Equality Explorer_探索等式

Equality Explorer_探索等式 螢幕截圖  下載  嵌入
  • Solving Equations
  • Inequalities
  • Inverse Operations

標題

  • Solving Equations
  • Inequalities
  • Inverse Operations

描述

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!

學習目標

  • 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.
版本 1.0.10

教學提示

下載教師教學提示 PDF 檔 模擬教學的控制概觀、模型簡化與引導學生思考 ( PDF ).

老師提供的活動

Balancing Act A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Michael Reynolds 國中 指引 數學
What is Equality A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. David Wood 高中
國中
指引
作業
討論
實驗室
數學
Introduction to Inequalities A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Marleene Buttice 國中 指引 數學
Solving Multi-Step Equations A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Meenakshi Raghavan 國中 指引 數學
Middle School Math Sim Alignment 此貢獻是由 PhET 所作之設計 Amanda McGarry 國中 其它 數學
Equality Explorer - 6th Grade intro to solving Trevor Gibson 國中 指引 數學
Exploring Equations Akili Obika 國中
高中
指引 數學

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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.

設計團隊 第三方諮詢 感謝
  • 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