## Talk or Text

- Lesson

In this lesson, students compare different costs associated with two cell phone plans. They write equations with 2 variables and graph to find the solution of the system of equations. They then analyze the meaning of the graph and discuss other factors involved in choosing a cell phone plan.

Begin by asking students who has a cell phone. Ask what type of plan they have, and how they chose it. Discuss different options provided by plans, rates charged for text messaging, and rates for voice minutes. Some students may use pre-paid plans, and others may use a monthly contract. You may want to show a few examples of current plans offered by cell phone companies.

Tell students that they will be looking at two prepaid plans offered by two different cell phone companies. Distribute the Talk or Text? Activity Sheet to each student.

Depending on students' ability levels and familiarity with the concepts, you may want to put students in groups of 2 to 4. Explain to students that their parents have decided to but them their first cell phone, and the parents have agreed to prepay $25 each month to be used for voice minutes and text messaging. Allow students time to look at the chart and discuss which cell phone plan would be best under which circumstances before reading through the questions on the activity sheet.

Give groups time to complete Questions 1 to 5. Walk around the room and help students as needed. When they are finished, bring the whole class together to discuss the answers (found on the Talk or Text? Answer Key).

Students may have found *x*- or *y*-values that are fractions or decimals, such as sending 166^{2}/_{3} text messages for Plan A in Question 1. Ask them what this means. Is it possible to send 166^{2}/_{3} text messages? Students should realize that you cannot send ^{2}/_{3}
of a text message, so the answer to Question 1 is 166 text messages.
Ensure that everyone has the correct equation and understands what the
equations mean in the context of the problem situation.

Allow groups to complete the remainder of the activity sheet.
Direct students to graph their equations using whichever method they
choose (slope and *y*-intercept, *x*/*y* table, or *x* and *y* intercepts). You may also want to discuss the meaning of negative *x*- and *y*-values.
Is it possible to send a negative number of text messages or talk on
the phone for negative minutes? Students should realize that only
positive values make sense in this problem, and therefore they should
be graphing in quadrant I only.

When students have finished the activity sheet, lead a whole class discussion on what they have found out about the phone plans by answering the questions. Did they choose the plan they thought they would before working through the activity? Which plan did they choose and why? Which plan was most popular in the class? You can also create lists of pros and cons of each plan on the board. Emphasize to students that there is no right answer to this problem. The best choice for an individual is based on that person's phone habits. However, investigating plans mathematically can lead any person to make a better, more informed decision.

- Computer with Internet access (optional)
- Information about current cell phone plans (optional)
- Talk or Text? Activity Sheet
- Talk or Text? Answer Key

**Assessment Options**

- Ask students to solve a similar problem using two other cell phone plans.
- Ask students to write a journal entry explaining which plan they would choose and why. Under what circumstances would they choose the other plan?
- Give students the average number of text messages sent and the average number of minutes used by a particular person. Which plan should that person choose? Why? How much money would they save?

**Extensions**

- Students can research and compare plans offered by two or more different companies. Have them compare different factors, such as free evening and weekend minutes or cell phones offered from the company, and discuss how these variables would affect their choices.
- Students can compare individual versus family plans, weighing the benefits and drawbacks of each.
- Extend the lesson to other types of memberships, such as movie rental programs or gym memberships. Have students compare similarities and differences in features or types of membership categories.

**Questions for Students**

1. Under what circumstances is each cell phone plan better?

[Plan A is better when you talk on the phone more. Plan B is better when you send text messages more.]

2. What does the graph of each equation represent?

[Combinations of texts and minutes that cost exactly $25.]

3. What does the space underneath the graph of the line represent?

[Combinations of texts and minutes that cost less than $25.]

[Combinations of texts and minutes that cost more than $25.]

[No, because you cannot have negative minutes or negative text messages.]

[Answers will vary, but student comments may include activation fees, mobile-to-mobile minutes, weekend or evening minutes, cell phones available, or "extras" like voice mail and ring tones.]

**Teacher Reflection**

- Do students understand the meaning of each plan?
- Were students appropriately challenged? How could you modify the lesson for students at a higher or lower level?
- Were students able to explain why they would choose a particular plan? Did they demonstrate understanding of the mathematics?
- Did students have difficulty writing the equations? How could you scaffold this skill?

### Learning Objectives

Students will:

- Compare two cell phone plans through examples of different usage.
- Write equations to model allocation of money for cell phone usage.
- Graph and solve a system of equations.
- Analyze the solution and the meaning of the graph.

### NCTM Standards and Expectations

- Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

- Relate and compare different forms of representation for a relationship.

- Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

- Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases.

### Common Core State Standards – Mathematics

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.A.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.C.9

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Grade 7, Expression/Equation

- CCSS.Math.Content.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.''

Grade 8, Functions

- CCSS.Math.Content.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP7

Look for and make use of structure.