# Matematički model površina - Algebra

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Klikni i započni
Koristi ovaj HTML kod da bi se pojavio ekran sa natpisom "Klikni i započni" ("Click to Run"). Polinomi Factors Produkti PhET je podržаn od: i nаstаvnikа kаo što ste Vi!

• Polinomi
• Factors
• Produkti

### Description

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

### Primjeri obrazovnih ciljeva

• Develop and justify a method to use the area model to determine the product of a monomial and a binomial or the product of two binomials.
• Factor an expression, including expressions containing a variable.
• Recognize that area represents the product of two numbers and is additive.
• Represent a multiplication problem as the area of a rectangle, proportionally or using generic area.
• Develop and justify a strategy to determine the product of two multi-digit numbers by representing the product as an area or the sum of areas.

### Standards Alignment

#### Common Core - Math

3.MD.C.7
Relate area to the operations of multiplication and addition.
3.MD.C.7c
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.C.7d
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..
6.NS.B.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
8.EE.C.7b
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Version 1.2.1

### Teacher Tips

 Vodič za nastavnike (pdf) sadrži savjete kreirane оd strane PhET tima. ( PDF ).

### Teacher-Submitted Activities

Games Remote Lesson ideas Trish Loeblein K-5 (OŠ)
HS (VŠ)
MS (SŠ)
UG-Intro (VSŠ)
DZ
Remote
Hemija
Fizika
Matematika
Expanding and Factoring Algebraic Expressions Amanda McGarry MS (SŠ) Guided Matematika
Algebraic Expressions Amanda McGarry MS (SŠ) Guided Matematika
Exploring Factoring as Undoing the Distributive Property Sarah Hampton MS (SŠ)
HS (VŠ)
Guided Matematika
Middle School Math Sim Alignment Amanda McGarry MS (SŠ) Ostalo Matematika
Using the area model with expressions Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry MS (SŠ) Discuss Matematika
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López MS (SŠ)
HS (VŠ)
Ostalo Fizika
Biologija
Matematika
Hemija
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López HS (VŠ)
UG-Intro (VSŠ)
Ostalo Fizika
Matematika
Hemija
Would You Rather ... Karen Gann HS (VŠ) Guided Matematika
Area Model Algebra - Multiplying Polynomials Carolyn Felknor MS (SŠ) Guided Matematika
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira MS (SŠ) Lab
DZ
Matematika
Distributive Property Review Tim Kissinger and Larry Peters MS (SŠ) Guided
Discuss
Matematika
Modelo de Áreas, Cambio de Expresiones Andrés Gualberto Palomo Cuevas HS (VŠ) DZ
Remote
Matematika
Albanski All shqip Modeli Syprinës: Algjebër
Arapski All العربية جبر نموذج المساحة
Brazilski Portugalski All português (Brasil) Modelo de Área: Álgebra
Danski All Dansk Arealmodel, algebra
Engleski All English Area Model Algebra
Finski All suomi Pinta-ala ja algebra
Francuski All français Modélisation par les aires - Algèbre
Grčki All Ελληνικά Υπολογισμός εμβαδού
Gujarati All Gujarati ક્ષેત્રફળ મોડેલ - બીજગણિત
Hindu All हिंदी  बीजगणित -नमूने का क्षेत्रफल
Holandski All Nederlands Algebra van oppervlakte
Italijanski All italiano Rappresentazione grafica della moltiplicazione in algebra
Japanski All 日本語 面積と式の展開
Kazaški All Kazakh Ауданды есептеу
Kineski - Tradicionalni All 中文 (台灣) Area Model Algebra_面積模型與代數
Kineski - Uprošćen All 中文 (中国) 面积模型代数
Korejski All 한국어 면적 모형: 대수
Letonski All Latviešu Laukuma modeļa algebra
Marati All मराठी क्षेत्रफळाचे बीजगणित
Mađarski All magyar Területmodell: algebra
Mongolski All Монгол (Монгол) Талбайн загварын Алгебр
Njemački All Deutsch Flächenmodell Algebra
Persijski All فارسی جبر مدل مساحت
Poljski All polski Model pola - wyrażenia algebraiczne
Portugalski All português Modelo de Área: Álgebra
Ruski All русский Вычисление площади
Sinhaležanski All Sinhalese වර්ගඵල ආකෘති වීජ ගණිතය
Španski All español Modelo de Áreas: Álgebra
Španski (Meksiko) All español (México) Modelo de Áreas: Álgebra
Španski (Peru) All español (Perú) Modelo de Área con Álgebra
Srpski All Српски Математика преко површина - Алгебра
Švedski All svenska Areamodellen och algebra
Tamilski All Tamil மாதிரி உருவின் எண்(அட்சர) கணிதம்
Turski All Türkçe Alan Modeli İle Cebir
Ukrajinski All українська Площинна модель. Алгебра
Vijetnamski All Tiếng Việt Đại số với mô hình diện tích

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Dizajn tim Nezavisne baze i biblioteke Hvala:
• Jonathan Olson (developer)
• Karina Hensberry
• Susan Miller
• Ariel Paul
• Kathy Perkins
• Mariah Hermsmeyer (artwork)
• Diana López Tavares (artwork)
• almond-0.2.9.js
• base64-js-1.2.0.js
• FileSaver-b8054a2.js
• font-awesome-4.5.0
• game-up-camera-1.0.0.js
• he-1.1.1.js
• himalaya-0.2.7.js
• jama-1.0.2
• jquery-2.1.0.js
• lodash-4.17.4.js
• pegjs-0.7.0.js
• seedrandom-2.4.2.js
• text-2.0.12.js
• TextEncoderLite-3c9f6f0.js