つり合いを作ろう

つり合いを作ろう スクリーンショット  ダウンロード  組み込む
  • Solving Equations
  • Inequalities
  • Inverse Operations

コンテンツ

  • Solving Equations
  • Inequalities
  • Inverse Operations

Description

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Discover the rules for keeping it balanced. Collect stars by playing the game!

学習目標例

  • Solve and manipulate algebraic equations by applying properties of real numbers (in particular, the inverse properties of addition and multiplication) and properties of equality
  • Solve and manipulate algebraic equations by substituting different values for a variable
  • Use a balance model to solve an equation for an unknown, and justify your strategies for solving
  • Solve an equation using only universal operations

Standards Alignment

Common Core - Math

6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
8.EE.C.7
Solve linear equations in one variable.
8.EE.C.7a
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
HSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
HSA-REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
HSA-REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Version 1.0.12

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 ).

Teacher-Submitted Activities

Introducción a la igualdad 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。 Diana López 中学
高校
実験
Guided
宿題
数学
Games Remote Lesson ideas 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。 Trish Loeblein 中学
小学
高校
大学基礎
Remote
宿題
物理学
化学
数学
Balancing Act A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Michael Reynolds 中学 Guided 数学
What is Equality A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. David Wood 中学
高校
Discuss
実験
Guided
宿題
数学
Introduction to Inequalities A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Marleene Buttice 中学 Guided 数学
Solving Multi-Step Equations A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Meenakshi Raghavan 中学 Guided 数学
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) 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。 Diana López 高校
中学
その他 生物学
物理学
数学
化学
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) 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。 Diana López 大学基礎
高校
その他 化学
数学
物理学
PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) 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。 Diana López 小学
中学
証明
実験
宿題
Discuss
Guided
数学
化学
天文学
物理学
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
Equação e balança Alison Sousa da Silva, Ana Carolina Costa Pereira 中学 Guided
実験
数学
Equality Explorer - 6th Grade intro to solving Trevor Gibson 中学 Guided 数学
Exploring Equations Akili Obika 中学
高校
Guided 数学

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ブラジルポルトガル語 All português (Brasil) Download Run now Explorador da Igualdade
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ボスニア語 All Bosanski Download Run now Istraživač jednačina
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ポーランド語 All polski Download Run now Poznajemy równania
モンゴル語 All Монгол (Монгол) Download Run now Тэнцэтгэл Судлах
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HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 12+ 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, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.12+, Safari 12+, 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
  • Amanda McGarry (lead designer)
  • Chris Malley (developer)
  • Diana López Tavares
  • Ariel Paul
  • Kathy Perkins
  • Argenta Price
  • Beth Stade
  • David Webb
  • Mariah Hermsmeyer (graphic arts)
  • Cheryl McCutchan (graphic arts)
  • almond-0.2.9.js
  • base64-js-1.2.0.js
  • easing-equations-r12
  • 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
  • Tween-r12.js