1. MTH 231 Section 5.2 Addition and Subtraction of Integers

2. Overview In the previous section, we modeled integers largely by using counters and the number line. We will use the same models to represent addition and subtraction of integers.

3. Addition Using Counters The first thing we must do is to establish the existence of a “zero pair”.

4. Adding Using Counters 1.Model each integer. 2.Remove all zero pairs. 3.Count what’s left.

5. Adding Using the Number Line The first thing we must do is to establish the rules for movement: 1.Adding a positive integer means “move to the right” 2.Adding a negative integer means “move to the left”

6. Adding Using the Number Line

7. Subtracting Using Counters 1.Model the minuend using counters. 2.Using the notion of “take away”, remove counters representative of the subtrahend— that is, unless you don’t have enough counters to remove. 3.In this case, add enough “zero pairs” to have sufficient counters to remove the subtrahend. 4.Count what’s left.

8. Subtracting Using Counters

9. Subtracting Using the Number Line The first thing we must do is to establish the rules for movement: 1.Subtracting a positive integer means “move to the left” 2.Subtracting a negative integer means “move to the right”

10. Subtracting Using the Number Line

11. Future Implications 1.Ordering Integers: given two integers a and b, a < b if, on the number line, a is to the left of b. 2.“Subtraction is the same as adding the opposite” is a concept that is used frequently in algebra. It can be modeled easily here using either counters or the number line.