You can turn paragraphs into puzzles, showing kids how sentences work together within a paragraph. Write a few different paragraphs, print them out and cut them into separate sentences. Hand each sentence to a different kid, and let the kids work together to put the sentences in order. Reward the team with bonus points on an upcoming exam for each correct sentence, or a candy if they get all of their sentences in the correct order. Use this game to demonstrate how paragraphs have an introductory sentence and how description builds on prior statements.
Stories are another fun way to teach kids how to form paragraphs. Start by writing an introductory sentence on a piece of paper and reading it to your kids. Hand the paper to the first child, and ask her to write her own sentence that builds from yours and keeps the story progressing. Give each kid a point for every sentence that builds a correct paragraph. Periodically, tell a child to start a new paragraph with her own introductory sentence. Remember, each sentence within a paragraph should support or explain the introductory sentence while progressing the story. The kid with the most points at the end of your story wins.
Simple scenes give children a chance to practice writing descriptive paragraphs. Take the kids to a particular setting, such as your car in the parking lot or a view at a local park. Assign each kid a different observation method, such as one kid focusing on a single point and describing things outwardly from the point, another describing the scene from the sky downward and another describing the scene from where he is standing toward the point. Give them a few minutes to write paragraphs using the descriptive technique you assign and the scene as inspiration. Judge the winner based on which child best utilizes these elements.
Pictures, representing a series of events, can help kids understand the progression of a paragraph. Prepare a series of pictures, such as a football team lined up on the line, the quarter back moving backwards, the quarterback throwing the ball and the receiver catching the ball. Give a different picture to each child and ask them to write a single sentence describing the picture they see. Instruct the kids to place the pictures in order, and then have each student read his sentence. The winning group is the one with the most coherent paragraph when read together.