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• 多項式
• Factors
• 生成物

### 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!

### 学習目標例

• 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 インストラクター用ガイド（pdf）には、PhETチームが作成したヒント集が含まれています。 ( PDF ).

### Teacher-Submitted Activities

Games Remote Lesson ideas  Trish Loeblein 大学基礎

Remote

Expanding and Factoring Algebraic Expressions  Amanda McGarry 中学 Guided 数学
Algebraic Expressions  Amanda McGarry 中学 Guided 数学
Exploring Factoring as Undoing the Distributive Property Sarah Hampton 中学

Guided 数学
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López 高校

その他 数学

PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López 大学基礎

その他 物理学

Middle School Math Sim Alignment Amanda McGarry 中学 その他 数学
Using the area model with expressions Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry 中学 Discuss 数学
Modelo de Áreas, Cambio de Expresiones Andrés Gualberto Palomo Cuevas 高校 宿題
Remote

Would You Rather ... Karen Gann 高校 Guided 数学
Area Model Algebra - Multiplying Polynomials Carolyn Felknor 中学 Guided 数学
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira 中学 宿題

Distributive Property Review Tim Kissinger and Larry Peters 中学 Guided
Discuss

アラビア語 All العربية  جبر نموذج المساحة
アルバニア語 All shqip  Modeli Syprinës: Algjebër
イタリア語 All italiano  Rappresentazione grafica della moltiplicazione in algebra
ウクライナ語 All українська  Площинна модель. Алгебра オランダ語 All Nederlands  Algebra van oppervlakte
カザフ語 All Kazakh  Ауданды есептеу
ギリシャ語 All Ελληνικά  Υπολογισμός εμβαδού
グジャラート語 All Gujarati  ક્ષેત્રફળ મોડેલ - બીજગણિત
シンハラ語 All Sinhalese  වර්ගඵල ආකෘති වීජ ගණිතය
スウェーデン語 All svenska  Areamodellen och algebra
スペイン語 All español  Modelo de Áreas: Álgebra スペイン語（ペルー） All español (Perú)  Modelo de Área con Álgebra
スペイン語（メキシコ） All español (México)  Modelo de Áreas: Álgebra セルビア語 All Српски  Математика преко површина - Алгебра
タミル語 All Tamil  மாதிரி உருவின் எண்(அட்சர) கணிதம்
デンマーク語 All Dansk  Arealmodel, algebra
ドイツ語 All Deutsch  Flächenmodell Algebra
トルコ語 All Türkçe  Alan Modeli İle Cebir
バスク語 All Euskara  Azalera-modeloan algebra
ハンガリー語 All magyar  Területmodell: algebra
ヒンディー語 All हिंदी  बीजगणित -नमूने का क्षेत्रफल
フィンランド語 All suomi  Pinta-ala ja algebra
ブラジルポルトガル語 All português (Brasil)  Modelo de Área: Álgebra
フランス語 All français  Modélisation par les aires - Algèbre
ベトナム語 All Tiếng Việt  Đại số với mô hình diện tích
ペルシャ語 All فارسی  جبر مدل مساحت
ボスニア語 All Bosanski  Matematički model površina - Algebra
ポルトガル語 All português  Modelo de Área: Álgebra
ポーランド語 All polski  Model pola - wyrażenia algebraiczne
マラッタ語 All मराठी  क्षेत्रफळाचे बीजगणित
モンゴル語 All Монгол (Монгол)  Талбайн загварын Алгебр
ラトビア語 All Latviešu  Laukuma modeļa algebra
ロシア語 All русский  Вычисление площади

HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iOS 12+ Safari

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:

Macintosh Systems:

Linux Systems:

デザインチーム サードパーティのライブラリ 謝辞
• 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