Number Line Comparisons

Task

1. Plot the following numbers on the number line. $$456 \qquad \qquad 983\qquad \qquad 938 \qquad \qquad 425 \qquad \qquad 220 \qquad \qquad 202\qquad \qquad 799$$
   
2. Choose eight pairs of numbers from those you plotted on the number line. Compare them.
1. _______ $\gt$ _______
2. _______ $\gt$ _______
3. _______ $\gt$ _______
4. _______ $\gt$ _______
5. _______ $\lt$ _______
6. _______ $\lt$ _______
7. _______ $\lt$ _______
8. _______ $\lt$ _______
3. Is the number $a$ greater or less than the number $b$?


How do you know?

IM Commentary

The purpose of this task is for students to use the number line to make comparisons between 3-digit numbers. As students plot the numbers, they have to make many comparison as they think through, for example, where to plot 456. The four in the hundreds place tells them the number is larger than 400 and smaller than 500. The five in the tens place helps them locate the number near the center of the interval between 400 and 500. Students may need to use tick marks to sub-divide this increment to show the midpoint or smaller refinements.

The task is designed, in part, to help students understand how the number line works and that numbers on the right of the number line are greater than numbers on the left. Part (b) draws attention to this concept.

The task also calls on students to develop and apply a systematic approach to filling in the blanks to avoid duplicate entries.

Note: There is a student printable attached.

Attached Resources

Solution

1. 

2. There are numerous correct comparisons. First a list of > possibilities:

   • 220 $\gt$ 202
   • 425 $\gt$ 202, 220
   • 799 $\gt$ 202, 220, 425
   • 938 $\gt$ 202, 220, 425, 799
   • 983 $\gt$ 202, 220, 425, 799, 938

   Then the $\lt$ solutions:

   • 202 $\lt$ 220, 425, 799, 938, 983
   • 220, $\lt$ 425, 799, 938, 983
   • 425 $\lt$ 799, 938, 983
   • 799 $\lt$ 938, 983
   • 938 $\lt$ 983

3. The number $b$ is greater than the number $a$.

   Acceptable student responses are similar to the following:

   • $b$ is greater because it is on the right.
   • The more right, the greater the number.