📚 Practice With Worksheets
Practice locating integers, interpreting positive and negative direction, finding distance from zero, and adding and subtracting integers.
▶️ Learn With Videos
Review integer movement, addition and subtraction rules, and how visual models such as number lines and zero pairs represent integer operations.
🛠️ How to Use This Tool
Begin at zero and choose one of the positive or negative movement buttons. Each button shows how far and in which direction the point will move.
A positive move sends the point to the right, while a negative move sends it to the left. The arrow above the number line shows the most recent movement.
Use the current-position box and movement statement to track the starting value, the signed movement, and the resulting location.
🧠 Things to Notice
The sign of a movement tells its direction, while its absolute value tells how many units to move.
A point can move left and still finish to the right of zero, or move right and still finish to the left of zero. The final position depends on both the starting value and the movement.
Opposite movements have the same distance but different directions. For example, \(+6\) moves six units right, while \(-6\) moves six units left.
📘 Vocabulary
Integer: A whole number, its opposite, or zero. Examples include \(-7\), \(0\), and \(12\).
Number Line: A line on which numbers are placed in order according to their value.
Origin: The point located at zero on a number line.
Positive Direction: Movement toward greater values, usually shown by moving to the right.
Negative Direction: Movement toward lesser values, usually shown by moving to the left.
Position: The location of a point on the number line.
Distance: The number of units between two locations. Distance is never negative.
Absolute Value: The distance a number is from zero, without considering direction.
Opposites: Two numbers that are the same distance from zero but lie in opposite directions, such as \(8\) and \(-8\).
Additive Inverse: The opposite of a number. A number and its additive inverse combine to make zero.
↔️ Integers as Movement on a Number Line
An integer can describe both a distance and a direction. The sign tells the direction of movement, while the absolute value tells how many units to travel.
Positive Movement
A positive integer represents movement to the right, toward greater values.
\(+10\): Move 10 units to the right.
Starting at \(-4\) and moving \(+10\) places the point at \(6\).
Negative Movement
A negative integer represents movement to the left, toward lesser values.
\(-8\): Move 8 units to the left.
Starting at \(3\) and moving \(-8\) places the point at \(-5\).
Opposite Movement
A negative sign placed outside a number means to take the opposite of that number.
\(-(4)=-4\)
The opposite of moving right 4 units is moving left 4 units.
\(-(-6)=6\)
The opposite of moving left 6 units is moving right 6 units.
Direction versus location: A negative movement does not always produce a negative final position. For example, starting at \(10\) and moving \(-4\) ends at \(6\), which is still positive.
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