Understanding Teen Numbers (11 to 19) - First Grade Mathematics

Once you count past ten, you enter a magical kingdom of numbers known as the teen numbers: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, and nineteen. At first glance, teen numbers can seem tricky because their names do not always sound like their digits. However, all teen numbers share one incredible secret: every single teen number is made of one full group of ten plus some extra single ones. In this chapter, you will unlock this secret and master how teen numbers are built.

The Secret Structure of Teen Numbers

Every teen number from 11 to 19 can be split cleanly into two parts: a group of ten, and some loose ones.

The Structure of 14:
+---+---+---+---+---+
| * | * | * | * | * |  -> Full Ten-Frame (10)
+---+---+---+---+---+
| * | * | * | * | * |
+---+---+---+---+---+
        +
+---+---+---+---+---+
| * | * | * | * |   |  -> Extra Ones (4)
+---+---+---+---+---+
|   |   |   |   |   |
+---+---+---+---+---+
Total: 10 + 4 = 14

The Role of the Digit 1

Look at the numeral 14. The digit 1 on the left side does not mean one single object; it stands for ONE WHOLE GROUP OF TEN. The digit 4 on the right stands for 4 loose ones.

Seeing Ten as a Unit

When you have ten individual cubes, you can snap them together to make a solid rod of ten. Once they are snapped together, you can count them as "one ten." A teen number is always "one ten" and some leftover cubes.

Exploring Each Teen Number from 11 to 19

Let us walk through each teen number to examine its components and its special name.

Teen Number Breakdown Table:
Number   Name         Composition
  11     eleven       1 ten and 1 one    (10 + 1)
  12     twelve       1 ten and 2 ones   (10 + 2)
  13     thirteen     1 ten and 3 ones   (10 + 3)
  14     fourteen     1 ten and 4 ones   (10 + 4)
  15     fifteen      1 ten and 5 ones   (10 + 5)
  16     sixteen      1 ten and 6 ones   (10 + 6)
  17     seventeen    1 ten and 7 ones   (10 + 7)
  18     eighteen     1 ten and 8 ones   (10 + 8)
  19     nineteen     1 ten and 9 ones   (10 + 9)

The Tricky Names: Eleven and Twelve

The numbers 11 and 12 do not have "teen" in their names. Eleven comes from ancient words meaning "one left over after ten." Twelve comes from words meaning "two left over after ten." Remembering that eleven is 10 + 1 and twelve is 10 + 2 helps you connect their unusual names to their true values.

The Regular Teen Names

Starting with thirteen, the word ending "-teen" actually means "and ten." Fourteen means "four and ten." Sixteen means "six and ten." Seventeen means "seven and ten." Eighteen means "eight and ten." Nineteen means "nine and ten." Notice that thirteen sounds like "three-teen" and fifteen sounds like "five-teen."

Modeling Teen Numbers with Manipulatives

Using concrete tools makes teen numbers easy to see and build.

Building 16 with Base-Ten Blocks:
One Rod of Ten:   [#|#|#|#|#|#|#|#|#|#]   (Value = 10)
Six Single Units: [#] [#] [#] [#] [#] [#] (Value = 6)
Total Value: 10 + 6 = 16

Double Ten-Frames

When using double ten-frames, the first ten-frame is always completely full. You never need to count the dots in the first ten-frame one by one because you know a full ten-frame always equals ten. To find the total, you simply say "ten" and then count on the dots in the second frame: "ten... eleven, twelve, thirteen, fourteen, fifteen, sixteen!"

Practice Exercises

Exercise 1: What two parts make up the number 17? Write the addition equation that shows how 17 is built from a ten and some ones.

Exercise 2: If you fill one ten-frame completely with red counters and place 3 yellow counters in a second ten-frame, what total number have you built? What is its name?

Exercise 3: In the number 18, what does the digit 1 represent, and what does the digit 8 represent?

Exercise 4: A friend says that 12 is made of 10 ones and 3 ones. Is your friend correct? Explain why or why not.

Solutions and Explanations

Solution to Exercise 1: The number 17 is made of 1 ten and 7 ones. The addition equation that represents this is 10 + 7 = 17.

Solution to Exercise 2: You have built the number 13, because one full ten-frame is 10, and 3 more counters makes 10 + 3 = 13. Its name is thirteen.

Solution to Exercise 3: In the numeral 18, the digit 1 on the left represents one group of ten (10 items), while the digit 8 on the right represents eight individual ones (8 items).

Solution to Exercise 4: Your friend is not correct. The number 12 is made of 10 and 2 ones (10 + 2 = 12). If you had 10 ones and 3 ones, you would have 13, not 12.