Adding Three Single-Digit Numbers - First Grade Mathematics

What happens when you have three numbers to add together, like 3 + 4 + 7? While your brain can only combine two numbers at a time, you have the freedom to choose which two numbers you want to add first! A skilled mathematician scans all three numbers to look for friendly partnerships, like pairs that make 10 or doubles facts. By pairing up friendly numbers first, adding three numbers becomes an enjoyable puzzle. In this chapter, you will master the art of adding three single-digit numbers within 20.

The Two-Step Adding Process

Since you cannot add three numbers at the exact same instant, you always break the problem into two steps: Step 1: Pick two numbers and add them together to make a partial sum. Step 2: Add the third remaining number to that partial sum to get the final total.

Adding 2 + 5 + 3:
Step 1: Choose 2 and 5 -> 2 + 5 = 7
Step 2: Add the third number (3) -> 7 + 3 = 10!
Total: 10

Strategy 1: Look for Friends of 10

The smartest first move when adding three numbers is to search for two numbers that join together to make 10!

Finding Friends of 10 in 4 + 7 + 6:
Scan the numbers: Do you see two friends of 10?
YES! 4 and 6 make 10!

   4   +   7   +   6
   \               /
    \             /
     \___________/
           |
          10   +   7  =  17!

Why Finding 10 Is the Best Strategy

Once you combine the two friends of 10 into 10, adding the third number is instant: 10 + 7 is 17! You do not have to count on your fingers at all.

Strategy 2: Look for Doubles

If there are no friends of 10, look to see if two of the numbers are identical twins (a doubles fact).

Finding Doubles in 3 + 8 + 3:
Scan the numbers: 3 and 3 are twins!

   3   +   8   +   3
   \               /
    \_____________ /
           |
           6   +   8

Finish with a Strategy

Now you have 6 + 8. You can solve 6 + 8 using doubles plus two, or by making a ten (8 + 2 = 10, plus 4 = 14). Total is 14!

The Total Is Always the Same!

No matter which two numbers you choose to add first, the final answer will never change.

Three Ways to Add 2 + 3 + 4:
Way 1: (2 + 3) + 4 = 5 + 4 = 9
Way 2: 2 + (3 + 4) = 2 + 7 = 9
Way 3: (2 + 4) + 3 = 6 + 3 = 9
All three ways equal 9!

Practice Exercises

Exercise 1: Solve 3 + 8 + 7. Which two numbers make 10? Show how you combine them to find the final total.

Exercise 2: Solve 4 + 5 + 4. Which two numbers form a doubles fact? Show the steps to find the sum.

Exercise 3: Solve these three-number addition problems by looking for friendly pairs: 2 + 6 + 8 = __ 5 + 3 + 5 = __ 1 + 9 + 4 = __ 7 + 2 + 3 = __

Exercise 4: A student solves 3 + 2 + 5 by adding 3 + 2 first to get 5, then adding 5 + 5 to get 10. Another student adds 2 + 5 first to get 7, then adds 3 + 7 to get 10. Which student is correct?

Solutions and Explanations

Solution to Exercise 1: The numbers 3 and 7 make 10 (3 + 7 = 10). Then add the remaining number 8: 10 + 8 = 18. The total is 18.

Solution to Exercise 2: The numbers 4 and 4 form a doubles fact: 4 + 4 = 8. Then add the remaining 5: 8 + 5 = 13 (or 8 + 2 + 3 = 13). The total is 13.

Solution to Exercise 3: 2 + 6 + 8 = 16 (2 + 8 = 10, then 10 + 6 = 16) 5 + 3 + 5 = 13 (5 + 5 = 10, then 10 + 3 = 13) 1 + 9 + 4 = 14 (1 + 9 = 10, then 10 + 4 = 14) 7 + 2 + 3 = 12 (7 + 3 = 10, then 10 + 2 = 12)

Solution to Exercise 4: Both students are completely correct! In addition, you can group the numbers in any order you choose, and the sum will always be the same (10).