Number Line & Coordinate Explorer

What are negative numbers?

A negative number is a number less than zero. On a number line, zero sits in the middle, positive numbers go to the right, and negative numbers go to the left.

The sign tells you direction, and the number tells you distance from zero. So −5 is five steps to the left of zero, and 5 is five steps to the right. They are the same distance, opposite directions.

Think of a thermometer or a basement floor. Below zero is not "nothing". It is a real amount on the other side.

What is this module?

The module has two views. Line mode is a number line from −10 to 10. You enter an operand (a fraction or a decimal) and press Add or Subtract. The point hops along the line to show the operation. You can also drag the point by hand.

Plane mode is a coordinate plane, two number lines crossing at zero. You enter an x and a y and the point appears in one of the four quadrants.

What they're learning

The big idea is that positive and negative numbers measure direction and distance from zero.

• Adding a positive number moves right and adding a negative number moves left. Starting at 0 and subtracting 3/4 lands on −3/4.
• Opposites. −3/4 and 3/4 are the same distance from zero on opposite sides.
• Absolute value is distance from zero. The absolute value of −5 is 5, because it is five steps away.
• Comparing negative numbers. −2 is greater than −5, because −2 is further to the right.
• Quadrants. The signs of x and y tell you which quadrant a point is in. Both positive is Quadrant I, and so on around the plane.
• Reflections. Flipping a point across an axis changes one sign. Reflecting (3, −2) across the x-axis gives (3, 2).

Aliases

• Negative numbers
• Number line
• Coordinate plane
• Graphing points
• Absolute value
• Quadrants

Refresher

A negative number is less than zero. On the number line, zero sits in the middle, positive numbers go right, and negative numbers go left. The sign tells you direction and the number tells you distance from zero. The coordinate plane is two number lines crossing at zero.

Try this together

Two or three minutes is enough. The animation carries it.

1. In Line mode, leave the operand at 1/2. Press Add twice and count the hops: 0 to 0.5 to 1.
2. Now press Subtract from 0 and watch it go negative. Ask what number it lands on.
3. Drag the point to 3/4, then ask where its opposite is. Drag it there and check.
4. Switch to Plane mode. Type x = 3, y = −2 and read the quadrant out loud together.

If the signs feel backwards, you are not alone. Just follow the number line: right is bigger, left is smaller, always.

Words you might hear

• Integer: a whole number, positive, negative, or zero.
• Rational number: any number that can be written as a fraction, including negatives.
• Opposite: the number the same distance from zero on the other side. The opposite of 3/4 is −3/4.
• Absolute value: the distance from zero, always positive. Written |x|.
• Quadrant: one of the four regions of the coordinate plane, numbered I to IV starting top-right and going counter-clockwise.
• Coordinate: the pair (x, y) that locates a point, where x is horizontal and y is vertical.

Deeper dive

Start at 0 and subtract 3/4. You move left and land on −3/4. The opposite of 3/4 is the same distance on the other side, which is −3/4. Absolute value is just that distance from zero, so the absolute value of −5 is 5.

On the plane, the signs of x and y decide the quadrant. Both positive is the top right, positive x and negative y is the bottom right, and so on. Flipping across an axis changes one sign.