Math Background

Functions: Tips and Tricks

  • For functions relating to patterns, have beads, pattern blocks, or geometric shapes cut from construction paper available for students to use.
  • Remind students that function tables are the same as input-output tables, which they've worked with before. As was done in previous grades, provide examples of input-output tables with the rules missing. Let x stand for the input value and y stand for the output value and have students find and write the rule for the table in words and then write the equation that describes it.
    input (x) output (y) Rule: Add 4
    Equation: y = x+ 4
    7 11
    9 13
    14 18
    18 22
  • Have students work with functions in a variety of ways. Give them a pattern, a written description, an equation, or a function table and have them determine the other ways of expressing the function. For example, give the written description “y is 3 times x” and ask students to provide an example of the pattern it describes, to write the corresponding equation, and to create a function table.
  • If students have studied variables in science, relate independent and dependent variables in science and math. In both cases, the independent variable represents that which is acted upon or that which is purposefully changed. The dependent variable is the result; its value varies, depending upon the value of the independent variable.
  • Keep a class list of examples of functional relationships in daily life. Examples can include the distance traveled at a set rate over a period of time, the number of gallons of gas used while driving for a certain distance, and the unit cost of items sold in groups or packs of more than one. Have students bring in examples of functional relationships from newspapers and magazines.
  • Show students data tables from experiments that they have conducted, or have them conduct a brief experiment and then create a data table. A simple experiment could be to have the students drop the same ball from different heights and record the height of the first bounce. Have students use the data tables to generate a general statement about the relationship between the independent and dependent variables, such as, “As the release height increases, the height of the first bounce increases.”
  • Have students design a bracelet or necklace using embroidery floss or beads. Then have them determine the number of each color strand or bead needed for one necklace or bracelet. Students can then create function tables showing how many of each color strand or bead would be needed to make greater quantities of the same bracelet or necklace. Or have students use geometric shapes to design a quilt block or a T-shirt and then determine how many of each shape is needed for more blocks or shirts.
  • Have each student write a function and create the corresponding function table (with 4 sets of values filled in) on the computer. Print a reduced copy of each student's function and table and distribute the entire set to groups of 4 students. Have students work in teams of two to play “Function Concentration,” in which they must match the function with its table. The team with the most matches wins.

Houghton Mifflin Math Grade 5