## Elementary 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 Grades K-2

Describe numerical relationships using variables and patterns:

- Identify, describe and extend simple geometric and numeric patterns.
- Solve simple number sentences (e.g., 2 + = 5).

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

- Solve problems involving pattern identification and completion of patterns.

Solve problems using systems of numbers and their properties:

- Describe the basic arithmetic operations (addition, subtraction, multiplication, division) orally, in writing and using concrete materials and drawings.

Use algebraic concepts and procedures to represent and solve problems:

- Find the unknown numbers in whole-number addition, subtraction, multiplication and division situations.

### Learning Objectives Grades 3-5

Describe numerical relationships using variables and patterns:

- Identify, describe, extend and create geometric and numeric patterns.
- Construct and solve number sentences using a variable to represent an unknown quantity.

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

- Analyze a geometric pattern and express the results numerically.

Solve problems using systems of numbers and their properties:

- Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.

Use algebraic concepts and procedures to represent and solve problems:

- Solve linear equations involving whole numbers.

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