Skill: Add integers using models

To add integers, think of combining signed quantities:

• A positive integer means moving right on a number line or using a positive counter.
• A negative integer means moving left on a number line or using a negative counter.
• A positive and a negative make a zero pair because they cancel each other.

Example: $\boldsymbol{(-3)+(+5)}$

Step 1: Model the integers.

Use 3 negative counters and 5 positive counters:

$$(-\ -\ -) + (+\ +\ +\ +\ +)$$

Step 2: Make zero pairs.

Pair each negative counter with one positive counter:

$$(-,+),\quad (-,+),\quad (-,+)$$

Each pair equals $0$, so all three pairs cancel.

Step 3: Count what remains.

After the zero pairs are removed, 2 positive counters remain:

$$(-3)+(+5)=+2$$

You can also see this on a number line: start at $-3$ and move 5 spaces to the right. You land on $2$.

$$\boxed{(-3)+(+5)=2}$$

When adding integers with different signs, make zero pairs or compare the magnitudes. The sign of the unmatched counters determines the sign of the answer.