Equality Explorer

Equality Explorer Screenshot
  • Solving Equations
  • Inequalities
  • Inverse Operations

Topics

  • 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!

Sample Learning Goals

  • 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

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

Teacher-Submitted Activities

Games Remote Lesson ideas A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
K-5
MS
HS
Remote
HW
Mathematics
Chemistry
Physics
Balancing Act A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Michael Reynolds MS Guided Mathematics
What is Equality A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. David Wood MS
HS
Lab
Guided
HW
Discuss
Mathematics
Introduction to Inequalities A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Marleene Buttice MS Guided Mathematics
Solving Multi-Step Equations A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Meenakshi Raghavan MS Guided Mathematics
Middle School Math Sim Alignment This contribution was designed by PhET. Amanda McGarry MS Other Mathematics
Equality Explorer - 6th Grade intro to solving Trevor Gibson MS Guided Mathematics
Exploring Equations Akili Obika HS
MS
Guided Mathematics
Introducción a la igualdad A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Diana López MS
HS
HW
Guided
Lab
Mathematics
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López HS
MS
Other Biology
Physics
Chemistry
Mathematics
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López UG-Intro
HS
Other Physics
Mathematics
Chemistry
PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López K-5
MS
HW
Guided
Lab
Discuss
Demo
Physics
Chemistry
Astronomy
Mathematics
Equação e balança Alison Sousa da Silva, Ana Carolina Costa Pereira MS Guided
Lab
Mathematics

Language Download or Run Tips
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iPad:
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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:
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Macintosh Systems:
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Linux Systems:
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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)
  • 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