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Created 7/7/19. Updates available online.

Area Model Decimals

Area Model Decimals Screenshot
  • Multiplication
  • Decimals
  • Area Model

Topics

  • Multiplication
  • Decimals
  • Area Model
  • Factors
  • Partial Products

Description

Build rectangles of various sizes and relate multiplication to area. Partition a rectangle into smaller areas and discover new strategies for multiplying decimals!

Sample Learning Goals

  • Recognize that area represents the product of two numbers and is additive.
  • Develop and justify a strategy that uses the area model to simplify a decimal multiplication problem.
  • Devise a strategy to determine the product of two rational numbers (or an integer and a rational number) by representing the product as an area or the sum of areas.
  • Use an area model to understand why multiplying a given number by a decimal less than 1 results in a product smaller than the given number.
  • Interpret the product of two rational numbers using base-ten tiles

Standards Alignment

Common Core - Math

5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 5.NF.B.4a
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
 5.NF.B.4b
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 5.NF.B.5
Interpret multiplication as scaling (resizing), by:
 5.NF.B.5a
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 5.NF.B.5b
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Version 1.0.6

Language Download or Run Tips
Arabic All العربية Run now نموذج مساحة الأعداد العشرية
Basque All Basque Run now Azalera-modeloa hamartarrekin
Bosnian All Bosanski Run now Matematički model površina - Decimalni brojevi
Chinese (Simplified) All 中文 (中国) Run now 面积模型：小数
Chinese (Traditional) All 中文 (台灣) Run now Area Model Decimals_面積模型與小數
Danish All Dansk Run now Arealmodel, decimaler
Dutch All Nederlands Run now Oppervlakte model decimalen
Finnish All suomi Run now Pinta-alamalli desimaaleilla
French All français Run now Modélisation par les aires avec décimales
German All Deutsch Run now Flächenmodell Dezimalzahlen
Greek All Ελληνικά Run now Υπολογισμός εμβαδού - Δεκαδικοί
Gujarati All Gujarati Run now અપૂર્ણાંકમાં ક્ષેત્રફળનું મોડેલ - નિકુંજ સવાણી દ્વારા
Hindi All हिंदी Run now नमूने का क्षेत्रफल - दाशमिक 
Hungarian All magyar Run now Területmodell: tizedesjegyek
Italian All italiano Run now Rappresentazione grafica del prodotto di numeri decimali
Japanese All 日本語 Run now 面積と式の展開（小数）
Kazakh All Kazakh Run now Ауданды ондық бөлшектермен есептеу
Korean All 한국어 Run now 면적 모형: 소수
Latvian All Latviešu Run now Laukuma modeļa decimāldaļskaitļi
Mongolian All Монгол (Монгол) Run now Талбайн Загвар Бутархайгаар
Polish All polski Run now Model pola - ułamki dziesiętne
Portuguese (Brazil) All português (Brasil) Run now Modelo de Área: Decimais
Russian All русский Run now Вычисление площади с десятичными дробями
Serbian All Српски Run now Математика преко површина-Децимални бројеви
Spanish All español Run now Modelo de Áreas: Decimales 
Spanish (Mexico) All español (México) Run now Modelo de Áreas: Decimales
Spanish (Peru) All español (Perú) Run now Modelo de área con decimales
Swedish All svenska Run now Areamodellen och decimaltal
Tamil All Tamil Run now மாதிரிகளின் தசமப் பரப்பளவு
Vietnamese All Tiếng Việt Run now Số thập phân 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
  • 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
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