Ordering Three Objects by Length - First Grade Mathematics

Once you know how to compare two objects, you are ready to take on three! Ordering three objects by length means arranging them from shortest to longest, or from longest to shortest. Think of the classic story of Goldilocks and the Three Bears: there was a small bed, a medium bed, and a great big bed! In mathematics, arranging items in order creates a neat staircase of lengths. In this chapter, you will master lining up three objects against a common baseline, finding the extremes, and putting them into perfect sequential order.

Arranging Three Objects from Shortest to Longest

When ordering three objects from shortest to longest, you are building an ascending staircase where each item is longer than the one before it.

Three Pencils Ordered from Shortest to Longest:
Baseline
   |
   | Pencil 1: +--------+                     [ SHORTEST ]
   | Pencil 2: +-----------------+            [ MEDIUM   ]
   | Pencil 3: +------------------------+     [ LONGEST  ]
   |

The Three Positions:

Position 1: The Shortest (extends the least distance from the baseline). Position 2: The Medium (longer than the shortest, but shorter than the longest). Position 3: The Longest (extends the greatest distance from the baseline).

Step-by-Step Strategy for Ordering Three Objects

To order three objects without getting mixed up, follow this reliable method:

The 3-Step Ordering Plan:

Step 1: Line up all three objects against the same straight baseline!
Step 2: Find the SHORTEST object and place it first.
Step 3: Compare the remaining two objects:
        Put the medium one in the middle, and the LONGEST one last!

Ordering from Longest to Shortest

You can also order items in reverse, starting with the longest item and stepping down to the shortest: Longest -> Medium -> Shortest. Always read the directions carefully to know whether to start with the shortest or the longest!

The Connecting Cube Staircase

Connecting cubes are the best manipulative for seeing length order clearly.

Cube Trains in Length Order:
Train A (3 cubes): [#|#|#]
Train B (5 cubes): [#|#|#|#|#]
Train C (8 cubes): [#|#|#|#|#|#|#|#]

Order from Shortest to Longest: Train A (3), Train B (5), Train C (8).
Order from Longest to Shortest: Train C (8), Train B (5), Train A (3).

The Number Connection

Notice how ordering objects by length connects directly to ordering numbers! The lengths 3, 5, and 8 follow the exact same order as the numbers 3, 5, and 8 on a number path.

Practice Exercises

Exercise 1: You have three pieces of string: Red string is 10 cubes long, Blue string is 4 cubes long, and Green string is 7 cubes long. Order the strings by color from shortest to longest.

Exercise 2: Order the strings from Exercise 1 from longest to shortest.

Exercise 3: Name the three objects in the story of Goldilocks that are ordered by size, and explain how they relate to the concept of ordering by length.

Exercise 4: A student wants to order three paintbrushes by length. What tool or surface should the student use to make sure all three paintbrushes have the exact same starting point?

Solutions and Explanations

Solution to Exercise 1: In order from shortest to longest: Blue string (4 cubes), Green string (7 cubes), Red string (10 cubes).

Solution to Exercise 2: In order from longest to shortest: Red string (10 cubes), Green string (7 cubes), Blue string (4 cubes).

Solution to Exercise 3: The beds, chairs, and porridge bowls belonging to Baby Bear, Mama Bear, and Papa Bear are ordered by size. Baby Bear's items are the smallest/shortest, Mama Bear's items are medium, and Papa Bear's items are the largest/longest.

Solution to Exercise 4: The student should use a straight edge, such as the edge of a table, the straight spine of a hardcover book, or a ruler, to align the bottom bristles or handles of all three paintbrushes flush against a single baseline.