Positive and Negative Numbers

Opposite Directions and Values

In this lesson:

• Use positive and negative numbers to describe real-world quantities
• Explain what 0 represents in any context
• Read and write signed numbers in four key contexts

Learning Objectives for This Lesson

1. Explain that positive and negative numbers describe quantities with opposite meanings or directions
2. Write the correct signed number for a given real-world description
3. Explain what 0 represents in each context
4. Interpret a signed number — state both its magnitude and its direction

What Does the Minus Sign Mean?

The forecast: temperature drops from to overnight.

• means 5 degrees above zero
• : the minus sign means the other side of 0
• Our old number line only went right of 0 — what are we missing?

Introducing the Extended Number Line

• Right of 0 = positive direction
• Left of 0 = negative direction

Temperature: Above and Below Zero

• Above 0 → positive: means 15 degrees above zero
• Below 0 → negative: means 15 degrees below zero
• 0 = the reference (freezing point in °C; Fahrenheit's reference in °F)

0°F is not "no temperature" — it is a specific real value

Elevation: Above and Below Sea Level

• Above sea level → positive: a mountain peak at m
• Below sea level → negative: an ocean floor at m
• 0 = sea level (the average height of the ocean surface)

Money: Deposits Positive, Withdrawals Negative

• Deposit → positive: a deposit is
• Withdrawal → negative: a withdrawal is
• 0 = empty account; neither gaining nor losing

A debt is a real quantity — is not an error

Electric Charge: Positive and Negative

• Proton → positive charge ()
• Electron → negative charge ()
• Neutron → 0 charge (neutral)
• A neutral atom balances protons and electrons to reach 0

A negative charge is not "bad" — it is a real property

What Does 0 Mean Here?

In every context: 0 is the boundary between the two directions

You Say It: New Context

Floors in a building:

• Ground floor = 0
• Floors above ground = positive
• Basement levels = negative

In this building context: what does 0 represent?

Write your answer in one sentence before advancing.

The Four-Step Sign Assignment Routine

1. Identify the reference — what does 0 mean here?
2. Determine the direction — which side of 0 is this?
3. Assign the sign — positive (+) or negative (−)?
4. Write the magnitude — how far from 0?

Direction A: Description → Signed Number

Direction B: Signed Number → Description

Guided Practice: Try Both Directions Now

Try each problem — then advance for answers:

Direction A (description → number):

1. A temperature of 8°C below zero
2. An elevation of 1,609 meters above sea level
3. A withdrawal of

Direction B (number → description):
4. in a temperature context
5. in an elevation context
6. in a bank account context

Pause here and write your six answers.

Guided Practice: Check Your Answers Here

Direction A:

1. below zero →
2. m above sea level →
3. withdrawal →

Direction B:
4. → 31 degrees below zero
5. m → 430 meters below sea level
6. → deposit (or credit)

Can One Number Mean Different Things?

Yes — context determines meaning, not the number alone.

• — 12 degrees above zero
• m — 12 meters above sea level
• — 12 dollars received

What would mean in each of these three contexts?

Comparing Temperatures Across Five American Cities

• Which cities are above zero? Which are below?
• Which city is coldest? How many degrees below zero?
• What does represent in this context?

Elevation Snapshot: Writing Signed Numbers

What does 0 represent here? Sea level — average ocean surface height

Bank Statement: Each Transaction as Signed Number

Positive = money received; negative = money spent

What All Three Contexts Share

Every signed number situation has the same structure:

1. A reference point — what 0 means (specific, not "nothing")
2. Two directions — one positive, one negative
3. A sign — which direction the quantity is in

Football, building floors, golf score — all fit this structure too

You Try: Interpreting Signed Football Yards

A drive: , , , ,

1. What does 0 represent here?
2. Which plays gained yards? Which lost yards?
3. Write "a loss of 9 yards" as a signed number
4. Describe "" in words

Pause and write your four answers.

Key Takeaways from This Lesson

✓ Positive and negative numbers describe opposite directions from a reference point
✓ The sign shows the direction; the magnitude shows the distance from 0
✓ 0 is the reference — specific and meaningful in every context, never just "nothing"
✓ To assign a sign: identify the reference → find the direction → assign + or −

Watch out: Negative does not mean wrong — m is a precise location
Watch out: is not "no temperature" — it is a specific real value
Watch out: Underline the direction word first, then assign the sign
Watch out: already means below zero — never write " degrees below zero"

What Comes Next in 6.NS.C.6

Next: Locating Rational Numbers on the Number Line

• Extend to fractions and decimals: place and
• Define opposite numbers: the opposite of is
• Preview the coordinate plane: two number lines crossing at 0

Today's extended number line carries directly into 6.NS.C.6.