Inequality Statements Including Variables

Inequality Statements Including Variables

Swimming Class

Opening

Swimming Class

The size of a swimming class is limited to 10 or fewer students.

  • Talk with a partner. Can the swimming class have 5 students? 12 students? Exactly 10 students?
  • Let n represent the number of students who can participate in the swimming class. How can you write an inequality to represent this situation?

Math Mission

Opening

Write and interpret inequalities.

Write and Interpret Inequalities

Work Time

Write and Interpret Inequalities

Represent each situation below with an inequality that includes a variable.

For each situation, give three numbers that solve the inequality.

  1. To ride the roller coaster, a rider must be at least 54 inches tall. (Use h to represent the height in inches of a rider.)
  2. The most you can spend on a movie and popcorn is $8.00.
  3. To run for sheriff, you must be at least 30 years old.
  4. Water freezes at a temperature of 32°F or below.
  5. Martin scored more than 300 points in the game.

Hint:

  • Roller coaster problem: Can the height (h) be equal to 54 when the problem says “at least” 54 inches?
  • Movie problem: Let d represent the amount you can spend in dollars.
  • Sheriff problem: Choose a variable to represent the age in years.
  • Water temperature problem: Choose a variable to represent the temperature in degrees Fahrenheit.
  • Game problem: Could Martin have scored exactly 300 points?

Is Mia’s Statement True?

Work Time

Is Mia's Statement True?

Mia says that 4 < x represents the same relationship as x > 4.

  • Is her statement true? Explain why or why not.

Hint:

Try replacing x with a number.

Prepare a Presentation

Work Time

Prepare a Presentation

Choose one of the scenarios and present the inequality you wrote for it.

  • Explain how you used an inequality sign to show the relationship between two quantities.
  • Support your explanation with your work.

Challenge Problem

For each of the inequality situations:

  • Describe the types of numbers (for example, integers, decimals, positive and/or negative numbers) that fit the situation.
  • Give an example of each type of number that could be a solution to the inequality.
  1. To ride the roller coaster, a rider must be at least 54 inches tall.
  2. The most you can spend on a movie and popcorn is $8.00.
  3. To run for sheriff you must be at least 30 years old.
  4. Water freezes at a temperature of 32°F or below.
  5. Martin scored more than 300 points in the game.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ representations and explanations of inequalities.

Hint:

As your classmates present, ask questions such as:

  • How did you decide which inequality symbol to use?
  • Why did you include 30 (in the inequality about age for running for sheriff)?
  • Why didn't you include 300 (in the inequality about points that Martin scored)?

Inequalities

Formative Assessment

Summary of the Math: Inequalities

Write a summary about inequalities.

Hint:

Check your summary:

  • Do you explain what each inequality symbol represents?
  • For each symbol, do you describe how to write an inequality using variables?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

I think an inequality is similar to an equation because …