L2 · The number line: magnitude and direction

Learning goal

“I can place positive and negative numbers on a number line, and I can find a number's magnitude - its distance from zero - which is never negative.”

Number line — a line where every number has a position: negatives to the left of 0, positives to the right, equally spaced.

Magnitude — a number's distance from zero. The magnitude of -4 is 4, written |-4| = 4. Magnitude is never negative.

Opposite — two numbers the same distance from zero, on opposite sides: 6 and -6 are opposites. (We use opposites fully in L4.)

Worked example

Plot -3 and 5, then find each magnitude. Step 1: On the number line, -3 sits 3 units to the LEFT of zero; 5 sits 5 units to the RIGHT. Step 2: Magnitude means distance from zero, and distance is measured without a direction: |-3| = 3 and |5| = 5. Step 3: Point back at L1: -3°C is 3 degrees from freezing; a balance of -$3 is $3 from $0. Model both ways, side by side: the horizontal number line with jump-arcs from 0 to -3 and 0 to 5, AND zero-pair counters: 3 negative counters lined up under the point -3, showing "3 units of distance, negative side." The sign gives the side; the magnitude gives the distance. Distance cannot be negative.

Check yourself — explain it

Why is the magnitude of -3 equal to 3, and not -3?

Paired problem — example still visible

Plot -6 and state its magnitude: -6 sits 6 units left of zero; |-6| = 6

Faded completion — last step is yours

"-8 is ___ units from zero, on the ___ side, so |-8| = ___." -> 8; left (negative); 8

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz