'string' is not assignable to type 'number'. The basic types are : number (both integers and floating point numbers) string boolean Array. You can specify the types of an array's elements. There are two equivalent ways to define array types: Array<T> and T[]. For example: number[] - array of numbers Array<string> - array of strings Tuples. Tuples have a fixed number of elements with specific types. [boolean, string] - tuple where the first element is a boolean and the second is a string. [number, number, number] - tuple of three numbers. GoalKicker.com – TypeScript Notes for Professionals 4 {} - object, you can define its properties or indexer {name: string, age: number} - object with name and age attributes {[key: string]: number} - a dictionary of numbers indexed by string enum - { Red = 0, Blue, Green } - enumeration mapped to numbers Function. You specify types for the parameters and return value: (param: number) => string - function taking one number parameter returning string () => number - function with no parameters returning an number. (a: string, b?: boolean) => void - function taking a string and optionally a boolean with no return value. any - Permits any type. Expressions involving any are not type checked. void - represents "nothing", can be used as a function return value. Only null and undefined are part of the void type. never let foo: never; -As the type of variables under type guards that are never true. function error(message: string): never { throw new Error(message); } - As the return type of functions that never return. null - type for the value null. null is implicitly part of every type, unless strict null checks are enabled. Casting You can perform explicit casting through angle brackets, for instance: var derived: MyInterface; (<ImplementingClass>derived).someSpecificMethod(); This example shows a derived class which is treated by the compiler as a MyInterface. Without the casting on the second line the compiler would throw an exception as it does not understand someSpecificMethod(), but casting through <ImplementingClass>derived suggests the compiler what to do. Another way of casting in TypeScript is using the as keyword: var derived: MyInterface; (derived as ImplementingClass).someSpecificMethod(); Since TypeScript 1.6, the default is using the as keyword, because using <> is ambiguous in .jsx files. This is mentioned in TypeScript official documentation. Classes Classes can be defined and used in TypeScript code. To learn more about classes, see the Classes documentation page. Section 1.3: Hello World class Greeter { greeting: string; constructor(message: string) { this.greeting = message; } greet(): string { return this.greeting; } }; GoalKicker.com – TypeScript Notes for Professionals 5 let greeter = new Greeter("Hello, world!"); console.log(greeter.greet()); Here we have a class, Greeter, that has a constructor and a greet method. We can construct an instance of the class using the new keyword and pass in a string we want the greet method to output to the console. The instance of our Greeter class is stored in the greeter variable which we then us to call the greet method. Section 1.4: Running TypeScript using ts-node ts-node is an npm package which allows the user to run typescript files directly, without the need for precompilation using tsc. It also provides REPL. Install ts-node globally using npm install -g ts-node ts-node does not bundle typescript compiler, so you might need to install it. npm install -g typescript Executing script To execute a script named main.ts, run ts-node main.ts // main.ts console.log("Hello world"); Example usage $ ts-node main.ts Hello world Running REPL To run REPL run command ts-node Example usage $ ts-node > const sum = (a, b): number => a + b; undefined > sum(2, 2) 4 > .exit To exit REPL use command .exit or press CTRL+C twice. Section 1.5: TypeScript REPL in Node.js For use TypeScript REPL in Node.js you can use tsun package Install it globally with GoalKicker.com – TypeScript Notes for Professionals 6 npm install -g tsun and run in your terminal or command prompt with tsun command Usage example: $ tsun TSUN : TypeScript Upgraded Node type in TypeScript expression to evaluate type :help for commands in repl $ function multiply(x, y) { ..return x * y; ..} undefined $ multiply(3, 4) 12 GoalKicker.com – TypeScript Notes for Professionals 7

en

Stack Overflow

CC BY-SA

c_001c3177a047

القواعد

exercise

حدّد أداة الاستثناء في الجملة الآتية: "وَبِالتّالي، عَدا عَنِ الآثارِ المادّيّةِ في حالِ حُدوثِ إِصابات، فَإنَّ حالاتِ العُنْفِ تُلْحِقُ بِالشّابِّ آثارًا نَفْسيَّةً وَاجْتِماعيَّةً". - وبالتّالي - عدا - فإنَّ - عن الآثار حدّد خبر إنّ في الجملة الاتية: "إِنَّ النُّشوءَ في مُجْتَمَعٍ غَيْرِ مُتماسكٍ اِجْتِماعيًّا أَوْ تَتَفاوَتُ فيهِ مُعَدَّلاتُ الدَّخْلِ بِشَكْلٍ كَبيرٍ وَتَنْعَدِمُ سياساتُ الحِمايةِ الِاجْتِماعيَّةِ فيه، قَدْ يَزيدُ بِدَوْرِهِ مِنِ احْتِمالِ انْتِشارِ الع - قد يزيد (جملة فعليّة) - تتفاوت (جملة فعليّة) - تنعدم (جملة فعليّة) - غير (اسم ظاهر) حدّد المبتدأ في الجملة الآتية: "أَمّا عَلى الصَّعيدِ الأَكاديميّ، فَهَذا الِاحْتِمالُ يَزيدُ عندَ الفَشلِ في الدِّراسةِ". - الصّعيد - الاحتمال - هذا - الدّراسة حدّد فاعل الفعل "ينقص" في الجملة الآتية: "نَجِدُ أَنَّ الِانْتِماءَ إلى أُسْرَةٍ يَنْقُصُها أَحَدُ الأَبَوَيْنِ أَوِ التَّعَرُّضَ للعُنْفِ داخِلَ الأُسْرَةِ...". - أحدُ - الأبوين - أحدُ الأبوين - أسرةٍ حدّد المعدود في الجملة الاتية من النّصّ: "تَتَسَبَّبُ حالاتُ العنفِ يوميًّا بِوفاةِ مئةٍ وَثمانينَ مُراهِقًا حولَ العالَم". - يوميًّا - حالات العنف - مئة وثمانين - مراهقًا ورد المصدر القياسيّ "الِانْتِماءَ" في الجملة الآتية من النّصّ: "نَجِدُ أَنَّ الِانْتِماءَ إلى أُسْرَةٍ يَنْقُصُها أَحَدُ الأَبَوَيْنِ"، حدّد وزنه. - افتعال - انفعال - إفعلال - استفعال حدّد المصدر القياسيّ في الجملة الآتية من النّصّ: "وَهُناكَ أَسْبابٌ عَديدَةٌ قَدْ تَدْفَعُ الشَّبابَ للِانْخِراطِ بِأَعْمالِ العُنْف". - أسباب - أعمال - انخراط - الشّباب ما علامة إعراب الفعل "تقتضي" في هذه الجملة: "لإِصاباتٍ تَقْتَضي دُخولَ المُسْتَشْفى للعِلاج"؟ - الضّمّة الظّاهرة على آخره - الضّمّة المقدّرة على الياء للثّقل - الضّمّة المقدّرة على الألف للتّعذّر - حذف النّون لأنّه من الأفعال الخمسة

ar

Kamkalima

CC BY-NC-ND

c_001c76404587

ela-grade-12.lc.l27.pdf

ela-grade-12.lc.l27.pdf

document

NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 Lesson 27 12 LC Introduction In this lesson, students read and analyze pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” by A. Leslie Harris (from “In Song of Solomon Toni Morrison has faced the tale-spinner’s recurring problem” to “carry much of the burden of the myth”), in which A. Leslie Harris presents the concept of mythology as a central structural support for Song of Solomon. Students participate in a discussion of Milkman’s journey in the context of other mythical figures before independently exploring how the literary criticism relates to prior analysis of existing unanswered questions. Student learning is assessed via a Quick Write at the end of the lesson: Choose a sentence from pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” and analyze how the sentence relates to the novel’s characters, central ideas, or structure. For homework, students read pages 71–73 of “Myth as Structure in Toni Morrison’s Song of Solomon” and annotate for how the article relates to their 12 LC Second Interim Assessment responses. Also, students conduct a brief search into the flight of Daedalus and Icarus. Standards Assessed Standard(s) CCRA.R.9 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take. RI.11-12.1 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. Addressed Standard(s) W.11-12.9.a, b Draw evidence from literary or informational texts to support analysis, reflection, and research. a. Apply grades 11–12 Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”). File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 1 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 b. Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”). L.11-12.4.a, b Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies. a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable). Assessment Assessment(s) Student learning is assessed via a Quick Write at the end of the lesson. Students respond to the following prompt, citing textual evidence to support analysis and inferences drawn from the text. • Choose a sentence from pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” and analyze how the sentence relates to the novel’s characters, central ideas, or structure. High Performance Response(s) A High Performance Response should: • Identify a sentence from pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” (e.g., “If we follow Morrison’s lead and concentrate on the growth of Macon Dead, known as Milkman because his mother nursed him too long, we find that her novel is cohesive, following the clear pattern of birth and youth, alienation, quest, confrontation, and reintegration common to mythic heroes as disparate as Moses, Achilles, and Beowulf.” (Harris, p. 70)). • Analyze how this sentence relates to the novel’s characters, central ideas, or structure (e.g., In this sentence, Harris presents Milkman’s story as a hero’s journey from “birth and youth, alienation, quest, confrontation, and reintegration” (Harris, p. 70). As Milkman’s character develops over the course of the text, he passes through each stage of the hero’s journey. Throughout his youth and young adulthood, Milkman is alienated from all those around him as evidenced by Guitar’s comment, “You don’t live nowhere. Not Not Doctor Street or Southside” (Morrison, p. 103). Milkman embarks on his quest, a journey that he wanted to do on his own with “no input from File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 2 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 anybody” (Morrison, p. 220), which further emphasizes his heroic alienation. Finally, Milkman is “reintegrate[ed]” (Harris, p. 70) with his community of ancestors by deciphering the song that tells the history of his family, which makes him “as eager and happy as he had ever been in his life” (Morrison, p. 304). Throughout the novel, Morrison develops Milkman’s character according to the hero’s journey as Harris defines it in “Myth as Structure in Toni Morrison’s Song of Solomon.”). Vocabulary Vocabulary to provide directly (will not include extended instruction) • perceptual (adj.) – of, relating to, or involving apprehending by means of the senses or of the mind • mythopoesis (n.) – the composition or making of myths • pervasive (adj.) – spread throughout • assimilation (n.) – the act of adopting (something) as part of a larger thing Vocabulary to teach (may include direct word work and/or questions) • inexplicable (adj.) – incapable of being accounted for or explained Additional vocabulary to support English Language Learners (to provide directly) • myth (n.) – a story that was told in an ancient culture to explain a practice, belief, or natural occurrence • presupposes (v.) – to be based on the idea that something is true or will happen • commended (v.) – praised (someone or something) in a serious and often public way • chronology (n.) – the sequential order in which past events occur • approximation (n.) – something that is similar to something else • loitering (v.) – remaining in an area when you do not have a particular reason to be there • genealogy (n.) – the study of family history Lesson Agenda/Overview Student-Facing Agenda % of Lesson Standards & Text: • Standards: CCRA.R.9, RI.11-12.1, W.11-12.9.a, b, L.11-12.4.a, b • Text: “Myth as Structure in Toni Morrison’s Song of Solomon” by A. Leslie File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 3 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 Harris, pages 69–71 Learning Sequence: 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Introduction of Lesson Agenda Homework Accountability Reading and Discussion Quick Write Closing 5% 10% 55% 25% 5% Materials • Student copies of the Short Response Rubric and Checklist (refer to 12 LC Lesson 1) (optional) Learning Sequence How to Use the Learning Sequence Symbol Type of Text & Interpretation of the Symbol 10% no symbol    Percentage indicates the percentage of lesson time each activity should take. Plain text indicates teacher action. Bold text indicates questions for the teacher to ask students. Italicized text indicates a vocabulary word. Indicates student action(s). Indicates possible student response(s) to teacher questions. Indicates instructional notes for the teacher. Activity 1: Introduction of Lesson Agenda 5% Begin by reviewing the agenda and the assessed standards for this lesson: CCRA.R.9 and RI.11-12.1. In this lesson, students read pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” by A. Leslie Harris, engaging in a discussion of Milkman’s journey in the context of other mythical figures before independently exploring how the literary criticism relates to prior analysis of existing unanswered questions.  Students look at the agenda. File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 4 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 Activity 2: Homework Accountability 10% Instruct students to take out their responses to the first part of the previous lesson’s homework assignment. (Respond briefly in writing to the following prompt: To what extent is mercy a central idea of Song of Solomon?) Instruct students to form pairs and discuss their responses.  Student responses may include: o o Mercy appears as a central idea early in the text with the description of “No Mercy Hospital” (p. 4). The hospital does not admit African-American patients until Milkman’s birth, so the building stands as a reminder of the lack of mercy that African Americans receive throughout the text. Morrison uses Mercy Hospital as backdrop in important moments in the text to reinforce the merciless society that looms over characters in the text. For example, when Macon tells the story of the gold, Milkman and Macon “met in the little public park across the street from Mercy Hospital” (p. 164), a setting that emphasizes the desperation the men have to get the gold and escape their social status. Mercy appears in the text often in relation to troubled characters of the story. Frequent exclamations of “mercy” such as Porter’s cry of “God have mercy. What I’m gonna do?” (p. 26) reflect the struggles of the characters to find compassion and kindness. Pilate exclaims, “I want mercy!” (p. 317) at Hagar’s funeral, asking for compassion for herself and her granddaughter.  Students will be held accountable for the annotations that they made for homework during Activity 3: Reading and Discussion. Activity 3: Reading and Discussion 55% Instruct students to form small groups. Post or project each set of questions below for students to discuss. Instruct students to continue to annotate the text as they read and discuss (W.11-12.9.a, b).  Differentiation Consideration: Consider posting or projecting the following guiding question to support students throughout this lesson: How is Milkman’s journey to the south similar to journeys of other mythic people? Instruct students to read pages 69–70 of “Myth as Structure in Toni Morrison’s Song of Solomon” (from “In Song of Solomon Toni Morrison has faced the tale-spinner’s recurring problem” to “to inform and control her narrative structure”) and discuss the following questions in groups before sharing out with the class. File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 5 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 Provide students with the definitions of perceptual, mythopoesis, and pervasive.  Students may be familiar with some of these words. Consider asking students to volunteer definitions before providing them to the group.  Students write the definitions of perceptual, mythopoesis, and pervasive on their copies of the text or in a vocabulary journal.  Differentiation Consideration: Consider providing students with the definitions of myth and presupposes.  Students write the definitions of myth and presupposes on their copies of the text or in a vocabulary journal. What challenge does Harris say Morrison “faced” (p. 69)? How does Harris say Morrison overcame this challenge?  Student responses should include: o o Harris states that Morrison “faced the tale-spinner’s recurring problem,” namely the challenge of making characters universally accessible so that readers understand her “characters’ background or experiences” (p. 69). Morrison had to provide enough information to readers who had no knowledge of American racial politics to ensure the readers could understand Milkman, or “one black man’s struggle for identity” (p. 69). Harris argues that “Morrison’s success” is because of her “use of myth to show man’s constant search for reassurance in myths” (p. 69). Harris suggests that Morrison engages readers in Song of Solomon by placing Milkman in his own mythic tale. The mythic structure of Milkman’s journey allows readers to better connect to the story that Morrison tells, because readers are already familiar with how a myth unfolds. What does Harris present as the function of myth?  Harris states that according to Mircea Eliade, “myth is sacred history” andthe goal of myth is to “explain the origins, destiny, and cultural concerns of a people” (p. 69). Even in an age of “scientific fact,” Harris claims that people depend “on myth for more than entertainment” and that people “are still drawn” to myths, heroes, and supernatural conflicts (p. 69). Myths serve as “agents of stability” that answer the “enduring questions” of the world (p. 69). People connect to mythic stories in order to explain the mysteries of the world and to give meaning to the struggles of humankind.  Differentiation Consideration: If students struggle, consider posing the following scaffolding questions: File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 6 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 How does the idea that people have “always turned to myth to explain the inexplicable” (p. 69) clarify the meaning of the word inexplicable? (L.11-12.4.a) What word parts in the word inexplicable confirm this meaning? (L.11-12.4.b)  According to Harris, people use myths to explain what is difficult to explain, so the word inexplicable must mean “difficult to explain.” The word parts in-, which means “not,” explic-, which looks like “explain,” and -able, “which means capable of,” confirm that the word inexplicable means “not able to be explained.” How does Harris describe the type of myth structure Morrison uses?  Harris states that Morrison “selects one of the oldest and most pervasive mythic themes, the hero and his quest, to inform and control her narrative structure” (p. 70). In Harris’s opinion, Morrison structures the novel towards and around Milkman’s heroic journey and personal growth. Lead a brief whole-class discussion of student responses. Instruct students to read pages 70–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” (from “In Song of Solomon Morrison creates a world both realistic and dreamlike” to “carry much of the burden of the myth”) and discuss the following questions in groups before sharing out with the class. Provide students with the definition of assimilation.  Students may be familiar with this word. Consider asking students to volunteer a definition before providing one to the group.  Students write the definition of assimilation on their copies of the text or in a vocabulary journal.  Differentiation Consideration: Consider providing students with the definitions of commended, chronology, approximation, loitering, and genealogy.  Students write the definitions of for commended, chronology, approximation, loitering, and genealogy on their copies of the text or in a vocabulary journal.  Differentiation Consideration: Consider providing students with the following information on Moses, Achilles, and Beowulf. o Moses – the Hebrew prophet who led the Israelites out of Egypt and delivered the Law during their years of wandering in the wilderness File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 7 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 o Achilles – the greatest Greek warrior in the Trojan War and hero of Homer's Iliad; He killed Hector and was killed when Paris wounded him in the heel, his one vulnerable spot, with an arrow o Beowulf – a legendary Geatish warrior and hero of the Old English poem Beowulf How does Milkman’s transition into adulthood connect to the idea of a “mythic hero[]” (p. 70)?  Student responses may include: o o Milkman’s final transition into adulthood ends with Milkman accepting his obligations to his family and community. Harris argues that “by the end of the novel [Milkman] knows himself and his obligations to both present and past, to himself and his world” (p. 70). Milkman’s final transition is the “reintegration” portion of the “mythic chronology” (p. 70) as described by Harris. This acceptance of his community and his obligation to the people around him confirms Milkman as a heroic character. Harris argues that the hero’s quest ends with the hero becoming “an agent of the social consciousness” (p. 70), an individual who is connected to the community. Morrison uses Milkman’s growing connection to the people of Shalimar to illustrate his growing “external coherence” (p. 70) or connection to the larger social community. By building his connections and relationships with his community and family, Milkman fulfills his heroic “obligations to both present and past, to himself and his world” (p. 70). How does the structure of Song of Solomon compare to the structure of myths?  Harris claims that Morrison uses “myth to underpin [the] narrative” (p. 69) throughout Song of Solomon. Milkman’s story “[follows] the clear pattern of birth and youth, alienation, quest, confrontation, and reintegration common to mythic heroes” (p. 70). Milkman’s journey takes him from a “comfortable but loitering and wasted life” (p. 70) in Part 1 of Song of Solomon through a quest and confrontation in Part 2. Harris argues that Milkman gains “not only psychological and physical maturation but an approximation of the development of a true hero” (p. 70). Morrison makes Milkman’s story understandable and powerful by structuring it like a hero’s myth. How does Milkman’s character development throughout Song of Solomon relate to the idea of mythic structure?  Harris states that Milkman’s story in Song of Solomon follows a “clear pattern of … quest, confrontation, and reintegration common to mythic heroes” (p. 70). Like other mythic heroes, Milkman goes on a quest for gold, confronts himself and Guitar in the woods of Virginia, and is reintegrated into the community of Shalimar and his family community in Michigan. File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 8 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 How does the ending of Song of Solomon reflect the structure of myth?  Harris states that the final scene between Milkman and Guitar is “Milkman's emergence as a champion who understands and will defend his world” (p. 71). As he cannot return a hero “until he defeats the enemy” (p. 71), Milkman becomes a hero by leaping toward Guitar. Milkman’s mythic journey is complete even if the reader never discovers his fate, as “the final battle is both a confrontation and a confirmation” (p. 71) of Milkman’s personal growth and heroic nature. What does Harris identify as the root of the Song of Solomon’s “textual richness” (p. 71)? How is this richness connected to the idea of myth?  Student responses may include: o o The “textual richness” of the Song of Solomon “derives from a present which spans three generations” and the numerous “digressions, explanations, and expansions” (p. 71) that exist within the text. The reflections and echoes of stories from Milkman, Guitar, Macon, and Pilate expand the world of Song of Solomon. Harris argues that these “digressions” together with Milkman’s story create “an interlace, in which the dominant narrative is embellished and enhanced” (p. 71). The stories the characters tell about their past and ancestors enhance or improve the text, making it rich and multi-layered. Harris states that the “the constant themes of myth involve not the ‘why?’ (the causes) but the ‘whence?’ (the groundwork of human nature, belief, and endeavor)” (p. 69). These “meticulously articulated subplots and images” (p. 71), stories that the characters tell of their past and ancestors, work together to help Milkman and the readers answer questions about the meaning and purpose of human life. Lead a brief whole-class discussion of student responses.  Differentiation Consideration: To support students in their understanding of the elements of myths, consider completing the following annotation and discussion activity: Instruct student groups to reread pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” and identify and annotate for the elements that Harris presents as common to all myths. Then instruct student groups to examine the progression of Milkman through Song of Solomon in relation to the identified qualities of myth. Lead a brief whole-class discussion of student responses. Activity 4: Quick Write 25% Instruct students to respond briefly in writing to the following prompt: File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 9 NYS Common Core ELA & Literacy Curriculum Grade 12 • Literary Criticism Module • Lesson 27 Choose a sentence from pages 69–71 of “Myth as Structure in Toni Morrison’s Song of Solomon” and analyze how the sentence relates to the novel’s characters, central ideas, or structure. Instruct students to look at their annotations to find evidence. Ask students to use this lesson’s vocabulary wherever possible in their written responses.  Students listen and read the Quick Write prompt.  Display the prompt for students to see, or provide the prompt in hard copy. Transition to the independent Quick Write.  Students independently answer the prompt using evidence from the text.  See the High Performance Response at the beginning of this lesson.  Consider using the Short Response Rubric to assess students’ writing. Students may use the Short Response Rubric and Checklist to guide their written responses. Activity 5: Closing 5% Display and distribute the homework assignment. For homework, instruct students to read pages 71–73 of “Myth as Structure in Toni Morrison’s Song of Solomon” (from “The opening pages gives us the mandrel” to “the gold his Aunt Pilate and father stumbled across in a Pennsylvania cave”) and annotate for how the article relates to their 12 LC Second Interim Assessment responses (W.11-12.9.b). Also, instruct students to conduct a brief search into the flight of Daedalus and Icarus.  Students follow along. Homework Read pages 71–73 of “Myth as Structure in Toni Morrison’s Song of Solomon” (from “The opening pages gives us the mandrel” to “the gold his Aunt Pilate and father stumbled across in a Pennsylvania cave”) and annotate for how the article relates to your 12 LC Second Interim Assessment response. Also, conduct a brief search into the flight of Daedalus and Icarus. File: 12 LC Lesson 27 Date: 6/30/15 Classroom Use: Starting 9/2015 © 2015 Public Consulting Group. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License http://creativecommons.org/licenses/by-nc-sa/3.0/ 10

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