Skip to Main Content
PhET Home Page
University of Colorado
Created 7/7/19. Updates available online.

Area Model Multiplication

Area Model Multiplication Screenshot
  • Partial Products
  • Factors
  • Multiplication

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 1.0.6

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Share an Activity!

Language Download or Run Tips
Arabic All العربية Run now ضرب مساحة نموذج
Basque All Basque Run now Azalera-modeloan biderkaketa
Bosnian All Bosanski Run now Matematički model površina - Množenje
Chinese (Simplified) All 中文 (中国) Run now 面积模型乘法
Chinese (Traditional) All 中文 (台灣) Run now Area Model Multiplication_面積模型與乘法
Danish All Dansk Run now Arealmodel, gange
Dutch All Nederlands Run now Oppervlakte model vermenigvuldiging
Finnish All suomi Run now Pinta-alamallilla kertominen
French All français Run now Modélisation de la multiplication par les aires
German All Deutsch Run now Flächenmodell Multiplikation
Greek All Ελληνικά Run now Υπολογισμός εμβαδού - Πολλαπλασιασμός
Gujarati All Gujarati Run now ક્ષેત્રફળનું ગુણાકારનું મોડેલ - નિકુંજ સવાણી દ્વારા
Hindi All हिंदी Run now नमूने का क्षेत्रफल - गुणन 
Hungarian All magyar Run now Területmodell: szorzás
Italian All italiano Run now Rappresentazione grafica della moltiplicazione
Japanese All 日本語 Run now 面積を求める
Kazakh All Kazakh Run now Көбейту жолымен ауданын есептеу
Korean All 한국어 Run now 면적 모형: 곱셈
Latvian All Latviešu Run now Lauka modeļa reizinājums
Mongolian All Монгол (Монгол) Run now Талбайн Загварын Үржвэр
Polish All polski Run now Model pola - mnożenie
Portuguese All português Run now Modelo de Área: Multiplicação
Portuguese (Brazil) All português (Brasil) Run now Modelo de Área: Multiplicação
Russian All русский Run now Вычисление площади путем умножения
Serbian All Српски Run now Математика преко површина-Множење
Spanish All español Run now Modelo de Áreas: Multiplicación Download teacher tips PDF
Spanish (Mexico) All español (México) Run now Modelo de Áreas: Multiplicación  Download teacher tips PDF
Spanish (Peru) All español (Perú) Run now Modelo de Área con multiplicación
Swedish All svenska Run now Areamodellen - Multiplikation
Vietnamese All Tiếng Việt Run now Phép nhân với mô hình diện tích

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

iPad:
iOS 11+ Safari
iPad compatible sims

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

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge and Internet Explorer 11, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Design Team Third-party Libraries Thanks To
  • Amy Hanson (lead designer)
  • Amanda McGarry (co-lead)
  • 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
  • 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
English
©2019 University of Colorado.
Some rights reserved.