# Equality Explorer: Two Variables

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### Innhald

• 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.

### Døme på læringsmål

• 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 1.0.12

### Teacher Tips

 Lærarguiden (pdf) inneheld tips som er laga av PhET-teamet. ( PDF ).

### Teacher-Submitted Activities

Middle School Math Sim Alignment Amanda McGarry Ungdomsskule Anna Matematikk
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López vgs
Ungdomsskule
Anna Biologi
Kjemi
Fysikk
Matematikk
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López vgs
Student - intro
Anna Matematikk
Kjemi
Fysikk
Språk Download or Run Tips
Albanian All shqip Hulumtues barazishë: Dy ndryshore
Arabic All العربية مستكشف المساواة: متغيرين
Basque All Euskara Berdintasun-esploratzailea: bi aldagai
Bosnian All Bosanski Istraživač jednačina: Dvije promjenljive
Chinese (China) All 中文 (中国) 等式探索:两个变量
Chinese (Taiwan) All 中文 (台灣) Equality Explorer: Two Variables_探索等式：兩個變數
Danish All Dansk Ligevægts-visning: To variabler
Dutch All Nederlands Ontdek gelijkheid: twee veranderlijken
French All français Explorateur d'équation : Deux variables
German All Deutsch Gleichheit schaffen: Zwei Variablen
Greek All Ελληνικά Εξερευνητής εξισώσεων: δυο μεταβλητές
Hindi All हिंदी समानता का पता करें : दो चरांको के
Hungarian All magyar Egyenlőségvizsgálat: két változó
Italian All italiano Esplora le equazioni a due variabili
Japanese All 日本語 つり合いを作ろう: 2つの文字を用いて
Kazakh All Kazakh Екі айнымалы теңдік
Korean All 한국어 등식 연습하기: 2변수
Latvian All Latviešu Vienādību pētīšana: Divi mainīgie
Mongolian All Монгол (Монгол) Тэнцэтгэл Судлах: Хоёр Хувьсагч
Persian All فارسی کاوشگر برابری: دو متغیر
Polish All polski Poznajemy równania - dwie niewiadome
Portuguese All português Explorador de Igualdades. Duas Variáveis
Portuguese (Brazil) All português (Brasil) Explorador da Igualdade: Duas Variáveis
Russian All русский Равенства с двумя переменными
Serbian All Српски Истраживач једначина: Две променљиве
Slovak All Slovenčina Skúmanie rovnosti: Dve premenné
Spanish All español Explorador de Igualdades: Dos variables
Spanish (Mexico) All español (México) Explorador de Igualdades: Dos variables
Spanish (Peru) All español (Perú) Explorador de Igualdad: Dos Variables
Swedish All svenska Utforska likheter: Två variabler
Turkish All Türkçe Eşitlik Gezgini: İki Değişkenli
Ukrainian All українська Дослідник рівностей. Дві змінні
Vietnamese All Tiếng Việt Đẳng thức: 2 biến

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Designteam Tredjepartsbibliotek Takk til
• 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