Ordering Numbers from Least to Greatest - First Grade Mathematics

Once you can compare two numbers, you can take an exciting next step: putting three, four, or even more numbers into order! Ordering numbers means arranging them along a line based on their size. You can order numbers from least to greatest (starting with the smallest amount and stepping up to the biggest), or from greatest to least (starting with the biggest amount and stepping down to the smallest). In this chapter, you will master how to organize any set of numbers up to 20 into a clean, orderly sequence.

Understanding Least and Greatest

Before putting a set of numbers in order, you must identify the two extreme ends of your group: the least and the greatest.

Identifying Ends in the Set {14, 3, 9}:

    3                 9                14
 [LEAST]          [MIDDLE]         [GREATEST]
(Closest to 0)                  (Furthest from 0)

The Least

The least number is the smallest quantity in the group. On a number line, it sits closest to zero. In the group 14, 3, and 9, the number 3 is the least.

The Greatest

The greatest number is the largest quantity in the group. On a number line, it sits furthest to the right, furthest from zero. In the group 14, 3, and 9, the number 14 is the greatest.

Step-by-Step Method for Ordering from Least to Greatest

To put a collection of numbers in order from least to greatest without getting confused, follow these three clear steps:

Ordering the Set: { 12, 5, 17, 8 }

Step 1: Find the LEAST number and write it first:
        5 is the smallest! -> [ 5 ]

Step 2: Look at the remaining numbers { 12, 17, 8 }. Find the next smallest:
        8 comes next! -> [ 5, 8 ]

Step 3: Look at { 12, 17 }. Find the next smallest:
        12 comes next! -> [ 5, 8, 12 ]

Step 4: Write the final remaining number (the GREATEST):
        17 is last! -> [ 5, 8, 12, 17 ]

Cross It Off as You Go

When working with pencil and paper, draw a light line through each number in your list as you copy it into your ordered sequence. This ensures you do not write the same number twice or forget one of the numbers.

Ordering from Greatest to Least

Sometimes you need to arrange items from the biggest down to the smallest. This is called ordering from greatest to least.

Ordering { 4, 19, 11 } from Greatest to Least:
Start with the GREATEST:  19
Next biggest:             11
The LEAST goes last:       4

Final Ordered Sequence:   19, 11, 4

Thinking Like a Countdown

Ordering from greatest to least is just like walking backward on the number path. You find the number that is furthest along the path and work your way back toward zero.

Using a Number Line to Check Your Order

A number line is your best verification tool. If your numbers are ordered correctly from least to greatest, they will match the left-to-right order of points on a number line.

Checking { 2, 7, 13, 20 } on a Number Line:
0--1--[2]--3--4--5--6--[7]--8--9--10--11--12--[13]--14--15--16--17--18--19--[20]
       ^                ^                      ^                              ^
      1st              2nd                    3rd                            4th
Points go strictly from left to right: The order is verified!

Practice Exercises

Exercise 1: Put this set of numbers in order from least to greatest: 15, 2, 8.

Exercise 2: Put this set of numbers in order from least to greatest: 19, 7, 13, 10.

Exercise 3: Arrange these numbers in order from greatest to least: 6, 18, 12.

Exercise 4: A student ordered the numbers 4, 16, 9 from least to greatest and wrote: 4, 16, 9. Did the student order them correctly? If not, identify the mistake and write the correct order.

Solutions and Explanations

Solution to Exercise 1: The least number is 2, the middle number is 8, and the greatest number is 15. In order from least to greatest: 2, 8, 15.

Solution to Exercise 2: Comparing all four numbers: 7 is the least, followed by 10, then 13, and 19 is the greatest. In order from least to greatest: 7, 10, 13, 19.

Solution to Exercise 3: Starting with the greatest amount and stepping down to the least: 18 is the greatest, 12 comes next, and 6 is the least. In order from greatest to least: 18, 12, 6.

Solution to Exercise 4: The student did not order them correctly. The student placed 16 before 9, but 9 is less than 16 (9 comes before 16 on a number path). The correct order from least to greatest is 4, 9, 16.