Understanding the Count Back Strategy In Mathematics
The Connection With Subtraction
Count back is a strategy used in subtraction that involves counting backward from the minuend by the amount of the subtrahend. For example, to solve 9 – 3, start at 9 and count back three numbers: “8, 7, 6.” The answer is 6. The number you land on represents the difference. Counting back can be done by ones or in larger increments.
The Benefits Of This Strategy
The count back strategy supports students in developing a specific mental skill. When a student solves 8 – 3 by thinking “8… 7, 6, 5,” for example, they’re doing a few things simultaneously:
- They are holding 8 in their mind.
- They are tracking how many steps they’ve taken backward.
- They are keeping their place in the number sequence.
This kind of mental coordination builds working memory and sequential thinking.
This strategy also builds flexibility. Students who are comfortable counting back can choose their strategy based on the numbers in the problem. 9 – 2 is quick to count back, for example, while 9 – 7 might be easier to solve by counting on. This strategic thinking of knowing when a particular approach is efficient is what distinguishes procedural knowledge from mathematical reasoning.
A Note About Counting Backward
Before students can effectively use the count back strategy for subtraction, they need comfort with the backward number sequence itself. Counting backward is genuinely harder than counting forward, especially across decade boundaries (e.g., 21→20→19). The mental demand increases when students must simultaneously track the backward sequence AND count how many steps they’ve taken.
Be sure to build this fluency as a separate skill before connecting it to subtraction. Use backward counting songs, games like “Blast Off” (count down from 10 to 1), and practice tracing backward on number lines. When students can do these things confidently and automatically, they have the mental bandwidth to focus on the subtraction strategy itself.
Teaching Strategies For Count Back
Demonstrate Using a Number Line
A number line is a very helpful visual tool for demonstrating the count back strategy, as it helps students track each step as they count backward. For example, using the subtraction problem 10 – 3, place a marker on 10, and count backwards by ones: “9, 8, 7.” The final position, 7, is the answer.
Demonstrate by Walking the Number Line
Physical movement, such as stepping or hopping along a number line, can be an engaging way for students to “act out” the count back strategy. This type of kinesthetic experience helps students internalize the count back sequence and reinforces that subtraction is about finding the distance between numbers.
For example, create a number line on the floor using painters tape. Using the subtraction problem 10 – 3, have a student stand on 10, and hop or step as they count back by ones: “9, 8, 7.” Their final position, 7, is the answer. The three hops they made match the 3 being subtracted, making the connection between the number and the physical movement explicit.
Demonstrate Using Manipulatives
Use manipulatives like counters on a ten frame or Unifix cubes and remove one at a time as you use the count back strategy. For example, using the subtraction problem 10 – 3, start with ten counters on a ten frame and remove one counter at a time, counting each step out loud: “9, 8, 7.” The final count of objects shows the answer is 7.
Demonstrate with Fingers for Small Numbers
Fingers are also a simple, accessible tool for demonstrating this strategy, especially with smaller numbers. For example, using the subtraction problem 10 – 3, start with ten fingers up, then fold down one finger at a time while counting back, “9, 8, 7.” The number of fingers left up (7) represents the answer.
The Role of Count Back in Subtraction Development
The count back strategy is typically most useful in early subtraction instruction, when students are still building automaticity with basic facts. As students gain experience, they can move toward more efficient strategies such as thinking of 9 – 6 as “6 plus what equals 9?” or recognizing 10 – 3 instantly without counting. This is natural mathematical growth.
Count back will remain a valuable tool when students encounter an unfamiliar number combination or need to verify their thinking. It’s a foundational strategy that supports, but doesn’t replace, more sophisticated approaches.
