An easy game to teach sentence structure involves word cards representing different parts of a sentence that need to be put in the right order. You can give students more cards than necessary and ask them to choose only the right ones to make a sentence. Accept silly sentences, too, if their words are in the right syntactic order; it's even more fun. You can also select the cards for certain sentences beforehand; the choice depends on the proficiency of your students. Remind the children of the structure of a simple sentence and help them with the complex ones. You can use verbs of different tenses to reinforce previously acquired knowledge.
Tell children that sentences always begin with a capital letter; they end with a punctuation mark; and they contain a subject and a verb. Give them a paper with a short text that has no capital letters or punctuation. Ask the students to separate the sentences and make the text comprehensible with punctuation. Another variant is to give them a half a sentence ("I drink") and four variants of the other half ("milk every morning/in the elevator/to the office/with mustard sometimes") and ask the children to choose the right half to make a correct sentence.
Give children a text for which they must supply the punctuation marks (full stops, commas, question marks, exclamation points) and conjunctions (and, but, before, as). Model the activity first by supplying the wrong word and punctuation and make them aware of how weird the text may sound. Another game to form compound sentences is to give the students the first half of a compound sentence ("My brother studies French") and four variants for the other half ("and I study German/so he goes to school/when he sleeps/after the plane takes off"), asking them to choose the answer that forms a logical compound sentence.
Write a long sentence on the board and ask students to take out words so that what remains would still preserve the initial meaning of the sentence. Erase the words students suggest until the sentence can't be reduced anymore. A reverse process will increase their interest and make the activity more fun while checking their vocabulary. Ask the students to add words to the reduced sentence, not necessarily the ones they took out, but accept them if they remember them. The sentence must still have the same meaning, but they can add adjectives, adverbs and punctuation to make it more interesting.