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### Topics

• Partial Products
• Factors
• Multiplication
• Area Model

### Description

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying large numbers. Use the game screen to test your problem solving strategies!

### Sample Learning Goals

• 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.
Version 1.2.1

### Teacher Tips Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

### Teacher-Submitted Activities

Middle School Math Sim Alignment Amanda McGarry MS Other Mathematics
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López HS
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PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López UG-Intro
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PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) Diana López K-5
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Albanian All shqip  Modeli i Syprinës: Shumëzimi
Arabic All العربية  ضرب مساحة نموذج
Basque All Euskara  Azalera-modeloan biderkaketa
Bosnian All Bosanski  Matematički model površina - Množenje
Chinese (Simplified) All 中文 (中国)  面积模型乘法
Chinese (Traditional) All 中文 (台灣)  Area Model Multiplication_面積模型與乘法
Danish All Dansk  Arealmodel, gange
Dutch All Nederlands  Oppervlakte model vermenigvuldiging
Finnish All suomi  Pinta-alamallilla kertominen
French All français  Modélisation de la multiplication par les aires
German All Deutsch  Flächenmodell Multiplikation
Greek All Ελληνικά  Υπολογισμός εμβαδού - Πολλαπλασιασμός
Gujarati All Gujarati  ક્ષેત્રફળનું ગુણાકારનું મોડેલ - નિકુંજ સવાણી દ્વારા
Hindi All हिंदी  नमूने का क्षेत्रफल - गुणन
Hungarian All magyar  Területmodell: szorzás
Italian All italiano  Rappresentazione grafica della moltiplicazione
Japanese All 日本語  面積を求める
Kazakh All Kazakh  Көбейту жолымен ауданын есептеу
Korean All 한국어  면적 모형: 곱셈
Latvian All Latviešu  Lauka modeļa reizinājums
Mongolian All Монгол (Монгол)  Талбайн Загварын Үржвэр
Persian All فارسی  ضرب مدل مساحت
Polish All polski  Model pola - mnożenie
Portuguese All português  Modelo de Área: Multiplicação
Portuguese (Brazil) All português (Brasil)  Modelo de Área: Multiplicação
Russian All русский  Вычисление площади путем умножения
Serbian All Српски  Математика преко површина-Множење
Sinhalese All Sinhalese  වර්ගඵල ආකෘති ගුණ කිරීම
Spanish All español  Modelo de Áreas: Multiplicación Spanish (Mexico) All español (México)  Modelo de Áreas: Multiplicación Spanish (Peru) All español (Perú)  Modelo de Área con multiplicación
Swedish All svenska  Areamodellen - Multiplikation
Turkish All Türkçe  Alan Modelinde Çarpma İşlemi
Ukrainian All українська  Площинна модель множення
Vietnamese All Tiếng Việt  Phép nhân với mô hình diện tích

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Design Team Third-party Libraries Thanks To
• 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