glendale unified school district · on using place value strategies (area model, partial quotients,...

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Glendale Unified School District Math Curriculum Grade 4 Parent Information Unit 2: Multiplication and Division of Whole Numbers What Your Child Will Learn: In Unit 2, students will begin to develop an understanding of multiplication and division of whole numbers. Students will demonstrate an understanding of factors and multiples, as well as prime and composite numbers. Students will also continue to reason about number patterns, connecting a rule for a given pattern as it relates to multiplication or division. Students will solve multi-step contextual problems using a tape diagram or bar diagram to help visualize and solve multiplication and division problems in a real-world context. Students will deepen their foundational skills of multiplication and division to whole numbers greater than 100. Students will use visual representations such as area models and rectangular arrays and connect the visual model to an equation. The connection will be made for students to use multiplication in real-world scenarios, using area and perimeter formulas and problems involving distance measurements. MORE SPECIFICALLY, CHILDREN WILL LEARN HOW TO: Find all factor pairs for numbers up to 100 and identify whole numbers as prime or composite. Determine whether a given whole number is a multiple of another given one-digit number. Generate and analyze a number or shape pattern that follows a given rule. Multiply (two two-digit numbers) and divide (large numbers by one-digit divisors) using concepts of place value. Illustrate and explain multiplication and division using various strategies (equations, rectangular arrays, and area models). Identify and write a multiplication equation as a comparison of factors and a product (unknown product, unknown factors, unknown group size, and unknown number of groups). Solve multi-step word problems using multiplication and division. Use rounding to check the reasonableness of answers to problems involving multiplication and division. Solve division problems in which remainders must be interpreted. Represent word problems using equations with a symbol standing for the unknown quantity. Use the four operations to solve problems involving distances and apply the area and perimeter formulas for rectangles in real-world problems. Standards: 4.OA.4, 4.OA.5, 4.NBT.5, 4.NBT.6, 4.OA.1, 4.OA.2, 4.OA.3, 4.MD.2, 4.MD.3 For more information on the strategies, standards, and explanations, visit the California Framework at: http://www.cde.ca.gov/be/st/ss/documents/ccsmathstandardaug2013.pdf Sample Problems: 4.OA.5 Gain Familiarity with Factors and Multiples 4.NBT.5 Multi-Digit Multiplication Using Place Value Strategies (Area Model, Partial Products, Equations) 4.NB T.6 Multi- Digit Divisi

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Page 1: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

Glendale Unified School District Math Curriculum

Grade 4 Parent InformationUnit 2: Multiplication and Division of Whole Numbers

What Your Child Will Learn:In Unit 2, students will begin to develop an understanding of multiplication and division of whole numbers. Students will demonstrate an understanding of factors and multiples, as well as prime and composite numbers. Students will also continue to reason about number patterns, connecting a rule for a given pattern as it relates to multiplication or division. Students will solve multi-step contextual problems using a tape diagram or bar diagram to help visualize and solve multiplication and division problems in a real-world context. Students will deepen their foundational skills of multiplication and division to whole numbers greater than 100. Students will use visual representations such as area models and rectangular arrays and connect the visual model to an equation. The connection will be made for students to use multiplication in real-world scenarios, using area and perimeter formulas and problems involving distance measurements. MORE SPECIFICALLY, CHILDREN WILL LEARN HOW TO:

● Find all factor pairs for numbers up to 100 and identify whole numbers as prime or composite. ● Determine whether a given whole number is a multiple of another given one-digit number.● Generate and analyze a number or shape pattern that follows a given rule.● Multiply (two two-digit numbers) and divide (large numbers by one-digit divisors) using concepts of

place value.● Illustrate and explain multiplication and division using various strategies (equations, rectangular arrays,

and area models).● Identify and write a multiplication equation as a comparison of factors and a product (unknown product,

unknown factors, unknown group size, and unknown number of groups). ● Solve multi-step word problems using multiplication and division.● Use rounding to check the reasonableness of answers to problems involving multiplication and division.● Solve division problems in which remainders must be interpreted.● Represent word problems using equations with a symbol standing for the unknown quantity.● Use the four operations to solve problems involving distances and apply the area and perimeter

formulas for rectangles in real-world problems.Standards: 4.OA.4, 4.OA.5, 4.NBT.5, 4.NBT.6, 4.OA.1, 4.OA.2, 4.OA.3, 4.MD.2, 4.MD.3For more information on the strategies, standards, and explanations, visit the California Framework at: http://www.cde.ca.gov/be/st/ss/documents/ccsmathstandardaug2013.pdf Sample Problems:4.OA.5 Gain Familiarity with Factors and Multiples

4.NBT.5 Multi-Digit Multiplication Using Place Value Strategies (Area Model, Partial Products, Equations)

4.NBT.6 Multi-Digit Divisi

Page 2: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

on Using Place Value Strategies (Area Model, Partial Quotients, Equations)

4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using Tape Diagrams

Unknown Product: Skyler has Unknown Factor (Group Size Unknown Factor (Number of 4 times as many books as Unknown): Kiara sold 45 tickets Groups Unknown): A used bicycleAraceli. Is Araceli has 36 books, to the school play, which is 3 times costs $75; a new one costs $300. How many books does Skyler as many as the number of tickets How many times as much does theHave? sold by Tomas. How many tickets new bike cost compared with the did Tomas sell? used bike?4.MD.3 Apply the Area and Perimeter Formulas for Rectangles in Real-World Problems

Activities at Home:

● Draw pictures and make models of numbers.

● Discuss grocery shopping,

buying household supplies, or recipes in the context of wanting to purchase more than one (use multiplication) or how much a single item would be if more than one comes in a package (use division).

● Take a multiplication and/or division problem and illustrate using an area model, array, or partial products/quotients. ● Measure different locations in your home or outside. Ask for the formulas of area and perimeter and then have your child solve

for both. This will allow them to see real-world examples of how these two mathematical procedures are used in an everyday context. For example, if you wanted to purchase a new rug for the living room or a fence in a portion of the yard.

● Use a ruler to find the area and perimeter of plane figures. ● Have students create patterns with a given rule as it relates to multiplication and division.● Practice addition and subtraction facts.

Learning Links: 4.OA.5 Gain Familiarity with Factors and Multiples

● https://learnzillion.com/resources/72543-generate-number-or-shape-patterns-and-identify-pattern-features-4-oa-c-5 4.NBT.5 Multi-Digit Multiplication Using Place Value Strategies (Area Model, Partial Products, Equations)

● https://learnzillion.com/resources/73077-multiply-multi-digit-whole-numbers4.NBT.6 Multi-Digit Division Using Place Value Strategies (Area Model, Partial Quotients, Equations)

● https://learnzillion.com/resources/72478-find-whole-number-quotients-and-remainders-with-up-to-four-digit-dividends-4-nbt-b-64.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using Tape Diagrams

● https://learnzillion.com/resources/72926-interpret-multiplication-as-a-comparison ● https://learnzillion.com/resources/72311-solve-word-problems-using-multiplicative-comparisons ● https://learnzillion.com/resources/72712-solve-multi-step-word-problems

4.MD.3 Apply the Area and Perimeter Formulas for Rectangles in Real-World Problems● https://learnzillion.com/resources/73049-apply-formulas-for-area-and-perimeter

To see an electronic copy of this parent letter, with “clickable” links, please go to the Common Core page at http://www.gusd.net/. Follow the links to Mathematics, Grade 4. Scroll to the bottom of page and click on Unit 2.

Page 3: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

Translated  By:  GUSD  Intercultural  Office   Math  Unit  2  Parent  letter-­‐4th  grade  Armenian   Professional  Development  

Glendale Unified School District  Maj;matika\i ousoumnakan ‘ragir  

T;[;kouj\ounn;r 4-rd dasarani ‘no[n;ri famar  Bavin 2^ Ambo[= jw;ri baxmapatkoum … bavanoum  

 Inc ksowori ];r ;r;.an^  :rkrord bavnoum% a,ak;rtn;re ksowor;n … kfaskanan ambo[= jw;ri baxmapatkoume … bavanoume! A,ak;rtn;re ksowor;n … kfaskanan artadricn;re … baxmapatikn;re% incp;s na… parx … ba[adr\al jw;re! A,ak;rtn;re k,arounak;n ørinakn;re tramaban;l … gtn;l baxmapatkman kam bavanman f;t a®ncwo[ ørinaki skxbounqe! A,ak;rtn;re baxmaqa\l .ndirn;r klou‘;n ;rixa\in kam ]o[a\in diagramn;r øgtagor‘;low … klou‘;n irakan k\anqi baxmapatkman … bavanman .ndirn;r! A,ak;rtn;re kbar;law;n ir;nz% 100-iz m;‘ ambo[= jw;row baxmapatkoum kam bavanoum katar;lou fmtouj\ounn;re! A,ak;rtn;re mod;ln;r% incp;s ørinak^ tara‘qa\in kam ou[[ank\an mod;ln;r køgtagor‘;n … a\d mod;ln;re kkapakz;n fawasarman f;t! A\spisiw a,ak;rtn;re% mak;r;si … parag‘i bana]…;re øgtagor‘;low% baxmapatkman irakan .ndirn;r … tara‘akan ca'oumn;r parounako[ .ndirn;r klou‘;n!  MASNAWORAP:S% A<AK:RTN:RE KSOWOR:N J: INCP:S^  

● Gtn;l minc… 100 jw;ri artadricn;re … yanac;l parx … ba[adr\al jw;re!  ● Oro,;l j; ard\oq trwa‘ jiwe mi a\l miani, jwi baxmapatikn h j; oc!  ● Jw;row kam patk;rn;row ørinakn;r kaxm;l … w;rlou‘;l trwa‘ skxbounqin f;t…;low!  ● Baxmapatk;l (;rkou ;rkani, jw;r) … bavan;l (m;‘ jw;re miani, bavanararow) jwa\in arv;qi

faskazouj\ounn øgtagor‘;low!  ● Ørinakn;row lousaban;l … bazatr;l baxmapatkoume … bavanoume tarb;r strat;gian;r

øgtagor‘;low (fawasaroum% ou[[ank\an … tara‘qa\in ørinakn;r)!  ● Yanac;l … gr;l baxmapatkman fawasaroum orp;s artadricn;ri … artadr\ali fam;matouj\oun

(anfa\t artadr\al% anfa\t artadricn;r% anfa\t .mbi ca' … .mb;ri anfa\t jiw)!  ● Baxmaqa\l .ndirn;r lou‘;l baxmapatkoum … bavanoum øgtagor‘;low!  ● Klorazn;l^ baxmapatkoum … bavanoum parounako[ .ndirn;ri patas.ann;re stoug;lou famar!  ● Lou‘;l bavanman .ndirn;r% ort;[ mnazordn;re p;tq h m;knabanw;n!  ● >ndire n;rka\azn;l fawasaroumow … anfa\t qanaki famar simwol øgtagor‘;l!  ● Maj;matikakan cors gor‘o[ouj\ounn;rn øgtagor‘;l tara‘ouj\oun parounako[ .ndirn;re lou‘;lou

famar … kira®;l ou[[ank\ounn;ri mak;r;si … parag‘i bana]…;re irakan k\anqi .ndirn;roum!    Ca'oro,icn;r^4.OA.4, 4.OA.5, 4.NBT.5, 4.NBT.6, 4.OA.1, 4.OA.2, 4.OA.3, 4.MD.2, 4.MD.3    Strat;gian;ri% ca'oro,icn;ri … bazatrouj\ounn;ri masin faw;l\al t;[;kouj\an famar a\z;l;q

http://www.cde.ca.gov/be/st/ss/documents/ccsmathstandardaug2013.pdf ka\qh=!    Ørinakn;r^  4.OA.5 ’anojanal artadricn;ri … baxmapatikn;ri f;t  

           

   4.NBT.5 Baxmani, jw;ri baxmapatkoum^ jwa\in arv;qi strat;gian;r øgtagor‘;low (tara‘qa\in mod;l% masnaki artadr\al% fawasaroum)

   

#   Artadricn;r   Baxmapatikn;r  

4  9  12  

1,  2,  4  1,  3,  9  1,  2,  3,  4,  6,12  

4,  8,  12,  16…  9,  18,  27,  36…  12,  24,  36,  48…  

 

Page 4: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

Translated  By:  GUSD  Intercultural  Office   Math  Unit  2  Parent  letter-­‐4th  grade  Armenian   Professional  Development  

4.NBT.6 Baxmani, jw;ri bavanoum^ jwa\in arv;qi strat;gian;r øgtagor‘;low (tara‘qa\in mod;l% masnaki artadr\al% fawasaroum)  

 

   

4.OA.1-3 Irakan k\anqi baxmapatkman .ndirn;r^ ;rixa\in a[\ousak øgtagor‘;low!  

 Anfa\t artadr\al^ Aran

4 angam aw;li ,at girq ouni

qan Anan! Anan 36 girq ouni!

Qani# girq ouni Aran!

Anfa\t artadric (Anfa\t .mbi ca')^ Kar;ne .a[i famar 45 toms waya®;z% ore 3 angam aw;li ,at h Jowmasi waya®a‘ toms;riz! Qani# toms waya®;z Jowmase!

Anfa\t artadric (.mb;ri anfa\t jiw)^ Øgtagor‘wa‘ f;‘aniwe $75 arv;% nore^ $300! Nor f;‘anwi gine qani# angam aw;li ,at h fin f;‘aniwi f;t fam;mata‘!

4.MD.3 Ou[[ank\an mak;r;si … parag‘i bana]…;re øgtagor‘;l irakan k\anqi .ndirn;ri famar!      

Tane katarwo[ a,.atanqn;r  ● Nkarn;r nkar;q … jw;ri mod;ln;r patrast;q!  ● Qnnark;q par;na\in gnoumn;re% tna\in apranqn;ri gnoumn;re kam stazagr;re m;kiz aw;lin gn;lou famar kam

;j; apranqe kapozow h% m;ke incqan klini ( bavanoum øgtagor‘;q)!  ● W;rzr;q baxmapatkaman …/kam bavanman .ndir … a\n zouzadr;q tara‘qa\in mod;l% ,aran kam masnaki

artadr\al/qanord øgtagor‘;low!  ● Ca';q tarb;r wa\r;r ];r tane kam drsoum! :r;.a\in farzr;q mak;r;si … parag‘i bana]…;re% a\nouf;t…

fan]narar;q nran% or gtni a\d tara‘qi j; mak;r;se … j; paragi‘e! A\spisiw% ;r;.an kt;sni j; incp;s h a\s maj;matikakan gor‘o[ouj\ounn;re øgtagor‘woum irakan k\anqoum! Ørinak% zankanoum ;q nor gorg gn;l s;n\aki famar kam zankapat^ baki famar!  

● Gt;q parx patk;ri mak;r;se … paragi‘e qanoni øgnouj\amb!  ● A,ak;rtin fan]narar;q trwa‘ skxbounqow baxmapatkmane … bavanmann a®ncwo[ ørinakn;r st;[‘;l!  ● Goumarman … fanman warvouj\oun katar;q!  

 

Ousouzman fangou\zn;r  4.OA.5 ’anojanal artadricn;ri … baxmapatikn;ri f;t  

● https://learnzillion.com/resources/72543-generate-number-or-shape-patterns-and-identify-pattern-features-4-oa-c-5  4.NBT.5 Baxmani, jw;ri baxmapatkoum^ jwa\in arv;qi strat;gian;r øgtagor‘;low (tara‘qa\in mod;l% masnaki artadr\al% fawasaroum)  

● https://learnzillion.com/resources/73077-multiply-multi-digit-whole-numbers  4.NBT.6 Baxmani, jw;ri bavanoum^ jwa\in arv;qi strat;gian;r øgtagor‘;low (tara‘qa\in mod;l% masnaki artadr\al% fawasaroum)  

● https://learnzillion.com/resources/72478-find-whole-number-quotients-and-remainders-with-up-to-four-digit-dividends-4-nbt-b-6  4.OA.1-3 Irakan k\anqi baxmapatkman .ndirn;r^ ;rixa\in a[\ousakow  

● https://learnzillion.com/resources/72926-interpret-multiplication-as-a-comparison  ● https://learnzillion.com/resources/72311-solve-word-problems-using-multiplicative-comparisons  ● https://learnzillion.com/resources/72712-solve-multi-step-word-problems  

4.MD.3 Ou[[ank\an mak;r;si … parag‘i bana]…;re øgtagor‘;l irakan k\anqi .ndirn;ri famar  ● https://learnzillion.com/resources/73049-apply-formulas-for-area-and-perimeter  

 

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 4-rd dasarani bavin 2-e (Unit 2) !  

Page 5: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

글렌데일 통합교육구 수학 교과과정

4 학년 학부모 정보

단원 2: 자연수 곱셈 및 나눗셈    

귀 자녀는 무엇을 배울 것인가: 단원 2 에서, 학생들은 자연수 곱셈 및 나눗셈에 대한 이해를 발전시키기 시작한다. 학생들은 소수 및 합성수와 함께 약수와 배수에 대한 이해를 보일 것이다. 또한 학생들은 곱셈이나 나눗셈과 연관된 주어진 패턴 규칙과 연결하여 숫자 패턴에 대한 추리를 계속한다. 학생들은 실제 상황에서 곱셈 및 나눗셈 문제를 시각화하고 푸는데 도움이 되도록 테이프 도표 또는 막대 도표를 사용하여 다단계 응용문제들을 풀 것이다. 학생들은 100 이상의 자연수 곱셈 및 나눗셈에 대한 기초력이 깊어지도록 할 것이다. 학생들은 넓이 모델과 시각형 배열과 같이 시각적 표현을 사용하고 이 시각적 모델을 방정식으로 연결할 것이다. 이러한 연결은 학생들이 넓이 및 둘레 공식을 사용하여 거리 측정이 포함되는 문제들과 실제 시나리오에서 곱셈을 사용하도록 만들 것이다. 좀 더 구체적으로 학생들은 다음의 것들을 배울 것이다:  

• 100 까지 숫자에서 모든 약수의 짝을 찾고 자연수를 소수와 합성수로 판별하기. • 주어진 자연수가 달리 주어진 한자리 숫자의 배수인지 여부 결정하기. • 주어진 규칙을 따르는 숫자 또는 도형 패턴을 만들고 분석하기. • 자리값 개념을 사용한 곱셈 (2 개의 두 자릿수) 및 나눗셈 (큰 숫자를 한 자릿수 숫자로 나누기). • 다양한 방법들을 사용하여 곱셈 및 나눗셈을 보이기 및 설명하기 (방정식, 사각형 배열 및 넓이 모델). • 약수 및 곱 비교로서 곱셈 방정식을 판별하기 및 작성하기 (미지수 곱, 미지수 약수, 미지수 그룹 사이즈,

미지수 숫자 그룹). • 곱셈 및 나눗셈을 사용하여 다단계 응용문제 풀기. • 곱셈 및 나눗셈이 포함되는 문제들에 대한 답의 타당성을 점검하기 위해 반올림 사용하기. • 나머지를 이해해야만 되는 나눗셈 문제 풀기. • 모르는 양을 대신하는 심볼이 있는 방정식을 사용하여 응용문제 표현하기 • 실제 문제에서 거리 및 사각형 넓이 및 둘레 공식 응용이 포함되는 문제들을 풀기 위해 네가지 연산

사용하기.  표준 : 4.OA.4, 4.OA.5, 4.NBT.5, 4.NBT.6, 4.OA.1, 4.OA.2, 4.OA.3, 4.MD.2, 4.MD.3    방법, 표준 및 설명에 대한 더 많은 정보에 대해선, 가주 프레임워크를 방문하시오: http://www.cde.ca.gov/be/st/ss/documents/ccsmathstandardaug2013.pdf    샘플 문제 :  4.OA.5 약수 및 배수와 익숙하게 되기  

     

   4.NBT.5 자리값 방법을 사용한 다자릿수 곱셈 (넓이 모델 , 부분 곱 , 방정식 )  

 

약수 배수

Page 6: Glendale Unified School District · on Using Place Value Strategies (Area Model, Partial Quotients, Equations) 4.OA.1-3 Multiplicative Comparison Problems in Real-World Context Using

4.NBT.6 자리값 방법을 사용한 다자릿수 나눗셈 (넓이 모델 , 부분 몫 , 방정식 )  

 

 

 4.OA.1-3 테이프 도표를 사용하여 실세상 상황에서의 곱셈 비교 문제  

 미지수 곱 : Skyler 는 Araceli 보다 미지수 약수 (미지수 그룹 미지수 약수 (미지수 숫자 그룹 ):  4 배나 많은 책을 갖고 있다. 사이즈 ): Kiara 는 학교 연극 티켓을 중고 자전거의 가격은 $75 이고;  Araceli 가 36 권의 책을 갖고 있다면, 45 장 팔았으며 이는 Tomas 가 판 새 자전거의 가격은 $300 이다.  Skyler 는 몇 권의 책을 갖고 있는가? 티켓보다 3 배나 많다. Tomas 는 새 자전거의 가격은 중고 자전거 가격에   몇 장의 티켓을 판매하였는가? 비해 몇 배나 더 비싼가?    

4.MD.3 실세상 문제에서 사각형 넓이 및 둘레 공식 응용      

가정에서의 활동:  ● 숫자 모델 그림을 그리고 만든다.  ● 식료품 쇼핑, 가정용품 구입 또는 한 품목에서 하나 이상 구입하는 상황 (곱셈 사용) 또는 한 봉투에 하나 이상 있는 경우, 한 개의

가격이 얼마 (나눗셈)인지 찾는 방법을 논의한다.  ● 곱셈 및/또는 나눗셈 문제를 갖고 넓이 모델, 배열 또는 부분 곱/몫을 사용하여 설명한다.  ● 집 안팎의 여러 다른 장소들을 측정한다. 넓이와 둘레에 대한 공식을 물은 후 자녀에게 넓이와 둘레 모두를 풀도록 한다. 이것은

자녀에게 이 두가지의 수학적 과정이 매일 매일의 상황 예를 들어, 거실에 새로운 양탄자를 깔거나 뒷마당에 치기 위한 울타리 구입의 경우, 이것이 어떻게 사용되는지 실세상 예를 보도록 허용한다.  

● 평면 도형의 넓이 및 둘레를 찾기 위해 자를 사용한다.  ● 자녀에게 곱셈 및 나눗셈과 관련된 주어진 규칙으로 패턴을 만들도록 한다.  ● 덧셈 및 뺄셈 연산을 연습한다.  

 학습 링크 :  4.OA.5 약수 및 배수 친밀성 습득  

● https://learnzillion.com/resources/72543-generate-number-or-shape-patterns-and-identify-pattern-features-4-oa-c-5  4.NBT.5 자리값 방법을 사용한 다자릿수 곱셈 (넓이 모델 , 부분 곱 , 방정식 )  

● https://learnzillion.com/resources/73077-multiply-multi-digit-whole-numbers  4.NBT.6 자리값 방법을 사용한 다자릿수 나눗셈 (넓이 모델 , 부분 몫 , 방정식 )  

● https://learnzillion.com/resources/72478-find-whole-number-quotients-and-remainders-with-up-to-four-digit-dividends-4-nbt-b-6  4.OA.1-3 테이프 도표를 사용하여 실세상 상황에서의 곱셈 비교 문제  

● https://learnzillion.com/resources/72926-interpret-multiplication-as-a-comparison  ● https://learnzillion.com/resources/72311-solve-word-problems-using-multiplicative-comparisons  ● https://learnzillion.com/resources/72712-solve-multi-step-word-problems  

4.MD.3 실세상 문제에서 사각형 넓이 및 둘레 공식 응용  ● https://learnzillion.com/resources/73049-apply-formulas-for-area-and-perimeter  

 

본 학부모 서한에 대한 “접속 가능한” 전자 사본 링크는 커먼 코어 (공통핵심 ) 페이지 www.gusd.net 를 보시오 . 4 학년 수학 링크를 따라가 페이지 맨아래로 가서 단원 2 (Unit 2)를 클릭하시오 .

Translated by: GUSD, Intercultural Department Professional Development – Parent Letter, Grade 4 Unit 2 Korean 9/2/16

둘레 공식

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Distrito Escolar Unificado de Glendale Plan de Estudios de Matemáticas

4º Grado - Información para los padresUnidad 2: Multiplicación y división de números enteros

Lo que su hijo aprenderá:En la Unidad 2, los estudiantes empezarán a desarrollar la comprensión de la multiplicación y división de los números enteros. Los estudiantes demostrarán su comprensión de los factores y múltiplos, así como los números primos y compuestos. Los estudiantes también continuarán a razonar sobre patrones numéricos, relacionando como la regla de un patrón corresponde a la multiplicación o división. Los estudiantes resolverán problemas contextuales de varios pasos utilizando un diagrama de cinta o diagrama de barras para ayudar a visualizar y resolver problemas de multiplicación y división en un contexto del mundo real. Los estudiantes profundizarán sus habilidades básicas de multiplicación y división de números enteros mayores que 100. Los estudiantes utilizarán representaciones visuales, tales como modelos de área y matrices rectangulares y relacionarán el modelo visual con una ecuación. Se efectuará la relación para que los estudiantes utilicen la multiplicación en escenarios del mundo real, usando fórmulas de área y perímetro y problemas que incluyan mediciones de distancia. MÁS ESPECÍFICAMENTE, LOS ALUMNOS APRENDERÁN CÓMO: ● Buscar todos los pares de factores de números hasta 100 e identificar los números enteros como primos o

compuestos. ● Determinar si un número entero dado es un múltiplo de otro número de un dígito dado. ● Generar y analizar un patrón de números o figuras que sigue una regla determinada. ● Multiplicar (dos números de dos dígitos) y dividir (números grandes entre divisores de un dígito) utilizando

conceptos de valor posicional. ● Ilustrar y explicar la multiplicación y división utilizando diversas estrategias (ecuaciones, matrices

rectangulares, y los modelos de área). ● Identificar y escribir una ecuación de multiplicación como una comparación de factores y un producto

(producto desconocido, factores desconocidos, el tamaño del grupo desconocido, y número desconocido de grupos).

● Resolver problemas de varios pasos usando la multiplicación y la división. ● Uso de redondeo para comprobar la razonabilidad de las respuestas a los problemas de multiplicación y

división. ● Resolver problemas de división en la que los residuos deben ser interpretados. ● Representar problemas usando ecuaciones con un símbolo que represente la cantidad desconocida. ● Usar las cuatro operaciones para resolver problemas de distancias y aplicar las fórmulas de área y

perímetro de rectángulos en problemas del mundo real.Estándares: 4.OA.4, 4.OA.5, 4.NBT.5, 4.NBT.6, 4.OA.1, 4.OA.2, 4.OA.3, 4.MD.2, 4.MD.3Para obtener más información sobre las estrategias, normas y explicaciones, visite el Marco de Referencia de California en: http://www.cde.ca.gov/be/st/ss/documents/ccsmathstandardaug2013.pdf Ejemplos de problemas: 4.OA.5 Familiarizarse con factores y múltiplos

4.NBT.5 Multiplicación de varios dígitos usando estrategias valor posicional (área del modelo, los productos parciales, ecuaciones)

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4.NBT.6 División de múltiples dígitos con Valor posicional Estrategias (área del modelo, cocientes parciales, ecuaciones)

4.OA.1-3 Problemas de comparación multiplicativa en el contexto del mundo real usando diagramas de cinta

Producto desconocido: Skyler tiene 4 veces más libros que Araceli. Araceli tiene 36 libros, ¿Cuántos libros tiene Skyler?

Factor Desconocido (Tamaño del grupo desconocido): Kiara vendió 45 entradas para la obra de la escuela, que es 3 veces más que el número de entradas vendidas por Tomas. ¿Cuántas entradas vendió Tomas?

Factor Desconocido (número de grupos desconocido): Una bicicleta usada cuesta $ 75; una nueva cuesta $ 300. ¿Cuántas veces más cuesta la bicicleta nueva en comparación con la bicicleta usada?

4.MD.3 Aplicar las fórmulas de área y perímetro para los rectángulos en problemas del mundo real

Actividades en el hogar:● Hacer dibujos y modelos de números. ● Analizar las compras de alimentos, la compra de artículos de uso doméstico, o ingredientes en el contexto de querer

comprar más de un artículo (uso de la multiplicación) o cuánto costaría un solo artículo si el paquete tiene más de uno (uso de la división).

● Imaginar un problema de multiplicación y / o división e ilustrar el uso de un modelo de área, matriz o productos / cocientes parciales.

● Medir diferentes lugares en la casa o en el exterior. Pedirle a su hijo que recite las fórmulas de área y perímetro y los resuelva. Esto les permitirá ver ejemplos reales de cómo se utilizan estos dos procedimientos matemáticos en un contexto cotidiano. Por ejemplo, si usted quiere comprar una nueva alfombra para la sala de estar o una muro en una parte del patio.

● Usar una regla para encontrar el área y perímetro de figuras planas. ● Hacer que los estudiantes creen patrones con una regla determinada en relación con la multiplicación y la división. ● Practicar la suma y la resta.

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Enlaces de aprendizaje: 4.OA.5 Familiarizarse con factores y múltiplos

● https://learnzillion.com/resources/72543-generate-number-or-shape-patterns-and-identify-pattern-features-4-oa-c-5 4.NBT.5 Multiplicación de varios dígitos usando estrategias valor posicional (área del modelo, los productos parciales, ecuaciones)

● https://learnzillion.com/resources/73077-multiply-multi-digit-whole-numbers4.NBT.6 División de múltiples dígitos con Valor posicional Estrategias (área del modelo, cocientes parciales, ecuaciones)

● https://learnzillion.com/resources/72478-find-whole-number-quotients-and-remainders-with-up-to-four-digit-dividends-4-nbt-b-64.OA.1-3 Problemas de comparación multiplicativa en el contexto del mundo real usando diagramas de cinta

● https://learnzillion.com/resources/72926-interpret-multiplication-as-a-comparison ● https://learnzillion.com/resources/72311-solve-word-problems-using-multiplicative-comparisons ● https://learnzillion.com/resources/72712-solve-multi-step-word-problems

4.MD.3 Aplicar las fórmulas de área y perímetro para los rectángulos en problemas del mundo real● https://learnzillion.com/resources/73049-apply-formulas-for-area-and-perimeter

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 4. Vaya a la parte inferior de la página y haga clic en la unidad 2.