Glendale Unified School District Math Curriculum Grade 6 Parent Information Unit 2: Numerical Expressions What Your Child Will Learn: In Unit 2, students will continue to work with positive rational numbers to write and simplify numerical expressions involving exponents and using the order of operations. Students will have the chance to explore order of operations as they relate to whole numbers and practice their arithmetic skills with decimal numbers and fractions. Students will evaluate variable expressions by substituting a given value into an algebraic expression and simplifying. Students will also explore measures of central tendency, especially the arithmetic mean (commonly known as the average), in the context of a numerical expression. MORE SPECIFICALLY, CHILDREN WILL LEARN HOW TO: Write and evaluate numerical expressions involving whole-number exponents. Identify parts of expressions: sum, term, product, factor, quotient, coefficient, etc. View one or more parts of an expression as a single entity. 2(8+7) the product of two factors; view (8+7) as a single entity and as the sum of two terms. Evaluate variable expressions. Perform order of operations, including expressions with exponents. Generate equivalent expressions, specifically using the distributive property, factoring and combining like terms. Create visual models to show equivalent expressions. Identify when two [numerical] expressions are equivalent. Justify that two expressions are equivalent. Find measure of center: mean, median, and mode. Describe patterns or striking deviations (such as outliers) in a data set. Standards: 6.EE.1, 6.EE.2.b, 6.EE.2.c, 6.EE.3, 6.EE.4, 6.SP.5.c For more information on the strategies, standards and explanations, visit the Grade 7 Chapter of the Mathematics Framework for California Public Schools: Kindergarten through Grade Twelve at: http://www.cde.ca.gov/ci/ma/cf/documents/mathfwgrade6lmg2.pdf A glossary is provided in the Guide for Extraordinary Mathematics for Students (GEMS). Activities at Home: Create numerical expressions to represent real life situations and solve. Use whole numbers, fractions, and decimals. Create order of operations problems and solve. Consider writing problems, then changing the placement of the parenthesis to see what happens! Make flashcards for vocabulary and properties. Look at the stock market page in the newspaper. Find three stocks, then find the mean of the prices. Choose three to five recipes from a cookbook. Pick an ingredient that is in all the recipes. Find the average amount of that ingredient needed for each recipe. Time yourself getting ready for school several mornings in a row. Determine the average time it takes to get ready for school.
Interactive Games and Websites: Some of the interactive games and websites use Java Script. Some browsers (for example Google Chrome) do not support Java. Try a different browser, such as Internet Explorer or Firefox. Order of Operations game: http://www.shodor.org/interactivate/activities/orderofoperationsfou/ Learning Links: Additional practice problems and videos can be found on KhanAcademy.org. Sign up for a free account at KhanAcademy.org Order of Operations and Exponents: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-ofoperations/e/evaluating-numerical-expressions-with-exponents https://www.khanacademy.org/math/pre-algebra/order-ofoperations/order_of_operations/e/order_of_operations_2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/world-ofexponents/e/positive_and_zero_exponents https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6thexponents/e/powers-of-fractions Algebraic (Variable) Expressions https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating-expressions-3 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6thparts-of-expressions/e/identifying-parts-of-expressions https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variablesexpressions/e/evaluating_expressions_1 https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating_expressions_2 Measures of Central Tendency (mean, median and mode) https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/mean-andmedian/e/calculating-the-mean https://www.khanacademy.org/math/probability/descriptivestatistics/central_tendency/e/mean_median_and_mode Create a free account at KhanAcademy.org To see an electronic copy of this parent letter, with clickable links, please go to the Common Core pages at www.gusd.net. Follow the links to mathematics, Grade 6. Scroll to the bottom of the page and click on Unit 2.
Glendale Unified School District Maj;matika\i ousoumnakan ragir T;[;kouj\ounn;r 6-rd dasaranzin;ri no[n;ri famar Bavin 2^ Jwa\in artafa\touj\ounn;r Inc ksowori ];r ;r;.an^ :rkrord bavnoum% a,ak;rtn;re k,arounak;n a,.at;l bnakan jw;ri f;t! Nranq astiyanazou\z parounako[ jwa\in artafa\touj\ounn;r kgr;n kparx;zn;n øgtagor ;low gor o[ouj\ounn;ri f;rjakanouj\oune! A,ak;rtn;re kousoumnasir;n gor o[ouj\ounn;ri f;rjakanouj\oune ambo[= jw;row kbar;law;n ir;nz maj;matikakan fmtouj\ounn;re tasnordakan jw;ri kotorakan;ri warvouj\ounn;r katar;low! A,ak;rtn;re klou ;n 'o'o.akann;row artafa\touj\ounn;r^ 'o'o.akann;re trwa jw;row 'o.arin;low parx;zn;low! A,ak;rtn;re na ksowor;n mi=ini masin (mi=in% mi=in jiw)! MASNAWORAP:S% A<AK:RTN:RE KSOWOR:N J: INCP:S^ Gr;l gnafat;l astiyanazou\zow jwa\in artafa\touj\ounn;re! Yanac;l artafa\touj\ounn;ri mas;re^ goumar% andam% artadr\al% artadric% qanord% gor akiz a\ln! Artafa\touj\an m;k kam aw;li mas;re dit;l orp;s a an]in tarr;r! 2(8+7)-e ;rkou artadricn;ri artadr\al (8+7)-e a an]in orp;s ;rkou tarr;ri goumar! Gnafat;l 'o'o.akann;row artafa\touj\ounn;re! Katar;l gor o[ouj\ounn;ri f;rjakanouj\oune% n;ra \al astiyanazou\zow artafa\touj\ounn;r! Famarv;q artafa\touj\ounn;r kaxm;l% fatkap;s ba,.akan fatkouj\oune øgtagor ;low% baxmapatkicn;ri bavan;l.mbawor;l mianman tarr;re! St;[ ;l t;so[akan mod;ln;r^ famarv;q artafa\touj\ounn;re zouzadr;lou famar! Yanac;l ;rkou famarv;q jwa\in artafa\touj\ounn;re! Apazouz;l% or ;rkou artafa\touj\ounn;re famarv;q ;n! Gtn;l mi=ine^ (mean, median, and mode)! Nkaragr;l ørinakn;re kam nkat;li,;[oumn;re (incp;s ørinak^,arqiz dours gntwo[e [outliers]) tw\aln;ri.mboum! Ca'oro,icn;r^ 6.EE.1, 6.EE.2.b, 6.EE.2.c, 6.EE.3, 6.EE.4, 6.SP.5.c Strat;gian;ri% ca'oro,icn;ri bazatrouj\ounn;ri masin faw;l\al t;[;kouj\an famar a\z;l;q Kali`ornia\i fanra\in dprozn;ri% mankapart;xiz 12-rd dasaran% 7- rd dasarani maj;matika\i ka ouzwa qi ka\qh=^ http://www.cde.ca.gov/ci/ma/cf/documents/mathfwgrade6lmg2.pdf Tramadrwoum h ªArtakarg maj;matika\i ou[;zou\z a,ak;rtn;ri famarº-i w;rab;r\al masnagitakan ba aran (GEMS)! Tane katarwo[ a,.atanqn;r Irakan k\anqi irawiyak n;rka\azno[ jwa\in artafa\touj\oun gr;q lou ;q! Øgtagor ;q ambo[= jw;r% kotorakn;r tasnordakan jw;r! Gor o[ouj\ounn;ri f;rjakanouj\an warvouj\ounn;r gr;q lou ;q! >ndirn;r gr;q% f;to 'akag ;ri t;[e 'o.;q t;s;q inc kpatafi! Ba ;ri fatkouj\ounn;ri famar qart;r patrast;q! Stoug;q lragri akzian;ri h=e! Gt;q ;r;q akzia% a\nouf;t gt;q dranz mi=in arv;qe! >ofararakan grqi m;= fing ba[adratoms entr;q! Entr;q mi ba[adramas% or bolor ba[adratoms;ri m;= ka! Gt;q a\d ba[adramasi mi=in ca'e% ore p;tq h bolor ba[adratoms;ri famar! Ca';q dproz gnalou famar patrastw;loun fatkazwa vamanake mi qani f;rjakan ør! Oro,;q mi=in ca'ow incqan vamanak h farkawor patrastw;lou famar! Translated By: GUSD Intercultural Office Armenian Math Unit 2 Parent letter- 6 th grade Professional Development
>a[;r ka\q;r Oro,.a[;r ka\q;r Java Script ;n øgtagor oum! Oro, orono[akan famakarg;r (browsers) (ørinak^ Gougl Qrome) Java-in n;zouk c;n fandisanoum! "or];q tarb;r orono[akan famakarg;r (browser) øgtagor ;l% incp;s ørinak^ Internet Explorer kam Firefox Gor o[ouj\an f;rjakanouj\an.a[ http://www.shodor.org/interactivate/activities/orderofoperationsfou/ Ousouzman fangou\zn;r Faw;l\al warvouj\ounn;r kam t;safolowakn;r kar;li h gtn;l KhanAcademy.org ka\qh=oum! KhanAcademy.org fasz;ow anwyar fa,iw baz;q! Gor o[ouj\an f;rjakanouj\oun astiyanazou\z https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-ofoperations/e/evaluating-numerical-expressions-with-exponents https://www.khanacademy.org/math/pre-algebra/order-ofoperations/order_of_operations/e/order_of_operations_2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/world-ofexponents/e/positive_and_zero_exponents https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6thexponents/e/powers-of-fractions Fanrafa,wakan ('o'o.akann;row) artafa\touj\ounn;r https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating-expressions-3 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6thparts-of-expressions/e/identifying-parts-of-expressions https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variablesexpressions/e/evaluating_expressions_1 https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating_expressions_2 Fa,wark;l mi=ine (mean, median and mode) https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/mean-andmedian/e/calculating-the-mean https://www.khanacademy.org/math/probability/descriptivestatistics/central_tendency/e/mean_median_and_mode KhanAcademy.org fasz;ow anwyar fa,iw baz;q! A\s namaki hl;ktronik paty;ne t;sn;lou famar% douq karo[ ;q øgtw;l http://www.gusd.net-iz! Mt;q common core h=e s;[m;q 6-rd dasarani bavin 2-e (Unit 2)! Translated By: GUSD Intercultural Office Armenian Math Unit 2 Parent letter- 6 th grade Professional Development
글렌데일통합교육구 수학교과과정 6 학년학부모정보단원 2: 수식 귀자녀는무엇을배울것인가 : 단원 2 에서, 학생들은연산순서를사용하여지수가포함되는수식을작성하고단순화하기위해유리수양수학업을계속할것이다. 학생들은자연수를말하고소수및분수를갖고산수기량을연습함에따라연산순서를탐구할기회를가질것이다. 학생들은주어진값을대수적표현으로대체하고단순화함으로써변동식의값을구한다. 또한학생들은수식의전후문맥속에서중심경향특히산술적중앙값 ( 일반적으로평균으로알려져있다 ) 을구한다. 좀더구체적으로, 아동들은다음의것들을배울것이다 : 자연수지수가포함된수식작성및값구하기 다음과같은부분식판별하기 : 합, 항, 곱, 인수, 지수, 계수등 단일체로서식의한부분또는그이상보기. 2(8+7) 두인수의곱 ; (8+7) 을하나의실체그리고두항의 합으로보기 변동식의값구하기 계수식을포함하여연산의순서수행하기 등식특히분배속성, 인수분해및등가항결합을사용하여등식만들기 등식을보이기위해시각적모델만들기 두 [ 수 ] 식의등가판별하기 두식이동등하다는근거제시하기 다음과같은중간값찾기 : 평균값, 중앙값및최빈수 데이타세트에서편차의패턴또는도출 ( 예를들어, 윤곽 ) 을설명하기 표준 : 6.EE.1, 6.EE.2.b, 6.EE.2.c, 6.EE.3, 6.EE.4, 6.SP.5.c 방법, 표준및설명에대한더많은정보에대해선, 유치원 -12 학년은학년가주공립학교수학프레임워크 : 찹터 7 을방문하시오 : http://www.cde.ca.gov/ci/ma/cf/documents/mathfwgrade6lmg2.pdf 용어풀이는학생들을위한수학특수용어안내집 (GEMS) 에서제공된다. 가정에서의활동 실제상황을나타내고풀기위해수식만들기. 자연수, 분수및소수사용하기 문제수행순서를정하고풀기. 문제를적은뒤어떻게되는지보기위해괄호의위치변경을고려한다. 어휘및속성에대한플레쉬카드만들기 신문에서증권시장페이지보기. 세가지의증권을찾아평균값찾기 요리책에서세가지부터다섯가지의조리법을찾는다. 모든조리에있는한가지재료를선택한다. 각조리에서필요한이재료의평균양을구한다. 다수의아침시간동안, 계속적으로스스로학교에갈준비를하는시간을정한다. 학교에갈준비에걸리는평균시간을결정한다.
상호작용게임및웹사이트 : 일부상호작용게임과웹사이트는자바스크립트 (Java Script) 를사용한다. 일부브라우저 ( 예를들어, 구글크롬 ) 들은자바를지원하지않으므로인터넷익스플로러또는파이어폭스와같은다른브라우저로시도한다. 연산순서게임 : http://www.shodor.org/interactivate/activities/orderofoperationsfou/ 학습링크 : 추가적인연습문제및비디오는 KhanAcademy.org 에서찾을수있다. KhanAcademy.org 무료구좌에서명하시오. 연산순서및지수 : https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-ofoperations/e/evaluating-numerical-expressions-with-exponents https://www.khanacademy.org/math/pre-algebra/order-ofoperations/order_of_operations/e/order_of_operations_2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/world-ofexponents/e/positive_and_zero_exponents https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6thexponents/e/powers-of-fractions 대수 ( 변동 ) 식 https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating-expressions-3 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6thparts-of-expressions/e/identifying-parts-of-expressions https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variablesexpressions/e/evaluating_expressions_1 https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating_expressions_2 중심경향측정 ( 평균값, 중앙값및최빈수 ) https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/mean-andmedian/e/calculating-the-mean https://www.khanacademy.org/math/probability/descriptivestatistics/central_tendency/e/mean_median_and_mode KhanAcademy.org 에서무료구좌를만든다. 본학부모서한의전자사본을보기위해선, GUSD.net 의커먼코어 (common core) 페이지로가시오. 6 학년링크를따라페이지아래로내려가단원 (Unit) 2 를클릭하시오. Translated by: GUSD, Intercultural Department Professional Development Parent Letter, Grade 6 Unit 2 Korean 9/2/2016
Distrito Escolar Unificado de Glendale Plan de Estudios de Matemáticas 6º Grado - Información para los padres Unidad 2: Expresiones numéricas Lo que su hijo aprenderá: En la Unidad 2, los estudiantes continuarán trabajando con los números racionales positivos para escribir y simplificar expresiones numéricas que tienen exponentes y utilizar el orden de las operaciones. Los estudiantes tendrán la oportunidad de explorar el orden de las operaciones que se relacionan con números enteros y practicar sus habilidades aritméticas con números decimales y fracciones. Los estudiantes evaluarán expresiones variables mediante la sustitución de un valor dado en una expresión algebraica y simplificarlas. Los estudiantes también explorarán las medidas de tendencia central, especialmente la media aritmética (comúnmente conocida como el promedio), en el contexto de una expresión numérica. MÁS ESPECÍFICAMENTE, LOS ALUMNOS APRENDERÁN CÓMO: Escribir y evaluar expresiones numéricas que tienen exponentes de números enteros. Identificar las partes de expresiones: suma, término, producto, factor, cociente, coeficiente, etc. Ver una o más partes de una expresión como una sola entidad. 2 (8 + 7) el producto de dos factores; vista (8 + 7) como una sola entidad y como la suma de dos términos. Evaluar expresiones variables. Llevar a cabo el orden de las operaciones, incluyendo las expresiones con exponentes. Generar expresiones equivalentes, específicamente utilizando la propiedad distributiva, factorización y la combinación de los términos semejantes. Crear modelos visuales para mostrar expresiones equivalentes. Identificar cuando dos expresiones [numéricas] son equivalentes. Justificar que dos expresiones son equivalentes. Encontrar medida de tendencia central: media, mediana y moda. Describir los patrones o desviaciones notables (como valores atípicos) en un conjunto de datos. Estándares: 6.EE.1, 6.EE.2.b, 6.EE.2.c, 6.EE.3, 6.EE.4, 6.SP.5.c Para obtener más información sobre las estrategias, normas y explicaciones, visita el capítulo del 7º grado del Marco de Referencia para Matemáticas para las Escuelas Públicas de California: jardín de niños hasta el grado doce en: http://www.cde.ca.gov/ci/ma/cf/documents/mathfwgrade6lmg2.pdf Encontrarás un glosario en la Guía de Matemáticas Extraordinarias para Estudiantes (GEMS). Actividades en el hogar: Crea expresiones numéricas para representar situaciones de la vida real y resolverlas. Utiliza números enteros, fracciones y decimales. Crea problemas de orden de operaciones y resuélvelos. Considera exponer problemas y luego cambiar la colocación de los paréntesis para ver qué pasa. Haz tarjetas de vocabulario y propiedades. Ve la página de la bolsa de valores en el periódico. Selecciona tres acciones, y luego encuentra la media de los precios. Elije entre tres y cinco recetas de un libro de cocina. Escoge un ingrediente que se encuentre en todas las recetas. Encuentra la cantidad media de ese ingrediente que se requiere para cada receta.
Mide el tiempo que usaste en prepararte para la escuela varias mañanas seguidas. Determina el tiempo medio que te tardas en ir a la escuela. Juegos interactivos y sitios web: Algunos de los juegos interactivos y sitios web utilizan Java Script. Algunos navegadores (por ejemplo Google Chrome) no son compatibles con Java. Intente un navegador diferente, como Internet Explorer o Firefox. Juego sobre el orden de las operaciones: http://www.shodor.org/interactivate/activities/orderofoperationsfou/ Enlaces de aprendizaje: Se pueden encontrar problemas y videos adicionales recomendados en KhanAcademy.org. Regístrate para obtener una cuenta gratuita en KhanAcademy.org El orden de las operaciones y los exponentes: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-ofoperations/e/evaluating-numerical-expressions-with-exponents https://www.khanacademy.org/math/pre-algebra/order-ofoperations/order_of_operations/e/order_of_operations_2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/world-ofexponents/e/positive_and_zero_exponents https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6thexponents/e/powers-of-fractions Expresiones algebraicas (variable) https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating-expressions-3 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6thparts-of-expressions/e/identifying-parts-of-expressions https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variablesexpressions/e/evaluating_expressions_1 https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variablesand-expressions/e/evaluating_expressions_2 Medidas de tendencia central (media, mediana y moda) https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/mean-andmedian/e/calculating-the-mean https://www.khanacademy.org/math/probability/descriptivestatistics/central_tendency/e/mean_median_and_mode Crea una cuenta gratuita en KhanAcademy.org Para ver una copia electrónica de esta carta a los padres, con los enlaces de "hacer clic", por favor vaya a las páginas del Tronco Común en www.gusd.net. Siga los enlaces para las matemáticas, grado 6. Vaya a la parte inferior de la página y haga clic en la unidad 2.