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Math · Grade 6 Math

Chapter 4: Negative Numbers and the Coordinate Plane

Numbers Below Zero

Zero is a starting point, not the end of the line.

Lesson
1
Time
About 17 minutes
0 of 8 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

A temperature of −5 degrees is 5 below zero. The minus sign says which direction.

Opposites

5 and −5 are opposites: the same distance from zero, on opposite sides.

Ordering is still left to right

On the line, −7 sits to the left of −3, so −7 is the smaller number.

A trap worth naming

−7 looks bigger than −3 because 7 beats 3. On the line it is further left, so it is smaller.

The number line does not stop at zero

Counting down from 3 goes 3, 2, 1, 0, then −1, −2, −3. Zero is a position on the line, not the end of it. Everything you know about the number line — further right is bigger — carries on unchanged into the negatives.

What a negative number means

Negative numbers describe quantities with a direction or a reference point: temperatures below freezing, debts, floors below ground, depths below sea level. The minus sign says "on the other side of zero", and what zero means depends on the context.

Bigger digits, smaller number

−7 is less than −3, even though 7 is bigger than 3. Further left on the line is always smaller. Temperature makes this intuitive: −7 degrees is colder than −3. When negatives confuse you, reach for the thermometer.

Zero is neither

Zero is not positive and not negative. It is the reference point both sides are measured from. That is why it needs no sign, and why "the opposite of zero" is zero itself.

Step 2: Try It Yourself

Tap and try it out.

Move along the line and watch which side of zero you land on.
-10-8-6-4-202468103-2
3 + (-5) = -2

Adding -5 walks 5 to the left.

Step 3: Watch an Example

One step at a time.

Watch Leo Order Four Temperatures

Leo orders −3, 2, −7, and 0 from coldest to warmest.

  1. Step 1

    He puts them on a line rather than comparing the digits.

Step 4: Your Turn

Practice makes it stick.

The Opposite

Problem 1 of 2

What is the opposite of −8?

The Colder Day

Problem 2 of 2

Which is colder, −4 degrees or −9 degrees?

Which Is Smaller?

1 of 4

Which is smaller, −6 or −2?

2 of 4

What is the opposite of 12?

3 of 4

Which is smaller, −1 or 0?

4 of 4

How far is −7 from zero?

Step 5: Quick Check

Show what you know.

Question 1 of 2

Which is smaller, −11 or −4?

Question 2 of 2

What does the minus sign in −5 say?

What You Learned

  • Negative numbers are on the other side of zero.
  • Opposites are the same distance from zero, in opposite directions.
  • Further left on the line always means smaller.