The Count-On Strategy - First Grade Mathematics

When beginners first learn to add, they often count everything from one. For example, to solve 5 + 3, they count: "1, 2, 3, 4, 5... 6, 7, 8." While this gets the right answer, counting from one takes a lot of time. Experienced first grade mathematicians use a much faster, smarter strategy called counting on! When you count on, you start with the bigger number, keep it locked securely in your head, and count forward only the extra steps needed. In this chapter, you will master the count-on strategy and learn how to add within 10 in seconds.

How the Count-On Strategy Works

Counting on means using your starting number as a launch pad.

Solving 6 + 3 by Counting On:
Don't recount 1 to 6!
Start at 6:  "SIX..." (Tap your head!)
Hop 1:       "Seven"  (Hold up 1 finger)
Hop 2:       "Eight"  (Hold up 2 fingers)
Hop 3:       "Nine!"  (Hold up 3 fingers)

Result: 6 + 3 = 9!

The Three Steps of Counting On:

Step 1: Identify the two addends (for example, 6 and 3). Step 2: Say the bigger number out loud firmly: "6!" You do not need to count 1, 2, 3, 4, 5, 6; you already know there are 6! Step 3: Count forward 3 more numbers: "7, 8, 9." The last number you say is your answer!

Always Start with the Bigger Number

What happens if the smaller number is written first, like in 2 + 7?

Comparing Two Ways to Solve 2 + 7:

Slow Way (Start at 2):
"TWO... 3, 4, 5, 6, 7, 8, 9"  -> Counted 7 times! (Tiring!)

Smart Way (Start at 7):
"SEVEN... 8, 9"                -> Counted only 2 times! (Super fast!)
Both ways give 9, but starting with 7 takes 2 seconds!

The Turn-Around Rule Saves Time

Because addition allows you to add numbers in any order, always scan the problem first and circle the larger number. Even if the problem says 3 + 8, flip it in your mind to 8 + 3, lock 8 in your head, and count on: "8... 9, 10, 11!"

Using a Number Path to Track Your Hops

A number path gives you a clear visual track for each forward hop.

Solving 5 + 4 on a Number Path:
          +1      +1      +1      +1
        /-----\ /-----\ /-----\ /-----\
| 1| 2| 3| 4|[5]| 6 | 7 | 8 |[9]|10|
            Start             Land

One Hop per Unit

Make sure each hop lands squarely in the next box. Hop 1 lands on 6, hop 2 lands on 7, hop 3 lands on 8, and hop 4 lands on 9. 5 plus 4 equals 9!

Practice Exercises

Exercise 1: Solve 7 + 2 using the count-on strategy. Describe the exact words you say out loud and how many hops you take.

Exercise 2: You need to solve 3 + 6. Which number should you lock in your head first, and why? What is the final sum?

Exercise 3: Solve these equations using mental counting on: 5 + 3 = __ 8 + 2 = __ 1 + 9 = __

Exercise 4: A student solves 4 + 3 by counting: "1, 2, 3, 4, 5, 6, 7." Explain to the student how to use the count-on strategy to solve it much faster.

Solutions and Explanations

Solution to Exercise 1: Lock 7 in your head and say: "Seven..." Then take 2 hops forward: "eight, nine." The final sum is 9 (7 + 2 = 9).

Solution to Exercise 2: You should lock 6 in your head first because 6 is the larger number. It is much faster to count on 3 hops from 6 ("6... 7, 8, 9") than to count on 6 hops from 3. The final sum is 9.

Solution to Exercise 3: 5 + 3 = 8 (5... 6, 7, 8) 8 + 2 = 10 (8... 9, 10) 1 + 9 = 10 (Start at 9: 9... 10)

Solution to Exercise 4: Tell the student: "Instead of starting at 1, lock the number 4 in your head because you already know you have 4. Then count on only 3 more numbers: 5, 6, 7! You get the same answer of 7 with much less counting."