Adding Multiples of 10 - Second Grade Mathematics

Multiples of ten—such as 10, 20, 30, 40, 50, 60, 70, 80, and 90—are known as friendly numbers because their ones digit is always zero. When you add a multiple of ten to any two-digit number, something wonderful happens: the ones digit of your number never changes! All the action takes place strictly in the tens column. In this chapter, you will learn how to add multiples of ten using mental place value math, explore vertical jumps on hundred charts, and model addition with base-ten rods.

The Secret of the Unchanging Ones Place

When adding a multiple of ten, think of the zero as an empty basket that adds no ones to your collection.

Adding Multiples of Ten:
    35 + 20 = 55
    ^^   ^^   ^^
Tens: 3 tens + 2 tens = 5 tens (50)
Ones: 5 ones + 0 ones = 5 ones (5)
Total Sum: 50 + 5 = 55

Focus Solely on the Tens Digits

Because 20 has 0 ones, the 5 ones in 35 are completely untouched. You simply look at the tens: 3 tens plus 2 tens equals 5 tens. Attach the 5 ones, and your answer is instantly 55! More examples: 42 + 30: 4 tens + 3 tens = 7 tens. Result = 72. 61 + 20: 6 tens + 2 tens = 8 tens. Result = 81. 18 + 50: 1 ten + 5 tens = 6 tens. Result = 68.

Connecting to Single-Digit Addition Facts

Notice that adding multiples of ten is just single-digit addition wearing a tens costume: 3 + 2 = 5 =====> 30 + 20 = 50 =====> 35 + 20 = 55 7 + 2 = 9 =====> 70 + 20 = 90 =====> 74 + 20 = 94

Navigating the Hundred Chart Vertically

On a standard 1 to 100 chart, numbers are arranged in rows of ten. This layout makes adding multiples of ten a visual adventure.

Hundred Chart Excerpt:
+----+----+----+----+----+
| 23 | 24 | 25 | 26 | 27 |
+----+----+----+----+----+
| 33 | 34 | 35 | 36 | 37 |   <--- 1 step down = +10
+----+----+----+----+----+
| 43 | 44 | 45 | 46 | 47 |   <--- 2 steps down = +20
+----+----+----+----+----+
| 53 | 54 | 55 | 56 | 57 |   <--- 3 steps down = +30
+----+----+----+----+----+

Stepping Down the Columns

Every time you move down one square in the exact same column, the number increases by exactly 10. To add 10: take 1 step down. To add 20: take 2 steps down. To add 30: take 3 steps down. If you start at 25 and need to add 30, put your finger on 25, jump straight down 3 boxes (35, 45, 55), and you land on 55. You never have to move left or right!

Open Number Line Jumps of 10

On an open number line, adding multiples of ten is represented by drawing large, smooth hops labeled +10.

Solving 46 + 30 on an Open Number Line:
          +10             +10             +10
     +----------->   +----------->   +----------->
-----+---------------+---------------+---------------+--->
    46              56              66              76

Breaking Multiples of Ten into Jumps of 10

The number 30 is three tens. Starting at 46, draw three hops of 10: First hop: 46 + 10 = 56 Second hop: 56 + 10 = 66 Third hop: 66 + 10 = 76 Final answer: 76.

Making a Single Big Jump

As your mental fluency grows, you can make one single large jump of +30: start at 46, think 4 tens + 3 tens = 7 tens, and jump directly to 76 in one leap!

Practice Exercises

Exercise 1: Calculate the sum of 54 + 30 using mental math. Explain what happened to the tens digit and what happened to the ones digit.

Exercise 2: If you start on number 38 on a hundred chart and jump straight down 4 rows, what number will you land on? Write the addition equation that models this move.

Exercise 3: Draw or describe the jumps you would make on an open number line to solve 27 + 40.

Exercise 4: A school library had 43 books on a cart. The librarian added 50 more books to the cart. How many books are on the cart now?

Solutions and Explanations

Solution to Exercise 1: To calculate 54 + 30, add the tens: 5 tens + 3 tens = 8 tens (80). Combine with the 4 ones to get 84. The tens digit increased from 5 to 8, while the ones digit remained 4 because 30 has 0 ones.

Solution to Exercise 2: Jumping straight down 4 rows means adding 4 tens, or 40. Starting at 38 and moving down 4 rows (48, 58, 68, 78) lands on 78. The addition equation is 38 + 40 = 78.

Solution to Exercise 3: On an open number line, start at 27. Since 40 is four tens, make four consecutive jumps of 10: from 27 jump 10 to 37, jump 10 to 47, jump 10 to 57, and jump 10 to 67. The final sum is 67.

Solution to Exercise 4: To solve 43 + 50, add the tens: 4 tens + 5 tens = 9 tens (90). Combine with the 3 ones: 90 + 3 = 93. There are now 93 books on the cart.