Base-Ten Blocks: Rods and Units - First Grade Mathematics

Mathematicians love using blocks you can touch and manipulate to make invisible ideas visible. One of the greatest math tools ever invented is the set of base-ten blocks. In first grade, you will work with two essential base-ten block pieces: the tiny unit cube and the long rod. These blocks allow you to build any number with your hands, compare values with your eyes, and solve addition and subtraction problems with certainty. In this chapter, you will master the names, values, and uses of rods and units.

The Two Core Pieces: Units and Rods

Base-ten blocks are precisely measured so that their sizes match their mathematical values.

The Unit and the Rod:

   Unit (Cube):
     +-+
     | |           Value = 1 One
     +-+

   Rod (Long):
     +-+-+-+-+-+-+-+-+-+-+
     | | | | | | | | | | |  Value = 10 Ones (1 Ten)
     +-+-+-+-+-+-+-+-+-+-+

The Unit

The unit is a small wooden or plastic cube that measures 1 centimeter on each side. A single unit stands for the number 1.

The Rod

A rod (often called a "long") is exactly ten unit cubes fused together into a straight bar. It is 10 centimeters long. A rod stands for one group of ten (1 ten = 10 ones).

Trading: 10 Units for 1 Rod

The golden rule of base-ten blocks is the trading rule: whenever you have ten units, you can trade them for one rod.

The Trading Rule:
  +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+
  | | | | | | | | | | | | | | | | | | | |   (10 loose units)
  +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+
                    ||  Trade!
                    vv
  +-+-+-+-+-+-+-+-+-+-+
  | | | | | | | | | | |                     (1 solid rod)
  +-+-+-+-+-+-+-+-+-+-+

Why Trade?

Trading makes your work neater and easier to count. Ten loose cubes can scatter and make a mess, but one rod is sturdy and easy to handle. In mathematics, we always prefer to group by tens whenever possible.

Building Numbers with Rods and Units

To build any two-digit number, gather the number of rods shown by the tens digit, and the number of units shown by the ones digit.

Building 43:
Rods (Tens):   [==========]  [==========]  [==========]  [==========]  -> 4 Rods  (40)
Units (Ones):  [#]  [#]  [#]                                           -> 3 Units (3)

Total: 4 tens + 3 ones = 43

Drawing Quick Sketches of Base-Ten Blocks

When you do not have plastic blocks in front of you, you can draw them quickly on paper: Draw a simple vertical line | to represent a rod of ten. Draw a small dot . or small square to represent a unit of one. To draw 43, draw 4 vertical lines and 3 dots: | | | | . . .. This quick sketch saves time and keeps your thinking organized.

Practice Exercises

Exercise 1: What is the name and value of the small single base-ten block? What is the name and value of the long bar block?

Exercise 2: How many unit cubes must you line up end-to-end to equal the exact length of one rod?

Exercise 3: Write the number that is shown by 5 rods and 8 units. Write an addition sentence showing the value of the rods plus the value of the units.

Exercise 4: Draw or describe the quick sketch you would make with lines and dots to represent the number 62.

Solutions and Explanations

Solution to Exercise 1: The small single block is called a unit (or cube) and has a value of 1. The long bar block is called a rod (or long) and has a value of 10.

Solution to Exercise 2: You must line up exactly 10 unit cubes to equal the length and value of one rod.

Solution to Exercise 3: 5 rods and 8 units represent the number 58. The addition sentence is 50 + 8 = 58 (since 5 rods equal 50 and 8 units equal 8).

Solution to Exercise 4: To sketch 62, draw 6 vertical lines to represent the 6 rods (tens) and 2 dots to represent the 2 units (ones): | | | | | | . ..