Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.8

Compare and Order Integers and Rational Numbers

Lesson 7-4 · Learn It — how the math works

Why we're learning this

Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

✱ Math Workbench

Learn It

How do you compare and order integers?

To compare integers means to see which one is greater or less. On a number line, numbers get bigger as you go right and smaller as you go left.

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

A dive team marks the depth of each treasure on a map, measured in feet relative to sea level. The gold coin is at -2 ft, the silver crown at -7 ft, the ruby ring at -5 ft, and a buoy floats at +3 ft.
Where you see this in real lifeA dive team marks the depth of each treasure on a map, measured in feet relative to sea level. The gold coin is at -2 ft, the silver crown at -7 ft, the ruby ring at -5 ft, and a buoy floats at +3 ft.

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

The problem looks like this
A number line with -7 and -5 marked so they can be compared. -8-6-4-202468-7-5
  1. I will -7 and -5. They are both negative, so I look at the .
  2. -7 is 7 steps left of zero. -5 is only 5 steps left of zero.
  3. -7 is farther to the left, so -7 is the smaller number.
  4. I write -7 < -5. The open side of the symbol points to the bigger number, -5.

Watch out — mistakes students make here

  • With negatives, -5 is less than -2 — reorder the negatives.
  • Negatives are less than 0 — they belong before 0.
  • The three readings are different numbers, so they cannot describe the same temperature. Place them on a number line and compare their positions.

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

Same steps, new numbers.

  1. Now let's -2 and 3. Which one is to the left on the ?
    Check this step
    The -2 is left of zero.
  2. Which one is to the right?
    Check this step
    The 3 is right of zero.
  3. So which is greater, and what symbol do we use?
    Check this step
    3 is greater, so -2 < 3.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot the treasure depths like -2, -7, and -5, then them from least to greatest.

Solve: Three cities have temperatures of -12°F, -5°F, and 3°F. Which city is warmest?

My answer

Stuck? Open one hint at a time.

Hint 1

Warmest = greatest temperature. On a thermometer, greater is higher — farther right on a number line.

Hint 2

Compare positions on a number line: temperatures farther right are warmer. Check where negatives sit versus positives.

Hint 3

Place -12, -5, and 3 on a number line and find the one farthest to the right. That city is warmest.

Check my answer
✅ Answer: 3°F
3°F is the greatest because it is farthest to the right on the number line. The order from coldest to warmest is -12, -5, 3.

Turn & TalkSay it out loud with a partner

Why is -3 2, even though 3 looks like a bigger number than 2?

Try starting with:

  • On the number line, -3 is to the ___ of 2.En la recta numerica, -3 esta a la ___ de 2.
  • Numbers get smaller as you move ___.Los numeros se hacen mas pequenos a medida que te mueves ___.
Use these wordsintegercomparenumber lineless thangreater than