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

Numbers and Operations

Understanding Numbers

Numbers are the foundation of all mathematics. They come in different types, including whole numbers, integers, fractions, decimals, and percents. Each type of number plays a unique role in problem solving.

Operations and Order

The four basic operations—addition, subtraction, multiplication, and division—are used to manipulate numbers. Remember the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to solve expressions correctly.

Working with Fractions and Decimals

Fractions and decimals often appear on the ISEE. Converting between them, comparing their sizes, and performing operations are essential skills.

Real-World Example

Imagine you are budgeting for a class event. You need to add up costs, split bills, and calculate discounts—these all rely on solid number sense and operational skills.

Useful Tips

  • Always check if answers make sense.
  • Estimate before solving for a quick check.

Examples

  • If a pizza is cut into 8 slices and you eat 3, what fraction of the pizza did you eat? You ate \( \frac{3}{8} \) of the pizza.

  • Convert 0.75 to a fraction: \( 0.75 = \frac{3}{4} \).

In a Nutshell

Mastering how to use and operate with different types of numbers is key to solving quantitative problems.

Key Terms

Integer
A whole number that can be positive, negative, or zero.
Fraction
A number that represents part of a whole, written as one number over another.
Decimal
A number that uses a decimal point to show a part of a whole.
Percent
A way to express a number as a part out of 100.