# Area Model Algebra

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### Popis

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!

### Ukážkové ciele vzdelávania

• 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.
Verzia 1.2.1

### Typy pre učiteľov

 Prehľad ovládacích prvkov simulácie, modelové zjednodušenie a postrehy o študentskom uvažovaní. ( PDF ).

### Video Primer

Prosím prihláste sa, pre sledovanie videa.

### Teacher-Submitted Activities

Games Remote Lesson ideas Trish Loeblein VŠ-zač
K-5
ZŠ-II

Remote
Chémia
Fyzika
Matematika
Expanding and Factoring Algebraic Expressions Amanda McGarry ZŠ-II Guided Matematika
Algebraic Expressions Amanda McGarry ZŠ-II Guided Matematika
Exploring Factoring as Undoing the Distributive Property Sarah Hampton
ZŠ-II
Guided Matematika
Middle School Math Sim Alignment Amanda McGarry ZŠ-II Iné Matematika
Using the area model with expressions Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry ZŠ-II Disk Matematika
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López ZŠ-II
Iné Fyzika
Matematika
Biológia
Chémia
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López
VŠ-zač
Iné Matematika
Fyzika
Chémia
Would You Rather ... Karen Gann Guided Matematika
Area Model Algebra - Multiplying Polynomials Carolyn Felknor ZŠ-II Guided Matematika
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira ZŠ-II
Lab
Matematika
Distributive Property Review Tim Kissinger and Larry Peters ZŠ-II Guided
Disk
Matematika
Modelo de Áreas, Cambio de Expresiones Andrés Gualberto Palomo Cuevas
Remote
Matematika
Albánčina All shqip Modeli Syprinës: Algjebër
Arabčina All العربية جبر نموذج المساحة
Bosnian All Bosanski Matematički model površina - Algebra
Čínština (Tradičná) All 中文 (台灣) Area Model Algebra_面積模型與代數
Čínština (Zjednodušená) All 中文 (中国) 面积模型代数
Dánčina All Dansk Arealmodel, algebra
Fínčina All suomi Pinta-ala ja algebra
Francúzština All français Modélisation par les aires - Algèbre
Gréčtina All Ελληνικά Υπολογισμός εμβαδού
Gujarati All Gujarati ક્ષેત્રફળ મોડેલ - બીજગણિત
Hindi All हिंदी  बीजगणित -नमूने का क्षेत्रफल
Holandčina All Nederlands Algebra van oppervlakte
Japončina All 日本語 面積と式の展開
Kazakh All Kazakh Ауданды есептеу
Kórejčina All 한국어 면적 모형: 대수
Latvian All Latviešu Laukuma modeļa algebra
Maďarčina All magyar Területmodell: algebra
Mongolian All Монгол (Монгол) Талбайн загварын Алгебр
Nemčina All Deutsch Flächenmodell Algebra
Perzština All فارسی جبر مدل مساحت
Poľština All polski Model pola - wyrażenia algebraiczne
Portugalčina All português Modelo de Área: Álgebra
Portugalčina (Brazília) All português (Brasil) Modelo de Área: Álgebra
Ruština All русский Вычисление площади
Sinhalese All Sinhalese වර්ගඵල ආකෘති වීජ ගණිතය
Srbčina All Српски Математика преко површина - Алгебра
Španielčina All español Modelo de Áreas: Álgebra
Španielčina (Mexico) All español (México) Modelo de Áreas: Álgebra
Španielčina (Peru) All español (Perú) Modelo de Área con Álgebra
Švédčina All svenska Areamodellen och algebra
Taliančina All italiano Rappresentazione grafica della moltiplicazione in algebra
Tamil All Tamil மாதிரி உருவின் எண்(அட்சர) கணிதம்
Turečtina All Türkçe Alan Modeli İle Cebir
Ukrajinčina All українська Площинна модель. Алгебра
Vietnamčina All Tiếng Việt Đại số với mô hình diện tích

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Autorský tím Iné knižnice Poďakovanie
• Jonathan Olson (developer)
• Karina Hensberry
• Susan Miller
• Ariel Paul
• Kathy Perkins
• Mariah Hermsmeyer (artwork)
• Diana López Tavares (artwork)
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