Unit 6 - Expressions, Equations, and Inequalities
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Learning Outcomes
• Use the order of operations to simplify numerical expressions
• Apply the properties of real numbers to simplify numerical expressions • Identify examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficient • Model and solve one-step equations using a variety of concrete materials • Solve one-step equations, demonstrating the steps algebraically • Write verbal expressions and sentences as algebraic expressions and equations |
Essential Questions
• What is the importance of operational relationships when solving equations?
• What are some ways that equality is demonstrated when solving for a variable? • What strategies can be used to determine what numbers on the number line satisfy an inequality? |
Unit Vocabulary
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Algebra
operational relationship numerical expression linear equation Order of Operations equivalence/equality inequality |
integers
isolate simplify expression coefficient variable constant term |
Properties:
Associative Property Commutative Property Distributive Property Identity Property Addition Property of Zero, Multiplication Property of Zero, Property of Equality |
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Algebra
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Operational relationships
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the system/order that addition, subtraction, multiplication, and division relate to each other
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Numerical expression
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a combination of numbers, integers combined using mathematical operators such as addition, subtraction, multiplication, or division.
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Linear Equations
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A linear expression is a mathematical statement defining an equality.
linear expression usually has a dependent variable and an independent variable. It contains an equality sign, signifying a balance between the left hand side and the right hand side of the equation. To solve a linear expression as many equations are required as there may be variables. |
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Order of Operations
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The rules that say which calculation comes first in an expression.
PEMDAS • do everything inside parentheses first: () • then do exponents, like x2, x3 etc • then do multiplies and divides from left to right • then do the adds and subtracts from left to right |
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Equivilance
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the condition of being equal or equivalent in value, worth, function, et
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Inequalities
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the relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
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integers
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a whole number; a number that is not a fraction. (+, -)
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Expression
term variable constant |
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Isolate
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The action taken to move all variables to one side of an equation and the constants to the other side.
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Simplify
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The action that combines variables and constants, first on each side of an equation/expression, then across the equal sign to solve the equation.
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Properties
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Visit Math-Aids.com for an awesome worksheet on the various propertied
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