面積と式の展開

面積と式の展開 スクリーンショット  ダウンロード  組み込む
  • 多項式
  • Factors
  • 生成物

コンテンツ

  • 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 1.0.10

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 ).

Video Primer

Please sign in to watch the video primer

Teacher-Submitted Activities

Expanding and Factoring Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. この貢献アクティビティは PhET によってデザインされました。 Amanda McGarry 中学 Guided 数学
Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. この貢献アクティビティは PhET によってデザインされました。 Amanda McGarry 中学 Guided 数学
Exploring Factoring as Undoing the Distributive Property A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Sarah Hampton 中学
高校
Guided 数学
Middle School Math Sim Alignment この貢献アクティビティは PhET によってデザインされました。 Amanda McGarry 中学 その他 数学
Using the area model with expressions この貢献アクティビティは PhET によってデザインされました。 Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry 中学 Discuss 数学
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 実験
宿題
数学
Distributive Property Review Tim Kissinger and Larry Peters 中学 Guided
Discuss
数学

言語 Download or Run Tips
アラビア語 All العربية Download Run now جبر نموذج المساحة
イタリア語 All italiano Download Run now Rappresentazione grafica della moltiplicazione in algebra
オランダ語 All Nederlands Download Run now Oppervlakte model algebra
カザフ語 All Kazakh Download Run now Ауданды есептеу
ギリシャ語 All Ελληνικά Download Run now Υπολογισμός εμβαδού
グジャラート語 All Gujarati Download Run now બીજગણિતનું ક્ષેત્રફળ મોડેલ -નિકુંજ સવાણી
スウェーデン語 All svenska Download Run now Areamodellen och algebra
スペイン語 All español Download Run now Modelo de Áreas: Álgebra
スペイン語(ペルー) All español (Perú) Download Run now Modelo de Área con Álgebra
スペイン語(メキシコ) All español (México) Download Run now Modelo de Áreas: Álgebra 
セルビア語 All Српски Download Run now Математика преко површина - Алгебра
タミル語 All Tamil Download Run now மாதிரி உருவின் எண்(அட்சர) கணிதம்
デンマーク語 All Dansk Download Run now Arealmodel, algebra
ドイツ語 All Deutsch Download Run now Flächenmodell Algebra
バスク語 All Basque Download Run now Azalera-modeloan algebra
ハンガリー語 All magyar Download Run now Területmodell: algebra
ヒンディー語 All हिंदी Download Run now  बीजगणित -नमूने का क्षेत्रफल 
フィンランド語 All suomi Download Run now Pinta-ala ja algebra
ブラジルポルトガル語 All português (Brasil) Download Run now Modelo de Área: Álgebra
フランス語 All français Download Run now Modélisation par les aires - Algèbre
ベトナム語 All Tiếng Việt Download Run now Đại số với mô hình diện tích
ボスニア語 All Bosanski Download Run now Matematički model površina - Algebra
ポルトガル語 All português Download Run now Modelo de Área: Álgebra
ポーランド語 All polski Download Run now Model pola - wyrażenia algebraiczne
モンゴル語 All Монгол (Монгол) Download Run now Талбайн загварын Алгебр
ラトビア語 All Latviešu Download Run now Laukuma modeļa algebra
ロシア語 All русский Download Run now Вычисление площади
英語 All English Download Run now Area Model Algebra
中国語-簡体字 All 中文 (中国) Download Run now 面积模型代数
中国語-繁体字 All 中文 (台灣) Download Run now Area Model Algebra_面積模型與代數
朝鮮語 All 한국어 Download Run now 면적 모형: 대수

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.

デザインチーム サードパーティのライブラリ 謝辞
  • 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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