Adding Integers Using Number Lines
Adding integers using number lines is a foundational Grade 7 skill in Big Ideas Math, Course 2. To add integers on a number line, start at the first integer, then move right for a positive addend and left for a negative addend. For example, to compute 3 + (−5): start at 3, move 5 units left, and land at −2. For −4 + 2: start at −4, move 2 units right, land at −2. The number line makes the concept of adding a negative number equivalent to subtraction visually clear. This model connects to the abstract rules: same signs add absolute values (keep sign), different signs subtract (keep sign of larger absolute value).
Key Concepts
To add integers using a number line: Start at the first integer, then move right for positive addends or left for negative addends. The distance moved equals the absolute value of the second integer: $a + b$ means start at $a$ and move $|b|$ units in the direction determined by the sign of $b$.
Common Questions
How do you add integers using a number line?
Place a point at the first integer. Move right for a positive addend and left for a negative addend. The landing point is the sum.
How do you compute 3 + (−5) on a number line?
Start at 3. Move 5 units to the left (because −5 is negative). Land at −2. So 3 + (−5) = −2.
How do you compute −4 + 2 on a number line?
Start at −4. Move 2 units to the right. Land at −2. So −4 + 2 = −2.
Why does adding a negative number move left on the number line?
Negative numbers represent movement in the opposite direction from positive. Adding a negative is equivalent to subtracting a positive, which means moving left.
What is the abstract rule for adding integers with different signs?
Subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the greater absolute value.
What is the abstract rule for adding integers with the same sign?
Add their absolute values and keep the common sign. For example, −3 + (−4) = −7.