What is a Number?
Something that expresses the “amount of or lack of.”
A number is a way of showing how many or how much of something there is. In math, a number is also a symbol that represents quantity, including zero (0) which represents the absence of quantity. For example, “7” is a symbol we use to describe seven days in a week or seven eggs in a basket.
Numbers help us count, measure, compare, and describe quantities—including when there’s some of something, or none at all.
We use numbers all the time:
- Counting: 1 apple, 2 friends, 3 pencils
- Measuring: 5 inches long, 10 pounds, 100 degrees
- Comparing: Which is more or less?
- Labeling: Jersey #7, Room 12
We often classify numbers into groups based on their properties:
- Whole numbers: 0, 1, 2, 3…
- Integers: ..., –3, –2, –1, 0, 1, 2, 3...
- Rational numbers: Numbers that can be written as fractions or decimals (including whole numbers and integers)
- Fractions and decimals: Parts of a whole (e.g., \(\frac{1}{2}\), 0.75)
- Even and odd numbers: Two types of integers where evens are divisible by 2, odds are not
- Prime and composite numbers: Prime numbers have exactly two factors (1 and itself); composite numbers have more than two factors
- Perfect squares: Numbers made by multiplying a whole number by itself (e.g., 4 = 2 × 2, 9 = 3 × 3, 16 = 4 × 4)
Every number tells us something. Even zero is important—the number that counts none, as we define it at Mathnasium—it tells us there’s none of something, which is just as meaningful as knowing how much.
How Do Students Learn About Numbers?
Students are introduced to numbers early in life, often before formal schooling begins. Their understanding grows as they explore different ways numbers can be used and what they mean.
Preschool & Kindergarten – Early Number Sense
Students learn to recognize numbers, count objects, and compare quantities like more, less, or the same.
Grades 1–2 – Working with Numbers
Students begin adding and subtracting, skip counting, and understanding place value. They explore even and odd numbers and build fluency with number facts.
Grades 3–5 – Exploring Types of Numbers
Students begin working with fractions, decimals, prime numbers, and factors. They also develop stronger estimation skills and number sense.
Grades 6+ – Applying Numbers in Advanced Math
Students use numbers in algebraic expressions, coordinate planes, scientific notation, and more.
