Measuring with Non-Standard Units (Clips, Cubes) - First Grade Mathematics

Before you ever pick up a wooden ruler with inches and centimeters, you can measure almost anything in your world using everyday objects! Measuring with non-standard units means using small, identical items—such as paperclips, connecting cubes, pennies, or craft sticks—to find out the length of an object. When you count how many paperclips long your shoe is, you are translating a length into a number! In this chapter, you will master the art of measuring with non-standard units and discover why all measuring units in a chain must be identical.

What Is a Non-Standard Unit?

A non-standard unit is any everyday object that you use repeatedly to measure length.

Popular Non-Standard Units:
- Standard Paperclips:  C===D   (Small and lightweight)
- Connecting Cubes:     [#]     (Snap together into straight rods!)
- Pennies:              (1c)    (Round and uniform in size)
- Craft Sticks:         [===]   (Great for measuring longer objects)

Measuring a Pencil with Paperclips

Look at how a pencil is measured with small paperclips:

Measuring a Pencil:
Pencil:     [=========================>]
Paperclips: C===D C===D C===D C===D C===D
Count:        1     2     3     4     5
Result: The pencil is 5 paperclips long!

Naming the Unit

In measurement, a number alone is never enough! You cannot just say: "The pencil is 5." You must state what you measured with: "The pencil is 5 paperclips long," or "The pencil is 8 cubes long." The unit is part of the answer!

The Golden Rule: Use Identical Units!

What would happen if you measured a book using two giant jumbo paperclips and three tiny baby paperclips?

The Mixed-Unit Disaster:
Book:       [====================================]
Clips:      C========D  C========D  C===D  C===D
Count:      "It is 4 paperclips long!"  -> WRONG AND CONFUSING!

Why Units Must Be Identical

If your units are different sizes, your number has no meaning! To get a true measurement, every single unit in your chain must be the EXACT SAME SIZE. If you choose small paperclips, use ONLY small paperclips. If you choose blue connecting cubes, every cube must be the same size.

Smaller Units vs. Larger Units

Here is a fascinating puzzle: if you measure the exact same pencil with paperclips and then with connecting cubes, will you get the same number?

Measuring the Same Pencil with Different Units:
With Paperclips (Longer Unit):  C===D  C===D  C===D  C===D  -> 4 Paperclips
With Cubes (Shorter Unit):      [#][#][#][#][#][#][#][#]    -> 8 Cubes!

The Size-Quantity Rule:

When your measuring unit is LONGER, you need FEWER units to cover the length. When your measuring unit is SHORTER, you need MORE units to cover the length. Because a cube is shorter than a paperclip, it takes more cubes to measure the pencil!

Practice Exercises

Exercise 1: You measure a book using connecting cubes. The cube train spans from one end of the book to the other and uses 9 cubes. How long is the book? State the number and the unit.

Exercise 2: A student measures a table using some small paperclips and some large paperclips mixed together. Explain why this measurement is invalid.

Exercise 3: You measure your notebook with pennies and get 10 pennies. Then you measure the same notebook with craft sticks and get 3 craft sticks. Why is the number of pennies so much larger than the number of craft sticks?

Exercise 4: Name three different non-standard objects you could find in your home to measure the length of your bed.

Solutions and Explanations

Solution to Exercise 1: The book is 9 connecting cubes long.

Solution to Exercise 2: This measurement is invalid because the units are not uniform (identical in size). When you mix large and small units, the resulting count does not represent a standard, reliable length. All units in a measurement must be the exact same size.

Solution to Exercise 3: Pennies are much shorter in length than craft sticks. According to the size-quantity rule, when measuring with a smaller unit, you need many more units to cover the same total distance.

Solution to Exercise 4: You could use your own shoes, standard hardcover books, or bath towels laid end-to-end to measure the length of your bed.