A number line is a visual model that places numbers in order on a straight line. It helps you see size, direction, distance, and position all at once. Zero is the center reference point, positive numbers extend to the right, and negative numbers extend to the left.
This makes the number line useful for comparing values, graphing solutions, and understanding operations.
Key Facts
- Numbers increase as you move to the right on a number line.
- Numbers decrease as you move to the left on a number line.
- The distance between a number x and 0 is its absolute value, written |x|.
- For any two numbers a and b, a < b means a is to the left of b on the number line.
- Adding a positive number moves right, and adding a negative number moves left.
- The distance between two numbers a and b is |a - b|.
Vocabulary
- Number line
- A number line is a straight line with evenly spaced marks used to show numbers in order.
- Origin
- The origin is the point labeled 0 on the number line.
- Integer
- An integer is a whole number, its opposite, or zero, such as -3, 0, or 5.
- Absolute value
- Absolute value is a number's distance from 0, so it is never negative.
- Inequality
- An inequality is a statement that compares quantities using symbols such as <, >, ≤, or ≥.
Common Mistakes to Avoid
- Spacing tick marks unevenly is wrong because equal numerical steps must have equal visual distances on a number line.
- Thinking -5 is greater than -2 is wrong because -5 is farther left, so it is less than -2.
- Plotting 1/2 at the same place as 0.2 is wrong because 1/2 = 0.5, which is to the right of 0.2.
- Reversing inequality shading is wrong because x < 3 means all values to the left of 3, while x > 3 means all values to the right of 3.
Practice Questions
- 1 Plot -4, 0.5, 2, and -1.5 on a number line from -5 to 5, then list them from least to greatest.
- 2 Use a number line to find -3 + 7 and 4 - 9.
- 3 Explain why a number can have a greater absolute value but still be less than another number.