Comparing Positive and Negative Numbers

10 min

Teacher Prep
Setup
Groups of 2–4. Display the 4 inequalities for all to see. 1 minute of quiet think time then time to share with their group. Follow with a whole-class discussion.

Narrative

This Warm-up prompts students to carefully analyze and compare four inequality statements. In making comparisons, students have a reason to use language precisely (MP6). The activity enables the terminologies that students know to be heard and enables the term “inequality” to be defined.

Launch

Arrange students in groups of 2–4. Display the inequality statements for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three statements that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A

54<2\frac{5}{4} < 2

B

8.5>0.958.5 > 0.95

C

8.5<78.5 < 7

D

10.00<10010.00 < 100

Sample Response

Sample responses:

A, B, and C go together because:

  • They all have a number that is not a whole number.
  • The numbers are all less than 10.

A, B, and D go together because:

  • They are all true statements.

A, C, and D go together because:

  • They each have a whole number.
  • They all have a “less than” symbol.
  • They all have values greater than 1.

B, C, and D go together because:

  • They all have a decimal.
  • They don’t have a fraction.
     
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “less than” or “greater than,” and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?

Explain to students that they have used the > and < symbols previously. Remind students that:

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

Tell students that a statement that uses these symbols to compare two values or expressions is called an inequality.

Standards
Building On
  • 4.NBT.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using &gt;, =, and &lt; symbols to record the results of comparisons.
  • 4.NBT.A.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using <span class="math">\(&gt;\)</span>, =, and <span class="math">\(&lt;\)</span> symbols to record the results of comparisons.
  • 5.NBT.3.b·Compare two decimals to thousandths based on meanings of the digits in each place, using &gt;, =, and &lt; symbols to record the results of comparisons.
  • 5.NBT.A.3.b·Compare two decimals to thousandths based on meanings of the digits in each place, using <span class="math">\(&gt;\)</span>, =, and <span class="math">\(&lt;\)</span> symbols to record the results of comparisons.
Building Toward
  • 6.NS.7.a·Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. <em>For example, interpret -3 &gt; -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.</em>
  • 6.NS.C.7.a·Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. <span>For example, interpret <span class="math">\(-3 &gt; -7\)</span> as a statement that <span class="math">\(-3\)</span> is located to the right of <span class="math">\(-7\)</span> on a number line oriented from left to right.</span>

15 min

10 min