Counting On as an Addition Strategy

Helping Students Recognize Strategies for Operational Fluency

Counting On as an Addition Strategy

Students with disabilities often struggle with math. They have difficulty visualizing addition, they have difficulty remembering numbers, they often struggle understanding one to one correspondence. At the same time, it is often difficult for us to find a strategy that will help students both succeed in solving mathematical equations while establishing foundational skills that they will be able to use in new situations.

In other words, do they really understand what it is that they are doing?

Certainly there is no "fix" for their challenges. But part of the solution is to offer lots of strategies that they can use to master the challenges offered by adding and subtracting, and later to solving algebraic formulas.

Counting

The first step in successful "counting on" is to be sure your students have strong counting skills. That counting needs to be paired with "one to one" correspondence, the understanding that for each cardinal number there is a matching.

Practice should include counting objects, matching objects to numbers, and counting games. How about:

Pass the ball Have children stand in a circle. Give a student a ball, a bean bag or even a toy. Have the child start counting. The child will hand or throw the ball or bean bag to another child, who will continue counting from that number. When that child gets the item, they continue counting and then pass it to another person to count.

When a child isn't ready to pick up the string, they sit down. For example:

  • Janet starts with the ball: "1, 2, 3, 4, 5, . . ." and passes it to John.
  • John continues: "6,7,8,9,10,11,12,13 . . . " and passes it to Alex.
  • Alex continues 14, 15, 16, 17 . . . and passes it to Lauren.
  • Lauren counts 18, 19, um, um, 30 . . . And sits down, so the next person can name 20.

    Counting On

    Be sure your students understand the "communicative property of addition," which means that the order of adding doesn't affect the operation. In other words, it doesn't matter which number you add first.

    Have students circle the largest number in the addition problem (math fact) i.e. in the problem 8 + 2, the student circles the 8.

    The student then counts up from the larger number. Using the previous fact, the student would count: 8, 9, 10. 8 plus 2 is ten.

    Notes:

    If your students struggle with the concept, start out by just adding one to a larger number. You can also pair it to using a number line. After circling the larger number, have the students point to it on the number line, and jumping the one or two jumps for the "counting on" number.

    Counting on is a great strategy to use with "Touch Math." You could start with the large number and add the touch points to the one, two or three. If it is successful, you may chose Touch Math as a total strategy for teaching calculation to students. Students can often become "Touch Math" dependent, and rely on it solely for solving math problems. For students who will always struggle with math, it may be enough to guarantee that they can do some basic cyphering.

    For other students, it may prevent them from gaining automaticity in math facts and succeed in other parts of the general education math curriculum, such as understanding and using rational numbers.