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描述

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!

示范 学习目标

  • 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.
版本 1.0.10

教师指南

下载教师指南 PDF 仿真程序控制概述,简化模型,学生视角的思考 ( PDF ).

视频引导

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教师提交的活动

Expanding and Factoring Algebraic Expressions 一颗金星 象征着 是通过PhET设计指南所设计出来的高质量的探究活动。 这个贡献是由PhET设计的。 Amanda McGarry 初中 指导 数学
Algebraic Expressions 一颗金星 象征着 是通过PhET设计指南所设计出来的高质量的探究活动。 这个贡献是由PhET设计的。 Amanda McGarry 初中 指导 数学
Exploring Factoring as Undoing the Distributive Property 一颗金星 象征着 是通过PhET设计指南所设计出来的高质量的探究活动。 Sarah Hampton 高中
初中
指导 数学
Middle School Math Sim Alignment 这个贡献是由PhET设计的。 Amanda McGarry 初中 其它 数学
Using the area model with expressions 这个贡献是由PhET设计的。 Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry 初中 讨论 数学
Would You Rather ... Karen Gann 高中 指导 数学
Area Model Algebra - Multiplying Polynomials Carolyn Felknor 初中 指导 数学
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira 初中 实验室
家庭作业
数学
Distributive Property Review Tim Kissinger and Larry Peters 初中 讨论
指导
数学

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新的HTML5类型的程序可以在iPad,Chromebook以及PC端(包含mac和linux系统)上运行。

iPad:

iOS 8+ Safari

iPad2或之后的iPad产品支持HTML5类型的程序。如果您是iPad用户,请点击这里。


Android:
无官方支持。如果您需要在安卓平台运行HTML5程序,我们建议您使用最新版本的谷歌浏览器和安卓4.1+版本。

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OS 10.9.5 或之后的系统版本,Safari 9+版本,或者火狐浏览器,谷歌浏览器的最新版本均支持我们的程序。

Linux 系统:
无官方支持。请联系phethelp@colorado.edu。


Java and Flash 程序:

Java 与 Flash程序可以在PC端,mac端,及linux系统上运行。具体的系统配置要求如下:

Windows 系统:
Windows 10, 8.1, 7
内存: 256 MB
浏览器: 微软Edge浏览器,IE 11浏览器,火狐浏览器,谷歌浏览器

Macintosh 系统:
Mac OS X 10.9.5+
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64位浏览器(例如Safari,火狐,谷歌等)

Linux 系统:
Oracle Linux 5.5+1
Oracle Linux 6.x (32位), 6.x (64位)2
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Ubuntu Linux 12.04 LTS, 13.x
Suse Linux Enterprise Server 10 SP2+, 11.x
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开发团队 第三方支持 感谢
  • 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)
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