Equality Explorer: Two Variables

Equality Explorer: Two Variables Screenshot  Download  Embed
  • Equations
  • Inequalities
  • System of Equations

Topics

  • Equations
  • Inequalities
  • System of Equations

Description

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with integers and variables on a balance. Find multiple ways to balance x and y to build a system of equations.

Sample Learning Goals

  • 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
  • Build a system of equations
  • Determine the solution set of a system of equations

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 1.0.11

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Middle School Math Sim Alignment This contribution was designed by PhET. Amanda McGarry MS Other Mathematics

Language Download or Run Tips
Arabic All العربية Download Run now مستكشف المساواة: متغيرين
Basque All Euskara Download Run now Berdintasun-esploratzailea: bi aldagai
Bosnian All Bosanski Download Run now Istraživač jednačina: Dvije promjenljive
Chinese (Simplified) All 中文 (中国) Download Run now 等式探索:两个变量
Chinese (Traditional) All 中文 (台灣) Download Run now Equality Explorer: Two Variables_探索等式:兩個變數
Danish All Dansk Download Run now Ligevægts-visning: To variabler
Dutch All Nederlands Download Run now Ontdek gelijkheid: twee veranderlijken
French All français Download Run now Explorateur d'équation : Deux variables
German All Deutsch Download Run now Gleichheit schaffen: Zwei Variablen
Greek All Ελληνικά Download Run now Εξερευνητής εξισώσεων: δυο μεταβλητές
Hindi All हिंदी Download Run now समानता का पता करें : दो चरांको के 
Hungarian All magyar Download Run now Egyenlőségvizsgálat: két változó
Italian All italiano Download Run now Esplora le equazioni a due variabili
Japanese All 日本語 Download Run now つり合いを作ろう: 2つの文字を用いて
Kazakh All Kazakh Download Run now Екі айнымалы теңдік
Korean All 한국어 Download Run now 등식 연습하기: 2변수
Latvian All Latviešu Download Run now Vienādību pētīšana: Divi mainīgie
Mongolian All Монгол (Монгол) Download Run now Тэнцэтгэл Судлах: Хоёр Хувьсагч
Polish All polski Download Run now Poznajemy równania - dwie niewiadome
Portuguese All português Download Run now Explorador de Igualdades. Duas Variáveis
Portuguese (Brazil) All português (Brasil) Download Run now Explorador da Igualdade: Duas Variáveis
Russian All русский Download Run now Равенства с двумя переменными
Serbian All Српски Download Run now Истраживач једначина: Две променљиве
Slovak All Slovenčina Download Run now Skúmanie rovnosti: Dve premenné
Spanish All español Download Run now Explorador de Igualdades: Dos variables Download teacher tips PDF
Spanish (Mexico) All español (México) Download Run now Explorador de Igualdades: Dos variables Download teacher tips PDF
Spanish (Peru) All español (Perú) Download Run now Explorador de Igualdad: Dos Variables
Swedish All svenska Download Run now Utforska likheter: Två variabler
Vietnamese All Tiếng Việt Download Run now Đẳng thức: 2 biến

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
  • 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)
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  • base64-js-1.2.0.js
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