You have a locked briefcase that you want to send to your friend on the other side of the country. You put a lock on it and keep the key around your neck. There is no second key, you can't duplicate this key, and you don't want to send it to your friend, because you're afraid it might get lost or stolen. How does your friend open the case?
That's a question that has a lot of relevance to the use of prime numbers!
But I digress: this is a set of activities designed to enhance your students' understanding of how factor work.
One of the activities involves listing the factors for each number from 1 to 36, and then graphic the number of factors on a set of axes. They then answer a set of questions about the graph, including making a prediction about what happens to the number of factors as a number gets larger and larger. They also answer "sometimes, always, never" questions relating to primes and composite numbers.
The second activity uses a set of "factoring riddles" to sharpen students understanding of fractions, as well as prepare them to factor quadratic equations a few years later. For example, suppose you had to find 2 factors whose sum is 10? The answer is 3 and 7, of course. But did you know this is also the method for factoring the equation X squared + 10X + 21?
There are two sets of factoring riddles: the second set gets into abundant, deficient and "perfect" numbers. There's also a page where your students can make up their own "factoring riddle."