## Middle School | Mathematics | Algebra

Algebra unites patterns and quantities in patterns with the means of describing change through the use of variables and functions. Its concepts and analytical methods allow people to consider general solutions to problems with common characteristics and develop related formulas. Algebra provides verbal, symbolic and graphical formats for discussing and representing settings as diverse as the pricing patterns of merchandise in a store, the behavior of a car as it accelerates or slows down, the changes in two chemicals as they react with one another, or the type of variation existing in a comparison of two factors in the economy. All people must be able to use algebraic methods to construct and examine tables of values; to interpret the relationships expressed by patterns in these tables; to relate change and variation in graphs and formulas; to reason about changes in quantities and the relationships involved in changes; and to find solutions to everyday problems using algebra’s symbolic manipulation and formulas.

### Learning Objectives

Describe numerical relationships using variables and patterns:

- Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.
- Solve problems using linear expressions, equations and inequalities.

Interpret and describe numerical relationships using tables, graphs and symbols:

- Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.

Solve problems using systems of numbers and their properties:

- Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences.

Use algebraic concepts and procedures to represent and solve problems:

- Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.
- Propose and solve problems using proportions, formulas and linear functions.
- Apply properties of powers, perfect squares and square roots.

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