Understanding Bundles of Ten - First Grade Mathematics

Have you ever tried holding twenty loose crayons in your hands? They can easily slip through your fingers and roll all over the floor! But if you wrap a rubber band around ten crayons, you have a tidy bundle that stays together. In mathematics, grouping ten individual ones into a single bundle of ten is the foundation of our entire place-value system. Once you understand that ten ones can become one ten, you can count and understand large numbers with ease. In this chapter, you will explore how loose ones are bundled into tens and how numbers are built from these two parts.

Making a Bundle of Ten

Ten single units can be grouped together to create a brand-new unit called a "ten."

The Bundling Transformation:
Ten Loose Ones:   *  *  *  *  *  *  *  *  *  *
                  \__________________________/
                               |
                        Wrap Together!
                               |
                               v
One Bundle of Ten:    [ ********** ]
                    (1 Ten = 10 Ones)

The Rule of Ten

Whenever you collect 10 loose items, you trade them in for 1 bundle. Ten loose sticks become 1 bundle of craft sticks. Ten single pennies have the exact same value as 1 dime. Ten small cubes snap together to form 1 rod.

The Big Idea: Unitizing

In math, "unitizing" means seeing a group of ten items simultaneously as ten individual units AND as one single larger object. Just like 1 carton holds 12 eggs, or 1 package holds 10 markers, 1 bundle holds 10 ones.

Building Two-Digit Numbers with Bundles and Singles

Every two-digit number from 10 to 99 is made of some bundles of ten and some leftover loose ones.

Representing 34 with Bundles:
Bundles of Ten:  [ ********** ]  [ ********** ]  [ ********** ]  -> 3 Tens (30)
Loose Singles:   *   *   *   *                                    -> 4 Ones  (4)

Total: 3 Tens and 4 Ones = 34

Reading the Two Digits

Look at the numeral 34: The digit on the left (3) tells how many complete bundles of ten there are. The digit on the right (4) tells how many loose single ones there are. 3 tens equals 30. 4 ones equals 4. 30 + 4 = 34!

Comparing Loose Ones to Bundles

Counting by ones takes a long time, while counting by tens and ones is fast and accurate.

Counting 26 Items:
Slow Way:  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 (26 counts!)
Fast Way:  "10, 20... 21, 22, 23, 24, 25, 26!" (Only 8 counts!)

Efficient Counting

Grouping items into tens before counting is how bank tellers count money and how scientists count specimens. It saves time and prevents counting errors.

Practice Exercises

Exercise 1: If you have 10 loose craft sticks and wrap a rubber band around them, what new math unit have you created? How many ones are inside that unit?

Exercise 2: You have 4 bundles of ten sticks and 7 loose single sticks. What two-digit number do you have in all?

Exercise 3: In the number 52, what does the digit 5 represent, and what does the digit 2 represent?

Exercise 4: If you have 28 counters, how many complete bundles of ten can you make, and how many loose counters will be left over?

Solutions and Explanations

Solution to Exercise 1: You have created 1 bundle of ten (one ten). There are exactly 10 ones inside that bundle.

Solution to Exercise 2: You have 47 sticks in all. 4 bundles of ten equal 40, and 7 loose sticks equal 7, giving 40 + 7 = 47.

Solution to Exercise 3: In the number 52, the digit 5 represents 5 tens (which has a value of 50), and the digit 2 represents 2 loose ones (which has a value of 2).

Solution to Exercise 4: With 28 counters, you can make 2 complete bundles of ten (using 20 counters), and you will have 8 loose counters left over.