Understanding Count On In Mathematics
Count On Strategy And Addition
Count on is an addition strategy where you start with one addend and count forward by the value of the other addend to find the sum. This can be done by counting by ones or in larger increments (skip counting). For example, for 5 + 3, start at five and count forward 3 spaces. The number you land on (8) is the answer:
The Benefits Of The Count On Strategy
The count on strategy teaches students a helpful efficiency: you don’t need to count every object from 1 to find a sum. If you’re adding 5 + 3, you already know you have 5 – you don’t need to recount them. Instead, start at 5 and count on three more: “6, 7, 8.” This shift from “counting all” to “counting on” represents a significant conceptual leap. Students are beginning to treat numbers as quantities that can be trusted and built upon, rather than collections that must be verified each time.
Using the count on strategy requires students to recognize their starting number in relation to the numbers immediately before and after it. This nested structure (the idea that each number is part of a continuous sequence) deepens their understanding of number relationships and patterns.
This understanding is necessary for developing fluency in addition, and can also be used to reinforce the commutative property of addition as students see that beginning with either addend will result in the same sum. As students become more comfortable with the count on strategy, they begin to apply it flexibly, gaining confidence in solving addition problems independently of formal algorithms.
Teaching Strategies For Count On
Demonstrate Using a Number Line
A number line is an excellent visual tool for demonstrating the count on strategy, as it helps students track each step as they count forward. For example, using the addition expression 5 + 3, place a marker on 5, and count forward by ones: “6, 7, 8.” The final position, 8, is the answer.
Reinforce the commutative property of addition by placing a marker on 3 and counting forward by ones: “4, 5, 6, 7, 8.” This is a great opportunity to discuss how the order doesn’t change the sum, but it may make a difference in terms of efficiency! This kind of conversation develops strategic thinking about when and how to use different approaches.
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 on strategy. For example, create a number line on the floor using painter’s tape. Using the addition expression 5+ 3, have a student stand on 5, and hop or step as they count forward by ones: “6, 7, 8.” Their final position, 8, is the answer.
Reinforce the commutative property of addition by having a student stand on 3 and count forward by ones: “4, 5, 6, 7, 8.”
Demonstrate Count On Using Manipulatives
Use manipulatives like counters on a ten frame, or Unifix cubes and add one at a time as you use the count on strategy. For example, using the addition expression 5 + 3, start with five counters and add one counter at a time, counting each step out loud: “6, 7, 8.” The final count of objects shows the answer is 8.
NOTE: You can also reinforce the commutative property of addition by starting with 3 counters and counting forward by ones: “4, 5, 6, 7, 8.”
Demonstrate Count On with Fingers for Small Numbers
Fingers are a simple, accessible tool for demonstrating the count on strategy, especially with smaller numbers. For example, using the addition problem 5 + 3, start with five fingers up, then lift one finger at a time while counting forward, “5, 6, 7, 8.” The number of fingers left up (8) represents the answer.
NOTE: You can also reinforce the commutative property of addition by starting with 3 fingers up and lifting one finger at a time while counting forward by ones: “4, 5, 6, 7, 8.”
