In this Grade 4 AMC Math lesson from AoPS Introduction to Algebra, students explore the classification of numbers, including integers, rational numbers, irrational numbers, and real numbers. The lesson introduces key distinctions such as positive versus negative integers, why zero is neither positive nor negative, and how numbers like the square root of 2 cannot be expressed as a ratio of integers. It lays the foundational vocabulary students need for algebraic reasoning throughout the AoPS curriculum.
Section 1
What is an Integer?
Integers are counting numbers, their opposites, and zero.
Section 2
Defining Integers and Opposites
Negative numbers are numbers less than 0.
The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.
The notation is read as “the opposite of .”
The whole numbers and their opposites are called the integers.
The integers are the numbers .
Integers expand our number system to include negative values, which are like mirror images of positive numbers across zero. The 'opposite' of a number is simply its reflection on the other side of the number line.
Expand to review the lesson summary and core properties.
Section 1
What is an Integer?
Integers are counting numbers, their opposites, and zero.
Section 2
Defining Integers and Opposites
Negative numbers are numbers less than 0.
The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.
The notation is read as “the opposite of .”
The whole numbers and their opposites are called the integers.
The integers are the numbers .
Integers expand our number system to include negative values, which are like mirror images of positive numbers across zero. The 'opposite' of a number is simply its reflection on the other side of the number line.