Addition Strategies

The equal sign. The equal sign signifies a relation between two numbers. Understanding that the equal sign means that expressions on the two sides of the equal sign represent the same numerical value is an important mathematical concept. Experiences that allow students to explore these ideas now will help them avoid common misconceptions later. For example, students who only see number sentences of the form 3 + 2 = 5 often come to the erroneous conclusion that the equal sign means, “The answer comes next” or “Do the operation.”

Students need many experiences using the equal sign flexibly. Early experiences include seeing problems as both 5 + 6 = and = 5 + 6. Other experiences can come in the form of identifying whether a number sentence is true or false or finding the missing number in an open number sentence (5 + 6 = 6 + ). At first, students may need to find the value of the expression on each side of the equal sign to solve these types of problems. With experience, students will develop the capability of reasoning such as, “I know that 9 + 4 = 10 + 3 because I take one from the four to make ten and I have three more to add.” Using the equal sign flexibly will allow students to represent their thinking more easily. For example, students can say that they know that 19 + 4 is 23 because 19 + 4 = 20 + 3.

What to avoid. Researchers caution against using the equal sign in ways in which it does not represent a relation between numbers. For example, avoid expressions such as “Jerome = 3 feet” or “Sara = 4.” Similarly, it is not appropriate to draw a picture of three objects and then write “ = 3”. Save the equal sign for representing relations between numbers.

It is also important to avoid writing number sentences that chain calculations together incorrectly. For example, to show a partitioning strategy for adding 10 + 17 = 27, avoid writing 10 + 10 = 20 + 7 = 27, since 10 + 10 does not equal 20 + 7. (Carpenter, et al., 2003; NCTM, 2000)

For more information, see the Background of this unit.