As math teachers, we are always looking for creative and effective ways to teach our students how to compare linear functions. This is an essential skill for students to have as they move through their math education and into the workforce. In this article, we will explore three activities that are great for teaching students how to compare linear functions using tables, graphs, and equations.

Activity 1: “What’s the Relationship?”

This activity is designed to help students see the relationship between two linear functions. To start, give students a pair of linear functions and have them create a table of values for each. Once they have completed this task, have them graph the data on a coordinate plane. Finally, ask students to compare the two graphs and identify any similarities or differences.

After students have had a chance to complete the activity, lead a class discussion about their findings. Ask students to explain how they determined the similarities and differences between the two graphs. Encourage them to think about the slope of each function, as well as the y-intercept, and how they can use these two pieces of information to compare the functions.

Activity 2: “Match It Up”

In this activity, students will work in small groups to match linear functions with their corresponding graphs and equations. Start by giving each group a set of linear functions, a set of graphs, and a set of equations. The groups will work together to match each function with its corresponding graph and equation.

Once all the groups have finished, have a class discussion about the activity. Ask students to explain how they determined which equation matched with which graph and function. Encourage them to think about the slope and y-intercept of each function as they make their matches.

Activity 3: “What’s the Pattern?”

This activity is designed to help students see the pattern in linear functions. Start by giving students a set of linear functions and have them create a table of values for each. Next, ask them to compare the values in each table to see if they can identify a pattern. Finally, have them graph the functions on a coordinate plane to see if the pattern holds true.

After students have completed the activity, lead a class discussion about the patterns they observed. Encourage them to think about how they can use the patterns they observed to predict values for a linear function, even if they don’t have a table or graph.

Conclusion

Incorporating these activities into your lesson plans can help students master the skill of comparing linear functions. By using tables, graphs, and equations, students can learn to identify patterns, match functions with their graphs and equations, and see the relationship between two or more functions. These skills will serve them well throughout their math education and into the workforce.