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Refresher · Signed numbers · about 12 min Pending teacher review

Where numbers live: the number line

Goal: Locate any integer on a number line, explain where zero sits, and describe a number's size as its distance from 0.

Before this: Needs counting and reading a scale (whole numbers). No signed-number work is assumed.

Step 1 · Launch (≈5 min)

Look at this number line. Zero is the middle marker, not the start. Numbers to the right of 0 are positive; numbers to the left are negative.

Find $-3$ and $3$. What do they have in common? What is different?

Say it out loud: "$-3$ is three units from zero, on the left."

Step 2 · Practice (≈10 min)

Pick the level that fits today. Hints are allowed — each one is recorded as assisted practice, which never changes an independent status.

Which number is marked by point $A$?

Answer

What number is the same distance from 0 as $9$, but on the other side?

Answer

Point $B$ is 2 units to the right of $-5$. What number is $B$?

Answer

Each tick on this line is 2 units. What number is point $C$?

Answer

Show me how it works — worked explanation

Reading a number line is two questions: **which side of zero?** and **how many units from zero?**

Find 0. Everything to the left is negative; everything to the right is positive.
Count units from 0 to the point. That count is the distance (always positive).
Attach the sign for the side: left → put a minus sign in front.
Example: a point 3 ticks left of 0 is $-3$; its distance from 0 is 3.

Step 3 · Wrap-up (≈5 min)

Every integer has two pieces of information: its side (the sign) and its distance from 0 (its size). $-3$ and $3$ have the same size and opposite sides. Zero is the balance point in the middle.

Step 4 · Independent check

4 fresh problems on this skill, done alone: no hints, no worked solutions, no feedback until the end. This is what moves the skill's status.

You can start the check any time, but the wrap-up is worth reading first.

Parent guide (for the adult)

What to notice

Does your learner find 0 before counting, or start counting from the left end of the line?
Do they say "negative three" or "minus three"? Either is fine — check they mean a position, not an operation.
On the 2-unit scale, do they count ticks as ones?

What to ask

"Where is zero on this line?"
"Is this number to the left or right of zero? How far?"
"Which two numbers are both 5 away from zero?"

Common errors — and a question that separates a slip from a misconception

Reads a negative position as positive
Looks like: Answers 4 for a point at −4
Ask: "Which side of zero is it on? What does that side mean?" — a slip if they self-correct instantly; a misconception if they say "left is still 4".
Counts every tick as 1 on a 2-unit scale
Looks like: Answers −4 for −8
Ask: "What do the labels say the ticks go up by?"
Gives a negative distance
Looks like: "−6 is −6 away from 0"
Ask: "If you walked from −6 to 0, how many steps would you take?"

When to show an example

If two support problems in a row go wrong, open the worked explanation together and let your learner narrate the next problem using its three steps.

Complete solutions (keep closed during the independent check)

Show practice solutions

Support

Count 2 ticks left of 0: $-2$.
Four steps left from 0 lands on $-4$.
Distance from 0 is 6 (distance has no sign).

Core

$A$ is 7 ticks to the left of 0: $-7$.
The mirror of $9$ across 0 is $-9$.
From $-5$, two steps right: $-4$, then $-3$.
Four ticks left × 2 units each = 8 units left: $-8$.

Extension

Distance 5 on the negative side: $-5$.
The numbers are $4$ and $-4$; they cancel to $0$.

Repeat or move on?

Move on when the independent check shows 4 of 4 (or 3 of 4 with a self-corrected slip). Repeat the core set another day if two or more were wrong — the next lesson depends on this one.