Ordering Rational Numbers

10 min

Teacher Prep
Setup
3 minutes of quiet work time followed by whole-class discussion.

Narrative

The purpose of this Warm-up is for students to review strategies for using inequality symbols and comparing whole numbers, decimal numbers, and fractions. The numbers in each pair have been purposefully chosen based on misunderstandings students typically have when comparing numbers.

Launch

Give students 3 minutes of quiet work time, and follow with a whole-class discussion.

Representation: Develop Language and Symbols. Provide students with access to definitions of the recently defined symbols for less than and greater than.
Supports accessibility for: Language, Memory

Student Task

Use the symbols >, <, or = to compare each pair of numbers. Be prepared to explain your reasoning.

  • 12 ‾ 1912~ \underline{\hspace{0.5in}}~19
  • 212 ‾ 190212~ \underline{\hspace{0.5in}}~190
  • 15 ‾ 1.515~ \underline{\hspace{0.5in}}~1.5
  • 9.02 ‾ 9.29.02~ \underline{\hspace{0.5in}}~9.2
  • 6.050 ‾ 6.056.050~ \underline{\hspace{0.5in}}~6.05
  • 0.4 ‾ 9400.4~ \underline{\hspace{0.5in}}~\frac{9}{40}
  • 1924 ‾ 1921\frac{19}{24}~ \underline{\hspace{0.5in}}~\frac{19}{21}
  • 1617 ‾ 1112\frac{16}{17} ~ \underline{\hspace{0.5in}}~\frac{11}{12}

Sample Response

  • 12<1912 < 19. Sample reasoning: 12 is farther left on the number line than 19. 
  • 212 >190212  > 190. Sample reasoning: 212 is farther right on the number line than 190. 
  • 15>1.515 > 1.5. Sample reasoning: 15 is 10 times farther to the right on the number line than 1.5.
  • 9.02 < 9.29.02 <  9.2. Sample reasoning: Both numbers have 9 wholes, 9.2 has 2 tenths, and 9.02 doesn’t have any.
  • 6.050=6.056.050 = 6.05. Sample reasoning: Both numbers have the same number of ones, tenths, hundredths, and thousandths.
  • 0.4>9400.4>\frac{9}{40}. Sample reasoning: 0.4 is greater than 14\frac14, and 940\frac{9}{40} is less than 14\frac14.
  • 1924<1924\frac{19}{24}<\frac{19}{24} . Sample reasoning: Both fractions are the same number of pieces, and 121\frac{1}{21} is greater than 124\frac{1}{24}. 
  • 1617>1112\frac{16}{17}>\frac{11}{12} . Sample reasoning: Both fractions are 1 unit from a whole, and 117\frac{1}{17} is less than 112\frac{1}{12}. 
Activity Synthesis (Teacher Notes)

The goal of this discussion is to address any misconceptions the class has when comparing rational numbers. Begin by inviting 1–2 students to share their reasoning for each pair of numbers. Record and display their reasoning for all to see.

Since there are many pairs of numbers to compare, it may not be possible to share all of the students’ strategies for each pair. Consider sharing only one strategy for each pair if all of the students agree and more than one if there is a disagreement among the students. 

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·Understand ordering and absolute value of rational numbers.
  • 6.NS.C.7·Understand ordering and absolute value of rational numbers.

15 min

10 min