One of the examples my students have absolutely loved in the past is Hill cipher. It is a "real" application although outdated but the students do love playing with it. Using some sort of a encoding, convert a message to a bunch of numbers, and then a key matrix is chosen. The message can be organized into an array and multiplied by the key for encryption. And the encrypted message can be multiplied by the inverse of the key matrix to be decrypted. It is fun to give messages to students and them encrypt/decrypt them. It is also very simple to ask them to break a scheme and figure out the key by giving them a couple of plaintext/ciphertext pairs. You can also demonstrate some man-in-the-middle attacks and how a malicious eavesdropper can change the contents of the message without having to know the key at all.
If you want to be a bit more advanced, you can also do modular arithmetic so that you can take the English language and add any three symbols like space, comma, and a period to have a total of 29 symbols and then work modulo 29. 29 is a prime number so it avoids a whole bunch of invertibility issues. Matrix arithmetic in a finite field like Z/29Z illustrates some concepts very clearly. A smaller modulus will make it easier to do this by hand if you want to try that.