Buttons can be a great math manipulative. To make a literature-math connection, read "The Lost Button" in Frog and Toad Are Friends. Using buttons, either real ones or paper ones, for props for each of the buttons he finds is a great interactive way of reading the story.
Then you can further explore various types of buttons. Have each student pick out their favorite button and play a game in which you announce an attribute and have them raise their hand if their button has that attribute. This can get really fast-paced.
Then hide a button and play a hide and seek type game using "warmer" and "colder" for indicators as to how close the seeker is.
Another early reader that features the concept of sorting and buttons is 3 Little Fire Fighters. In this story three small fire fighters need to get dressed for a parade, but are all missing their buttons. They mix and match the buttons several times until they can find a way for them all to have matching buttons. We then sorted our buttons in all kinds of ways such as by color and by size.
Sometimes sorting is not as easy as one would think. As my son Sam said, "Sometimes it is hard to tell where one leaves off and another begins."
Then play a game in which your students pick buttons, but do not let them tell what criteria they have sorted them by. Then you and the rest of your students have to guess in what way each student has sorted! Sorting can get more sophisticated and can involve shades of color and number of button holes.
Your students can now make their own paper buttons, designing them any way they want. Once they are completed, you can begin graphing them in several ways, using different criteria. Use a piece of posterboard or a dry erase board to make your graph and they can place their buttons on where it is appropriate. First you can graph them according to how many holes they have and then you can graph them according to what shape they are, continuing on for as long as you want. This a great beginning graphing experience and you can later move on to more symbolic bar graphing.