Give your fifth-graders a worksheet that features basic math equations and inequalities. Also provide them with counter objects, such as marbles or bottle caps. Students will then set up the equations by replacing the given numbers with the correct number of counter objects. This allows students to visualize the equation, after which they can add in the correct number of counters for the variable of the equation or inequality. Alternatively, give them a treat to use as a counter, such as candy. Allowing them to eat the treat after correct answers provides your fifth-graders with a reward system for correct solutions.
Divide your fifth-graders into groups and provide each group with a pair of dice. Students will then take turns rolling the dice and recording the numbers that land face-up. After several rounds, students will multiply each set of numbers together and add up all of the products. Students will then arrange their scores as a system of inequalities, from the largest score to the smallest. Demonstrate to students how each dice roll can be viewed as a function of two variables, and that these can be arranged into inequalities based on the values as given by the dice.
Choose a mystery number, represented by "X" on the board. Divide your fifth-graders into groups, and allow each group to ask questions to figure out the mystery number, such as greater-than or less-than questions. Students will record your answers to their questions by writing inequalities. For example, if a student asks "Is X greater than 12?" and the answer is yes, the student will record "X > 12" on their worksheets. The first group to answer with a correct equation for the value of "X" wins the game.
Have your fifth-graders solve beginner-level Sudoku puzzles. Tell them to think of each blank space as a variable in the addition equation of that row and column. Once they solve the puzzle, have students replace the numbers they filled in with letters, such that 1 through 9 correlate with R through Z. This rewritten puzzle depicts a variable equation in place of the blank Sudoku boxes. Students can then create inequalities by switching the variables before substituting with numbers, which will demonstrate how the rows no longer add to the correct sum without the proper variables.