My heart overflows with a goodly theme; I address my psalm to a King. My tongue is like the pen of a ready writer.--Psalm 45:1, AMPC

As one who has written and published many poems, many of which could be considered songs, I like to teach my English Language Arts (ELA) students how to write both rhyming and non-rhyming poetry. 

There are a few distinctive differences, and I will use excerpts from my own work to illustrate them. I really like water--especially the Spirit of God, Who is Jesus the Living Water!---so I write a lot about it.  

Here is an excerpt from a non-rhyming poem I wrote:

In the desert of my soul,

Your smile is rain

Your laughter a shimmering pool

Amid the cool oasis of Your love.

Notice that the last word of each line does not rhyme with the last word on the line before or after it. This is a non-rhyming poem, but it still has rhythm and structure. The words evoke imagery that compares a desert (a "thirsty soul") to the refreshing, life-giving Water of the Word of God. 

Here are the first four lines from my poem, "Water is a Living Thing":

Water is a living thing,

A necessary brook or spring;

All its fountains lithe and living,

Ever moving, ever giving

Here, every last syllable rhymes with the last syllable of the line before or after it. Also, "giving" and "living" rhyme with one another. 

Rhyming poems often use alliteration and assonance (internal rhyme), but the only required thing to create a "rhyming poem" is to make sure the last syllable of every other line rhymes, or every line with its mate, in a couplet.

Enjoy and share and may this enhance your pleasure and that of your students' too!

Tonja and her husband live to exalt God. They lift Him up in books (P.O.W.E.R. Girl!; LEGACY; Visions of the King; Your Holy Health; more); presentations; service in church, community, and the world; and via the "River Rain Creative" (309 videos) and "POWERLight Learning" You Tube channels.