Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.5

Explore Integers and Their Opposites

Lesson 7-1 · Learn It — how the math works

Why we're learning this

The lowest elevation in North America is Badwater Basin in Death Valley: 86 meters below sea level. When we measure elevation, sea level is defined as 0. So 86 meters below sea level cannot be written as plain 86 — that would put it ABOVE the water. Numbers less than zero are negative numbers, written with a − sign, so the elevation of Badwater Basin is −86 meters. On a number line, −86 is 86 units to the LEFT of 0, while 86 is 86 units to the RIGHT of 0. Those two numbers are opposites.

✱ Math Workbench

Learn It

How do you use integers to describe quantities above and below zero?

Counting numbers, their opposites, and 0 are integers. A negative integer is less than zero and is written with a − sign. Opposites are the same distance from 0, but on opposite sides of the number line.

Picture itSee what the math looks like before you read about it

The lowest elevation in North America is Badwater Basin in Death Valley. A sign there reads 86 meters below sea level. On the same sign, sea level itself is marked as 0.
Where you see this in real lifeThe lowest elevation in North America is Badwater Basin in Death Valley. A sign there reads 86 meters below sea level. On the same sign, sea level itself is marked as 0.

Watch me solve itI do — read one step at a time

The problem looks like this
Number line: −86 is 86 units left of 0, and its opposite, 86, is 86 units right of 0.−80−4004080−8686
  1. Badwater Basin is 86 meters below sea level, and sea level is defined as 0.
  2. Below 0 means a , so I write the elevation as −86 meters.
  3. On a , I count 86 units to the LEFT of 0 and mark that point.
  4. The of −86 is 86. Both are 86 units from 0, just on different sides.

Watch out — mistakes students make here

  • Above sea level is above 0, so this is +15, not -15.
  • A deposit adds money to the account, which moves the balance above 0. A withdrawal would be the negative one.
  • A gain moves the team forward from the line of scrimmage, so it is +15. A loss would be negative.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. One day in January the temperature in Toronto was 9°C and in Reykjavik it was −9°C.
  2. Which one is to the left of 0 on the ?
    Check this step
    The sign tells us: −9.
  3. How many units from 0 is 9?
    Check this step
    How many units from 0 is −9? Both are 9 units.
  4. So 9 and −9 are — same distance from 0, opposite sides.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, decide whether each real-world quantity is above 0, below 0, or exactly at 0, then name its .

Solve: Which list of is ordered from LEAST to GREATEST?

My answer

Stuck? Open one hint at a time.

Hint 1

Least to greatest means left to right on a number line.

Hint 2

Split the list into negatives and positives first — every negative integer is less than 0 and less than every positive integer.

Hint 3

Between -8 and -3, which one is farther to the left of 0? That number starts the list.

Check my answer
✅ Answer: -8, -3, 0, 5
Least to greatest reads left to right on the number line: -8, then -3, then 0, then 5.

Turn & TalkSay it out loud with a partner

Why does 0 represent sea level instead of meaning 'nothing at all'?

Try starting with:

  • In elevation, 0 means ___.En la elevación, 0 significa ___.
  • Anything below that point is written as ___.Todo lo que está debajo de ese punto se escribe como ___.
Use these wordsintegernegativepositivesea levelnumber line