Math Lesson Plan on Positive and Negative Integers

Integers are whole numbers. The set of integers includes all of the positive and negative whole numbers including zero. Positive integers are also known as counting numbers. Zero is considered neither positive nor negative, and it is included in the set of non-negative integers.

Teaching about Positive and Negative Numbers

Negative numbers are not an intuitive concept for students. They are used to dealing with concrete objects rather than abstract math concepts, and the idea of less than nothing may not make sense to them. Using a number line is helpful for students to see how numbers can continue on the "other side of zero."

To introduce the lesson, draw a number line on the board. Put a 0 in the middle, and number out to the right to 10. Use the number line to illustrate a few simple examples of adding and subtracting, such as, if we start at 2 and add 3, where do we end up on the number line? If we start at 10 and subtract 6, where will we be? Then subtract 1 from 5 to get to 4, and continue subtracting one by one until you get to zero. Now ask students what happens if you subtract 1 from 0. They may be confused, but put a mark for -1 to the left of zero, and explain that in math, there are negative numbers. Continue to subtract 1 from each successive number as you build the number line to the negative side out to negative 10.

Do several examples of adding positive numbers to the negative numbers. For example, what is negative 5 plus positive 3? Illustrate this equation on the number line by starting at -5 and counting 3 in the "positive direction" to end up at -2.

Then say, what do we get if we add negative 3 to positive 6? Tell students that adding a negative integer will give the same result as subtracting a positive integer with the same value. Write on the board several equations adding and subtracting negative and positive integers, and have students solve them. For each equation, count on the number line so that students can see for themselves how to move back and forth between positive and negative integers. Point out that when we write equations with negative integers, we put parentheses around the negative numbers so that the negative sign does not get confused with a subtraction sign.

5 + (-3) = 2
(-4) + 8 = 4
(-6) + (-4) = -10
1 + (-9) = -8

The next step is subtracting negative numbers. When we subtract a negative number, the two negatives cancel out, and the result is the same as adding a positive number. Tell students, when you subtract a negative number, simply change the sign and add. Write some example equations on the board and have the students solve them.

8 - (-2) = 8 + 2 = 10
-4 - (-6) = -4 + 6 = 2
5 - (-3) = 5 + 3 = 8
-6 - (-1) = -6 + 1 = -5

Here is a worksheet with simple equations to practice adding and subtracting positive and negative integers.

Many more worksheets can be found here.