First, decide what topic you want your students to practice. I have made some for short vowel words (-ell, -ack, -op) and kindergarten sight words as a review. Simply write the math fact, letter, or word on the bottom of each egg whole. Then, using something small (penny, button, bead) place it in the carton, close, and shake. Students open up the carton, see where the small object landed, and they either have to solve the math fact, read the word, make up a word that rhymes, give the letter sound,etc... I created a recording sheet for my Shake a Word game. It is saved at school, so I cannot upload it now.
The picture below shows a Shake a Sight Word game. The words are kindergarten review words. When students read the sight word, they also say the word in a sentence.
The way my family goes through eggs, I hope to expand my egg carton games for math. My students in the past have loved to play these games during centers.