|Grade span:||9 to 12|
|Duration:||30 to 45 minutes|
Description:Students compare cell phone plans by analyzing tables, graphs, and equations in this sample lesson. Tools are available and useful to students during their analysis, and provide opportunities to make sense of the different rate plans. Mainly, students analyze the data they generate from the various phone plans, plot that data on a graph, and make recommendations for the "best" phone plan, based on their analysis. Students are also encouraged to share their thinking with their classmates, and report their findings to the class.
- Communicate about mathematics (e.g., use mathematical language and notation effectively, compare their own thinking with other students' thinking)
- Use strategies to understand new math content
- Develop efficient solution methods
- Effectively construct algorithms
- Understand equivalent representations of a problem situation or mathematical concept
- Solve problems involving rate as a measure
- Understand the concept of algebraic expressions and equations
- Understand properties of graphs and the relationship between a graph and its corresponding equation (e.g., y-intercepts and slope).
- Use a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships
- Use a variety of methods (e.g., with graphs and algebraic methods) to solve systems of equations
- Use tools available to understand the mathematics in ways they otherwise might not
- PDF - Teacher's Guide (PDF)
- PDF - Student Worksheet (PDF)
- Pencils (colored pencils as needed)
- Paper (graphing and other as needed)
- Ruler or straightedge
- Graphing calculators (required)
- Print out accompanying PDFs and familiarize yourself with the scenarios students will be involved with.
- If necessary, make time to share the lesson with a day time mathematics instructor to converse about the standards and mathematics involved, and practice working through the graphs on a graphing calculator and/or by hand.
- Organize students in small groups that will allow them complimentary discussion partners if necessary.
- Make sure all materials and tools are available for all students
- Prepare a brief introduction of the problem the students will be involved with and the tools that are available for their use while solving it. Clarifying the task and the tools for use, and peaking student interest in the problem are the goals of this discussion.
What to Do:
- Briefly introduce the problem. Students should find choosing a cell phone plan interesting and relevant. You might ask how much students (or their parents) pay for their cell phones. You might also ask how students would decide which cell phone plan to purchase and if there are any tools that might be helpful to them in making a decision?
- Provide students with the two different cell phone plans (see PDF), and before they do any analysis, ask them which they would choose, and why. Next, have students begin working on the analysis of the cell phone plans.
- Students might find it helpful to work together, and bounce ideas off of the instructor. Stay involved with students' work, and ask questions as you circulate among them. Watch for students who get stuck or don't know how to create a graph. Also, stay tuned in to how students are using mathematical tools and provide appropriate guidance as necessary. (Note: The calculator makes sophisticated mathematics accessible to students who might not be able to "jump in" algebraically. A goal is for the tools to allow students to see and understand the mathematics in ways they otherwise might not.)
- Depending on student's autonomy and problem solving experience, they may be able to create a graph on their own, or they may need additional guidance from you. Base your decision to scaffold the graphing activity on your knowledge of students' background. Use the teacher's guide (see PDF) for specific information. The more students can accomplish and figure out on their own, the better.
- The x-axis should be labeled with the number of minutes, and the y-axis is labeled with cost (the cost depends on the number of minutes, the cost is the dependent variable, and thus belongs on the y-axis). You might want to discuss this with students.
- Some students may not be familiar with the graphing calculator. If you find this to be the case, you may choose to share some of the examples from the Teacher's Guide with students to help them get started. Typically, setting an appropriate window is problematic for students. The more they can see the connection between the graph they draw on graph paper and what they see on the calculator, the better.
- An extension activity is included for students who are experienced with algebra and need a challenge. Or, you might extend the activity to two days and ask all students to complete the extension problem. The extension adds a third phone plan for students to analyze.
Evaluate (Outcomes to look for):
- All students are engaged and actively seeking answers
- Students are communicating effectively about mathematics (e.g., using mathematical language, comparing their own thinking with other students' thinking, gaining clarification from each other)
- Students are using strategies effectively
- Students are developing efficient solution methods
- Students are effectively constructing algorithms
- Students are using a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships effectively
- Students are using a variety of methods and tools (e.g., with graphs and algebraic methods, graphing calculators and tables) to solve systems of equations effectively
- Students are using tools (e.g., graphs, calculators) to see connections among algebraic ideas and symbols
- Students are able to access sophisticated mathematics, made possible through the use of tools.
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.