Lesson 4

Ordering Rational Numbers

Lesson Narrative

This lesson solidifies what students have learned in the past several lessons about the ordering of rational numbers on the number line. Students practice ordering rational numbers and use precise language to describe the relationships between numbers plotted on a number line (MP6). These phrases include “greater than,” “less than,” “negative,” and “opposite.”

Learning Goals

Teacher Facing

  • Compare rational numbers without a context and express the comparisons using the terms “greater than,” “less than,” and “opposite” (orally and in writing).
  • Comprehend that all negative numbers are less than all positive numbers.
  • Order rational numbers from least to greatest, and explain (orally and through other representations) the reasoning.

Student Facing

Let’s order rational numbers.

Required Preparation

Make 1 copy of the “Ordering Rational Number Cards” activity blackline master for every 2 students, and cut them up ahead of time. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Learning Targets

Student Facing

  • I can compare and order rational numbers.
  • I can use phrases like “greater than,” “less than,” and “opposite” to compare rational numbers.

CCSS Standards

Building On


Building Towards

Glossary Entries

  • negative number

    A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.

    number line with arrow that extends from 0 to -7
  • opposite

    Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.

    For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.

    Number line that extends from -5 to 5, with points at -4 and 4.
  • positive number

    A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.

    Number line with green arrow extending from 0 to 7
  • rational number

    A rational number is a fraction or the opposite of a fraction.

    For example, 8 and -8 are rational numbers because they can be written as \(\frac81\) and \(\text-\frac81\).

    Also, 0.75 and -0.75 are rational numbers because they can be written as \(\frac{75}{100}\) and \(\text-\frac{75}{100}\).

  • sign

    The sign of any number other than 0 is either positive or negative.

    For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.