Grade 6 Math · Topic 25

Positive and Negative Numbers

Numbers can be positive (greater than zero) or negative (less than zero). Zero itself is neither. Together with zero, the positives and negatives extend the number line both ways and let us describe opposites like profit/loss, above/below sea level, or hot/cold.

Lesson alignment: 6.NS.C.5 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Place an integer on the number line

Move one point. Its position relative to zero shows whether it is positive or negative and how far it is from zero.

Think first: Before moving point A from −4, predict which side of zero it belongs on and how far it is from zero.

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Write an integer to represent “a loss of $45.”

A loss decreases value, so we use a negative number. “Loss of $45” becomes -45.

Answer: -45

Worked example 2

Write an integer for “300 feet above sea level.”

Above sea level is positive, so +300 or simply 300.

Answer: +300 (or 300)

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. A profit of $120 ⇒
    Check

    +120

  2. A loss of $60 ⇒
    Check

    -60

  3. 15^∘F below zero ⇒
    Check

    -15

  4. 500 feet above sea level ⇒
    Check

    +500

  5. A debt of $80 ⇒
    Check

    -80

  6. 7 yards gained ⇒
    Check

    +7

  7. Withdrew $25 ⇒
    Check

    -25

  8. 250 meters below sea level ⇒
    Check

    -250

Try this situation 1

A diver descends 35 feet below the surface of the ocean. Write his depth as an integer.

Show a worked solution

Answer: -35 feet.

Below the surface is negative, so we write -35.

Try this situation 2

On Monday, Carla's checking account changed by -$48. What does that mean?

Show a worked solution

Answer: She spent or withdrew $48 (her balance went down by $48).

A negative change to a balance means money was taken out.

Fresh questions · saved on this device

Practice this skill

52 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A hiker starts 12 meters above sea level and then descends 20 meters. Which integer represents the hiker's new elevation?

2. At sunrise, the temperature in Dallas was -5°F. By afternoon, it had increased by 18°F. What was the afternoon temperature?

3. A submarine is at a depth of 150 meters below sea level. Which integer represents this depth?

4. A thermometer reads -8°C. Later, the temperature increases by 12°C. What is the new temperature?

5. A diver is 20 feet below the ocean surface. Which number represents the diver's position?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Integers & the Coordinate Plane quiz ↗Try a full practice test ↗