Add integers using models

Integer addition represents combining signed quantities. On a number line, adding a positive integer moves right and adding a negative integer moves left; with integer counters, opposite signs form zero pairs, so only unmatched units determine the sum. When signs agree, magnitudes combine; when signs differ, their absolute values are compared and the sign of the greater magnitude is retained, supporting later work with subtraction, rational numbers, and algebraic expressions.

Detailed Explanation: 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.

Learn by doing: Add integers using models

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Negative Integer Addition

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