Inequalities

Inequalities

Look For and Use Structure

Opening

Look for and Use Structure

Watch the video to see how Emma and Jan talk about the structure of the number line as they look at temperatures on a thermometer.

  • Discuss how Emma and Jan used the structure of the number line to order the temperatures.
  • What problems would you see in the world if there was no structure or pattern in the number line?

VIDEO: Look for and Use Structure

Look for and Use Structure

 

Mathematical Statements

Opening

Mathematical Statements

Write a mathematical statement to express that –5°F is warmer than –24°F.

  • The symbol < means “is less than.”
  • The symbol > means “is greater than.”

Math Mission

Opening

Understand the meaning of < and > when using positive and negative numbers.

Evaluate Inequalities

Work Time

Evaluate Inequalities

Determine if the inequality is true or false.

Justify your answer on a number line.

  • −10 < −15
  • −12 < −1
  • −2 > −2.5
  • 52 ≤ 1
  • 73 > −2
  • −2.53 < −2.23

When you locate the numbers on the number line, what do you know about the number to the right?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you ordered positive and negative numbers. Use your work to support your explanation.

Challenge Problem

  • Write a procedure to explain how to compare any two numbers.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about how to compare any two rational numbers.

As students present, ask questions such as:

  • How do you know if the inequality is true or false?
  • How does your number line model the math?
  • How did you resolve any disagreements with your partner?
  • What advice would you give someone who was trying to determine whether an inequality was true or false?
  • What do the inequality symbols < and > mean?

Positive and Negative Numbers

Formative Assessment

Summary of the Math: Positive and Negative Numbers

Write a summary of what you learned about ordering and comparing positive and negative numbers.

Check your summary:

  • Do you use the term inequality?
  • Do you describe how to use a number line to compare two numbers?
  • Do you use the inequality symbols < and >?
  • Do you explian how to order numbers?

Check Your Understanding

Formative Assessment

Check Your Understanding

Complete this Self Check by yourself.

Answer the questions. Explain your thinking.

Use the Number Line Tool if you find it to be helpful.

  1.  Which of these numbers is least?
     −0.6, −6, −6.06, −6.6, 6.6, or 0.6
  2.  What is the opposite of the opposite of −2.7 ?
  3.  Do the two expressions below have the same value?
     −|−7| and −|7|
  4.  Which of these two numbers is farther from 1?
     −6.6 or 6.

HANDOUT: Integers and Rational Numbers Self Check

INTERACTIVE: Number Line Tool

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.

A strategy I use to tell which of two numbers is greater is…