Gather students on the carpet for a math story-time session. Draw a three-column function table on the chart paper before beginning. Label the left column "In," the middle column "Rule" and the right column "Out." Title the table "Goblin's Picnic."
Begin telling them the following story: "Twenty goblins began skipping into the forest for their annual hike and picnic. One tripped over a rock and scraped his knee before reaching the forest. Seventeen friends stayed with him to perform first aid." Stop to ask students how many goblins are in the forest (2). Record the number in the top row and left-hand "In" column of the table.
Continue the story: "The goblins who stayed behind were surprised to hear a shriek and see one goblin run out of the forest." Record the number "1" in the top row and right-hand column. Leave the middle column blank. Ask students what these numbers mean (2 goblins went in, but only one came out.)
Tell the class, "Now there were 19 goblins outside of the forest. They couldn't understand the screaming goblin, so they sent 4 goblins in to search for their lost friend. Then they heard shrieks and saw two of their friends zoom out of the forest." Stop to record 4 in and 2 out. Resume the storytelling: "More scared than ever, they sent 8 goblins into the forest. Only 4 came running out. Now there were 13 goblins outside the forest." Record 8 in and 4 out.
Tell the class to look for a pattern in the "in" and "out" table. Ask for predictions of how many goblins would run out of the forest if 10 were sent in. Write these predictions to the side of the table. Ask some of the students who guessed correctly about the rule (divide by 2) about how they determined it. Write the rule in the function box.
Discuss whether it is possible for the goblins to continue sending larger numbers into the forest (no, because only 8 are left outside after the 10 go in and 5 come out).
Extend the lesson to language arts time by asking students to write about what they think happened to the missing goblins. Practice future function stories two other ways with inputs or outputs missing. Explore function rules involving addition, subtraction and multiplication. Follow up with online practice such as the interactive function machine game at the Los Angeles County Office of Education distance learning website (See Resources).