Adding 1-Digit to 2-Digit Numbers - Second Grade Mathematics

Adding a single-digit number to a two-digit number is your first big step into multi-digit mathematics. It bridges your mental facts within 20 to larger numbers all the way to 100. Sometimes the addition stays comfortably within the same decade, while other times it gathers enough ones to spill over into the next decade. In this chapter, you will master two distinct cases: adding without crossing a decade (such as 34 + 3) and adding with crossing a decade using the make-a-next-ten strategy (such as 38 + 5).

Case 1: Adding Without Crossing a Decade

When the sum of the ones digits is 9 or less, the tens digit of the two-digit number stays completely unchanged.

Solving 43 + 5:
Tens in 43: 4 tens (value = 40)
Ones in 43: 3 ones
Addend:     5 ones

Combine Ones:  3 + 5 = 8
Recombine:     40 + 8 = 48

Breaking Apart Tens and Ones

Think of 43 as 40 + 3. You only need to add the single digit 5 to the 3 ones. Since 3 + 5 = 8, you recombine the 40 and 8 to get 48. More examples: 52 + 6: Add ones 2 + 6 = 8. Attach to 50 = 58. 71 + 7: Add ones 1 + 7 = 8. Attach to 70 = 78. 24 + 4: Add ones 4 + 4 = 8. Attach to 20 = 28.

Visualizing on a Hundred Chart

On a hundred chart, adding without crossing a decade simply means moving to the right along the same row. If you are on square 43 and take 5 steps to the right, you land on square 48 in that exact same row.

Case 2: Crossing a Decade (Make the Next Ten)

When the sum of the ones digits equals 10 or more, you must bundle 10 ones to create a brand-new ten, moving the number into the next decade.

Solving 38 + 6 by Making the Next Ten:

Step 1: Look at 38. The next friendly decade is 40.
        How many does 38 need to reach 40?
        38 needs 2 more.

Step 2: Decompose the single digit 6 to lend 2 to 38.
        6 breaks into 2 and 4.

Step 3: Add 38 + 2 to make 40.
        38 + 2 = 40

Step 4: Add the leftover 4 to 40.
        40 + 4 = 44

The Bridge-to-Ten Mental Model

Think of crossing into the next decade like crossing a bridge. In the problem 57 + 6: Start at 57. Walk 3 steps across the bridge to land on the solid ground of 60. You had 6 steps to take in total, and you used 3 to cross the bridge. Take your remaining 3 steps forward from 60: 60 + 3 = 63!

Number Line Bridge for 57 + 6:
        +3               +3
   +---------->     +---------->
---+------------+---+------------+--->
  57           60               63

Using Base-Ten Sketches to Verify

Whenever you want to verify your mental bridge, draw a quick base-ten sketch using lines for tens and dots for ones.

Sketching 28 + 5:
Original 28:   |  |   . . . . .
                      . . .
Add 5:                . . . . .

Count Ones: 8 dots + 5 dots = 13 dots.
Circle 10 dots and draw an arrow to create 1 new ten line |
Remaining dots: 3 dots.
Total Lines: 2 original + 1 new = 3 lines (30).
Total: 30 + 3 = 33!

Connecting the Trade to Mental Math

Notice how the sketch matches the mental math: the 13 ones gave us 1 new ten and 3 leftover ones. Adding 1 ten to 2 tens gave 3 tens (30), plus 3 ones = 33.

Practice Exercises

Exercise 1: Solve 62 + 7. Explain whether this problem crossed into a new decade, and state how you know.

Exercise 2: Solve 48 + 5 using the make-the-next-ten strategy. Show how the number 5 was decomposed.

Exercise 3: Solve 76 + 8 using a number line bridge model. Describe the jump to the friendly decade and the final jump.

Exercise 4: A basket contains 35 apples. A farmer adds 9 more apples to the basket. How many apples are in the basket now? Show your mental strategy.

Solutions and Explanations

Solution to Exercise 1: To solve 62 + 7, add the ones: 2 + 7 = 9. Recombining with 60 gives 69. This problem did not cross into a new decade because the sum of the ones digits (9) did not reach 10, so the tens digit remained 6.

Solution to Exercise 2: To solve 48 + 5, 48 needs 2 to reach the next friendly decade of 50. Decompose 5 into 2 and 3. Add 48 + 2 = 50. Then add the remaining 3: 50 + 3 = 53.

Solution to Exercise 3: For 76 + 8, the next decade is 80. Starting at 76, make a jump of 4 to reach 80. Since you need to add 8 in total and you have jumped 4, you have 4 left to jump. Make a second jump of 4 from 80 to land on 84. The sum is 84.

Solution to Exercise 4: To solve 35 + 9, use the make-the-next-ten strategy. The number 35 needs 5 to reach 40. Decompose 9 into 5 and 4. Add 35 + 5 = 40, then add the remaining 4: 40 + 4 = 44. There are 44 apples in the basket.