# Addition and Subtraction of Integers

**Strand:** Number

**Outcome:** 6

## Step 1: Identify Outcomes to Address

### Guiding Questions

- What do I want my students to learn?
- What can my students currently understand and do?
- What do I want my students to understand and be able to do, based on the Big Ideas and specific outcomes in the program of studies?

See Sequence of Outcomes from the Program of Studies

### Big Ideas

Operations with integers build on operations with whole numbers. Just as decimals are an extension of the whole number place value system to represent numbers between the whole numbers, so also the set of integers is an extension of the whole number system to include the opposite of every whole number. The properties for whole numbers apply to integers and, in addition, the integers are closed under subtraction. Van de Walle and Lovin (2006, p. 131) reaffirm this in the following excerpt:

Integers add to number the idea of opposite, so that every number has both size and a positive or negative relationship to other numbers. A negative number is the opposite of the positive number of the same size.

Since integers include the whole numbers and their opposites (negative numbers), it can be said that integers are numbers that deal with direction as well as magnitude (Cathcart 1997, p. 349). In everyday life there are many uses of integers, so problem solving plays a major role in developing understanding of adding and subtracting integers.

Students need a solid conceptual foundation in whole numbers as a necessary prerequisite for integer computation. Strategies in problem solving with whole numbers can be transferred to solving problems with integers. Subtraction is related to addition in both the whole numbers and the integers. As students make these connections, they develop number sense. Number sense is defined as follows:

"Number sense refers to an intuitive feeling for numbers and their various uses and interpretations; an appreciation for various levels of accuracy when figuring; the ability to detect arithmetical errors; and a common sense approach to using numbers" (Reys 1992, p. 3).

Students develop understanding of operations with integers by making sense of the ideas internally. To guide this process, it is necessary to encourage flexibility in thinking and provide learning opportunities in connecting:

- operations with whole numbers to operations with integers
- subtraction of integers to addition of integers
- concrete, pictorial and symbolic representations
- operations with integers to real world problems.