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 realworld 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 multistep reallife 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 realworld 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.
HSACED.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.
HSACED.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.
HSAREI.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.
HSAREI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Version 1.0.3
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Teacher Tips
Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). 
TeacherSubmitted Activities
Title  Authors  Level  Type  Subject  

What is Equality  David Wood  HS MS 
Discuss Guided Lab HW 
Mathematics  
Introduction to Inequalities  Marleene Buttice  MS  Guided  Mathematics  
Solving MultiStep Equations  Meenakshi Raghavan  MS  Guided  Mathematics 
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