Let young mathematicians exercise their creativity by having them draw imaginative function machines. A basic function machine is drawn as a box with an opening at the top for the input number, a line inside the box for the function (such as addition, subtraction), and an opening at the bottom for the output number. Students may elaborate by turning boxes into robots, giving them gears, or adding other creative elements. This activity works well on a whiteboard, so students can erase the numbers and insert new ones into the same "machine."
Third graders are still learning abstract thinking, so understanding the quantities represented by numbers may be challenging. Students may benefit from using props to represent input and output numbers. Using small items such as beads, blocks or dry beans, ask students to count out enough items to represent the input number. Then let them determine whether they need more or fewer items to reach the output number. Use this activity for addition and subtraction functions.
Students can get extra input/output practice with online function generators. Websites such as Math Playground and TEAMS Educational Resources provide interactive function machines that let students feel like they're playing video games while doing math homework. These sites allow the user to choose different levels of difficulty, and some sites also let students choose to solve for the input or output instead of the function.
Reading a book or telling a story that uses functions will help students see math problems as more than numbers on a page. An example of a book that teaches functions is Two of Everything, in which a man finds a magic pot that makes everything he puts in it turn into two things. Read this picture book with third graders, then place them in pairs and give them their own "magic" pots (or buckets) and some small objects. Tell students to take turns creating functions for their pots and using the objects to help their partners determine what the function is.