Teaching prime numbers

Grade school kids have algebra looming in their immediate future, so they’re gonna have to learn about factoring.  A critical first step is understanding prime numbers.   [CCSS Standard.4.OA.B.4]

Prime numbers, essentially, are the components from which integers are constructed. A prime number is a number, greater than 1, that can only be evenly divided by 1 or by itself.

Prime numbers, essentially, are the components from which integers are constructed.  A prime number is a number, greater than 1, that can only be evenly divided by 1 or by itself.  A composite number is a number greater than 1 that can be evenly divided by a number other than 1 or itself.  So if a number greater than 1 is not a prime number, it is a composite number.

12 = 2 x 6 = 2 x 2 x 3.  So 12 is a composite number.  In the future there will be times that your kid will need to think of 12 as 2 x 2 x 3 or as 2² x 3.

13, on the other hand, does not cooperate.  13 = 1 x 13.  It can’t be broken down any further.  So 13 is a prime number.

Figuring out whether or not a number is prime will be something of a trial and error process for grade schoolers.  We know that all even numbers greater than 2 are composite numbers, since they’re all divisible by 2.  We also know that any number with a 5 in the ones place is also a composite number and will be divisible by 5.  So as candidates for prime numbers we’re left with numbers ending in 1, 3, 7 and 9.

The foolproof trial-and-error method for determining whether a number is prime is to try dividing it by every number from 2 through the square root of the number.  If none divide evenly then the number is prime.  That, however, gets tricky for big numbers.  The method I’m trying with my kids is simply to have them study and remember this chart.  There’s only 25 primes between 1 and 100 – and the ones below 20 (8 in all) are the most important.

Here’s a study sheet showing the Grid of Prime Numbers from 1 to 100.  And you can find study worksheets on the fourth grade math worksheet page.