Adding 2-Digit and 1-Digit Numbers (No Regrouping) - First Grade Mathematics

What happens when you add a small single-digit number to a two-digit number, like 43 + 5? It looks like a big problem, but here is the golden secret: the tens stay completely relaxed, and only the ones do the work! Because the ones do not add up to ten or more, you do not need to make any new bundles. You simply combine the ones with the ones, and leave the tens alone. In this chapter, you will master adding a two-digit number and a one-digit number without regrouping, and discover how place value keeps your work tidy.

The Rule of Like Units: Add Ones to Ones!

In mathematics, you must always add like units together: add apples to apples, tens to tens, and ones to ones!

The Place-Value Alignment of 43 + 5:

           Tens    Ones
             4       3
         +           5
         -----------------
             4       8   (3 ones + 5 ones = 8 ones!)

Result: 48!

Why the Tens Digit Stays 4

Look at the problem 43 + 5. The number 43 has 4 tens and 3 ones. The number 5 has 0 tens and 5 ones. Since you are adding 0 tens to 4 tens, the tens digit remains 4! Only the ones place changes from 3 to 8.

Modeling with Base-Ten Blocks

Let us build 52 + 6 using base-ten blocks.

Building 52 + 6:
Start with 52:
Rods (Tens):   [===] [===] [===] [===] [===]    -> 5 Tens (50)
Units (Ones):  [#] [#]                          -> 2 Ones (2)

Add 6 Units:
Units (Ones):  [#] [#] [#] [#] [#] [#]          -> 6 Ones (6)

Combine:
The 5 Rods stay untouched: 5 Tens
The Units combine: 2 + 6 = 8 Units
Total: 5 Tens + 8 Units = 58!

Check the Total Ones

Before finishing, always look at your new pile of units. 2 + 6 = 8. Since 8 is less than 10, no new rod can be made. The answer is simply 58!

Using the Count-On Strategy

For quick mental math, you can also lock the two-digit number in your head and count on the single-digit number!

Solving 64 + 3:
Lock 64 in your head: "64..."
Count on 3 steps: "65, 66, 67!"
Answer: 67!

Fast and Easy for Small Numbers

When the single-digit number is 1, 2, or 3, counting on is fast and effortless!

Practice Exercises

Exercise 1: Solve 34 + 5. Explain which digits you add together and why the tens digit does not change.

Exercise 2: Solve each equation mentally: 51 + 7 = __ 73 + 4 = __ 82 + 6 = __ 25 + 3 = __

Exercise 3: Maya has 42 stickers in her album. She finds 5 more stickers under her bed. How many stickers does Maya have now? Write the addition equation.

Exercise 4: A student solved 63 + 4 and wrote 103. What mistake did the student make, and what is the correct answer?

Solutions and Explanations

Solution to Exercise 1: 34 + 5 = 39. You add the ones digit 4 to the single digit 5 (4 + 5 = 9). The tens digit stays 3 because you added zero tens to the 3 tens.

Solution to Exercise 2: 51 + 7 = 58 (1 + 7 = 8) 73 + 4 = 77 (3 + 4 = 7) 82 + 6 = 88 (2 + 6 = 8) 25 + 3 = 28 (5 + 3 = 8)

Solution to Exercise 3: Maya started with 42 and found 5: 42 + 5 = 47. Maya has 47 stickers now.

Solution to Exercise 4: The student accidentally added the single digit 4 to the tens place (6 + 4 = 10) instead of the ones place! 4 represents 4 ones, not 4 tens. The correct calculation is to add 4 ones to 3 ones: 3 + 4 = 7, so 63 + 4 = 67.