Equality Explorer
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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 1.0.6
Teacher Tips
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Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). |
Teacher-Submitted Activities
| Title |
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Authors | Level | Type | Subject |
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| Balancing Act |
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Michael Reynolds | MS | Guided | Mathematics | |
| What is Equality |
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David Wood | MS HS |
Discuss Lab HW Guided |
Mathematics | |
| Introduction to Inequalities |
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Marleene Buttice | MS | Guided | Mathematics | |
| Solving Multi-Step Equations |
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Meenakshi Raghavan | MS | Guided | Mathematics | |
| Equality Explorer - 6th Grade intro to solving | Trevor Gibson | MS | Guided | Mathematics | ||
| Exploring Equations | Akili Obika | HS MS |
Guided | Mathematics |
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 |
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