Numbers and Number Lines
How can a number show a place?
How this lesson unfolds.
Begin with How can a number show a place? The sequence then connects Zero as the reference point and builds toward Ordering and movement.
How can a number show a place?
A number line turns numbers into locations using equal intervals.
A number line turns numbers into locations using equal intervals.
- Helpful foundationsCounting whole numbers
- Next connectionChoose zero as the shared reference point.
More context
Three dots show an amount of three. On a number line labelled zero through five, a marked dot sits at three. Every gap represents one unit. A number may name an amount or a position.
Where does the number line begin?
Zero is a reference position on a line that extends in both directions.
- Helpful foundationsEqual unit intervals
- Next connectionUse signs to describe direction from zero.
More context
A number line from negative four to positive four has arrows at both ends. Zero is highlighted as the reference. Two is two unit intervals to the right of zero. Zero is not an endpoint; the line continues indefinitely in both directions.
What do + and − tell us?
Positive numbers lie right of zero; negative numbers lie left of zero.
- Helpful foundationsZero as a reference · Equal unit intervals
- Next connectionSeparate a signed position from its distance from zero.
More context
From zero, an arrow travels three units left to negative three and another travels three units right to positive three. Positive three and three name the same position. Zero is neither positive nor negative.
Is −3 a negative distance?
Absolute value measures distance from zero and is always non-negative.
- Helpful foundationsPositive and negative positions
- Next connectionUse position, rather than distance alone, to compare numbers.
More context
Negative three and positive three are marked on opposite sides of zero. Each is three units from zero. Their positions differ, but both absolute values equal three. Vertical bars denote absolute value. The absolute value of zero is zero; distance cannot be negative.
Which number is greater?
Values increase to the right; adding a positive number moves right.
- Helpful foundationsSigned positions · Distance versus position
- Next connectionExplore addition and subtraction as directed movement.
More context
A number line marks negative three and negative one. Negative one lies farther right, so negative three is less than negative one even though its distance from zero is larger. Starting at negative three and adding two means moving two units right, ending at negative one.