To understand functions, students must learn how to look at an equation and recognize the input, output, and relationship. Create a classroom game that allows students to break whole equations into individual components. Write functions on rectangular cards and cut the equations into smaller parts. Make a column for inputs, outputs and relationships of functions on the top of a board and challenge students to take a full equation puzzle and separate the pieces into their proper columns.
Once students understand the components of mathematical functions, they can practice further by setting up their own functions. As a class game, students can break into small groups to set up functions based on word problems. Write a word problem on the board and provide information that students can plug into an equation that relates an input to an output. The students will review the structure of math functions while having a friendly competition.
When you feel the class has a firm grasp on the concept of functions, set up a classroom competition challenging them to solve functions on the board. Break the class into two teams and invite them to participate in a function-solving relay race. Split the whiteboard down the middle, write the same list of matching functions on each side and cover each problem with a strip of paper. One student from each team will approach the board, remove the cover from the problem and quickly solve it. Team members will continue solving problems in relay fashion until they complete the lists.
After solving linear functions, students graph the values for y and x, creating a straight line that shows the relationship between the input and output. To illustrate the process of graphing linear functions, create a human graph in which students will take the place of x and y values. Find a large floor space and use masking tape to mark off a vertical y axis and horizontal x axis. Students will work in pairs to solve linear functions, stand on the proper spots as the x and y lines intercept, and hold ends of a rope to make sure they have graphed a straight line.