Square Numbers
3 Minutes
Prime numbers and composite numbers for kids: learn how to identify them using a simple ball grouping game. A short maths lesson in English.
- Rules of the grouping game using equal groups of balls
- Testing numbers 2, 3, and 4 to find prime and composite numbers
- Why number 1 is neither prime nor composite
What this lesson teaches
A prime number is a number that can only be arranged into two distinct types of equal groups, whereas a composite number can be arranged into more than two types of equal groups. These classifications describe how whole quantities can be separated into equal collections without leaving any remainders.
Rules of the grouping game
- Start with a set of balls representing the number being tested, using more than one ball.
- Divide the balls into groups where every single group has an exact equal number of balls.
- Discard any division that has unequal groups, such as placing two balls on one side and one ball on the other.
- Count the total number of valid ways the balls can be grouped together.
Identifying prime numbers
Taking two balls allows only two valid groupings: separating them into two individual groups of one ball each, or keeping both balls together in one single group. Taking three balls also yields only two valid arrangements, which are three individual groups of one ball, or all three balls together in one group. Because both two and three can only be split into two types of equal groups, they are prime numbers. Other numbers such as 5, 7, 11, 13, and 17 follow this exact rule, and prime numbers continue onward past 17.
Identifying composite numbers
Testing four balls demonstrates how a composite number behaves under the same grouping rules. Four balls can be grouped as four separate individual balls, or as one single group containing all four balls together. In addition, four balls can be separated into two groups of two balls each, giving three different types of equal groupings in total. Because the number four can be split into more than two types of equal groups, it is defined as a composite number. All numbers other than prime numbers that can be split into more than two types of groups are composite numbers.
The special rule for number one
- The number one is not tested like the other numbers in the grouping game.
- It does not fit the definition of a prime number.
- It also does not fit the definition of a composite number.
- Because of these rules, the number one is classified as neither prime nor composite.