# 2.2 Linear equations

## Learning outcomes

Students will use hypothetical scenarios to explore the concept of linear equations.

## Teacher preparation

### Time required for lesson

Approximately 55-70 minutes. Some homework time may be needed.

### Materials needed

- Student handouts:
- Cell phone charts
- Linear equation scenarios worksheet

- Linear equation scenarios worksheet answer key
- Overhead projector and pens
- Transparency copies of:
- Cell phone charts
- Mock cell phone plans
- Linear equation scenarios worksheet

## Activities

- Hand out the cell phone charts and project the transparency of the charts on the overhead projector. Ask the students how many of them have cell phones. Ask those who have cell phones what their rate plans are. Fill in the first chart on the overhead according to the students’ rate plans. If the students don’t know their plans, you may project the mock cell phone plans and use them to fill in the chart. Have the students fill in their charts as you work. Make the point that most cell phone plans consist of a set cost per month for a given number of minutes, plus a charge for additional minutes. (5 minutes).
- Choose one of the plans as an example and use it to fill in the second chart on the overhead. Have students calculate how much the monthly bill would be if the cell-phone user went over his or her monthly plan by 5, 10, 15, 20, 25, 30, 35, and 40 minutes. As you fill in the chart, be sure to write out on the board how you calculate the monthly bill. (10 min.)
- Ask students if they see a pattern forming; if so, what is it? (Students should answer that they multiply the number of minutes over and the cost per minute and then add the monthly charge.) (5 minutes)
- Ask the students what the constant amounts are in the calculation. (Answer: The cost per month and cost for additional minutes). Ask them which amount changes in each of the examples. (Answer: The number of minutes over) (5 minutes)
- Ask the students if they can figure out a mathematical formula that they could use to get the answer each time (use words first and then substitute with x and y). (5 minutes)
- Independent practice: Hand out the linear equation scenarios worksheet and have the students complete it. (The worksheet lists hypothetical scenarios and asks the students to write out, in words, a formula for each scenario. The worksheet also has them decide for each scenario what the constant amounts and variable amounts are. Students who don’t finish the worksheet in class should finish it for homework. (20 minutes)
- To wrap up the lesson, ask the students what jobs use these types of skills. (Answers include careers in advertising and marketing, construction managers, accountants and auditors, computer programmers, mathematicians, architects, aerospace engineers, and biomedical engineers. Have students discuss how people in these careers might use linear equations. (5-10 minutes)

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 7

**Goal 5**: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.**Objective 5.02**: Translate among different representations of algebraic expressions, equations and inequalities.**Objective 5.03**: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.**Objective 5.04**: Develop fluency in the use of formulas to solve problems.

- Common Core State Standards
- Mathematics (2010)
#### Grade 6

- Expressions & Equations
- 6.EE.6Use 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.
- 6.EE.9Use 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...

#### Grade 7

- 7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x...

- Expressions & Equations