ISEE Upper Level (grades 9-12) Quantitative Reasoning

ISEE Upper Level Quantitative Reasoning focuses on developing advanced mathematical skills and problem-solving abilities for high school students.

Basic Concepts

Algebraic Thinking

What Is Algebraic Thinking?

Algebra is about using symbols, usually letters, to represent unknowns or variables in mathematical relationships. This allows us to generalize and solve a wide variety of problems.

Expressions and Equations

An expression is a combination of numbers, variables, and operations, like \( 2x + 5 \). An equation is like a balance scale, showing that two expressions are equal, such as \( 2x + 5 = 15 \).

Solving for Variables

To solve equations, we use inverse operations to isolate the variable. This helps us find the value that makes the equation true.

Patterns and Relationships

Algebraic thinking also involves spotting patterns and making predictions. This skill is useful in everything from science to computer programming!

Real-World Connections

Algebra helps you figure out how long it will take to save for a new phone, or how many tickets you need to sell to break even at a fundraiser.

Examples

  • Solve for \( x \) in \( 3x + 4 = 19 \): Subtract 4, then divide by 3 to get \( x = 5 \).

  • If you earn $10 per hour, your earnings after \( h \) hours can be written as \( 10h \).

In a Nutshell

Algebraic thinking is using symbols and rules to solve problems and spot patterns.