Comparing and ordering integers

To compare integers, picture the number line: the number further right is greater, so −3 > −8. A quiz for kids, parent help below.

🧒 Kids: further right wins!

Find both numbers on the number line. The one on the right is bigger. The open mouth of < or > eats the bigger number! Then try the quiz.

▶ Quiz 🔢 More practice

−10−9−8−7−6−5−4−3−2−1012−8−3

💡 Trick: −3 is to the right of −8, so −3 > −8. Any positive beats any negative!

More integers: What are integers · Opposite numbers · Absolute value · Comparing integers · Integers on a number line · Zero pairs

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: further right is greater

On a number line, numbers grow from left to right. So of two integers, the one further right is greater. For two negatives, the one closer to 0 is greater.

Patterns to spot

Key words

Why it matters: Comparing integers trains children to trust the number line instead of the digits. That habit stops errors later with negative fractions and decimals, with inequalities in algebra and with reading graphs.

See it: pictures to draw with your child

Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.

−10−8−6−4−20246810−8−32
Left to right: −8, −3, 2. So −8 < −3 < 2.
−10−50510−7°C−10−50510−3°C−10−505104°C
Thermometers: −3°C is warmer than −7°C, so −3 > −7.
−10−8−6−4−2024681010 more−55
5 is 10 more than −5. Moving right always means greater.

What your child already knows

Children already compare whole numbers and use the symbols <, > and =. They also know a number line goes up from left to right. With negatives, the same rule holds, even when it looks backwards at first.

In real life: Which day was colder, −4°C or −9°C? Who is deeper, a diver at −15 m or one at −8 m? Which golf score is better, −3 or 2? Each is a comparison of integers.

Inequality statements in real life

Grade 6 writes and explains comparisons in context. “−3°C > −7°C” means −3°C is warmer than −7°C.

“−50 m < −20 m” means a depth of 50 m is lower than a depth of 20 m. The word matters: lower, colder or less money all mean further left.

Ask your child to say each statement in words. For example, “−12 < −5 because −12 is further left on the number line.”

Golf is a fun example. A score of −4 beats a score of −1, because lower is better in golf. But −4 is still less than −1. The number comparison stays the same; only the meaning of “better” changes.

Worked examples

Example 1: Two negatives

  1. Compare −6 and −11. −6 is closer to 0, so it is further right. −6 > −11.

Example 2: Order a list

  1. Order 4, −2, −9, 0 and −5 from least to greatest.
  2. Place them on a line and read left to right: −9, −5, −2, 0, 4.

Example 3: In context

  1. At 6 a.m. it was −5°C.
  2. At midnight it was −10°C. −10 < −5, so midnight was colder.

Common mistakes

Comparing digits onlySays −9 > −2 because 9 > 2.Fix: for negatives, the one closer to 0 is greater: −2 > −9.
Thinking 0 is the smallestPuts 0 first when ordering numbers with negatives.Fix: negatives come before 0 on the number line.
Flipping the symbolWrites −4 > −1 to mean −1 is bigger.Fix: the open side of < or > faces the bigger number: −4 < −1.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

  1. “Find −3 and −8 on the number line.”
  2. “Which one is further right?” (−3.)
  3. “So which is greater?” (−3.)
  4. “Which is colder, −3°C or −8°C?” (−8°C.)
  5. “Order −1, −6 and 2 from least to greatest.” (−6, −1, 2.)

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

  1. −7 ○ −2
  2. 0 ○ −4
  3. −10 ○ 3
  4. −15 ○ −51
  5. Order: 3, −8, −1, 0
  6. Order greatest to least: −4, −12, 6, −7
  7. Which is colder: −13°C or −6°C?
  8. Least of −20, −2, −200
  9. Stretch: a number is less than −5 and greater than −8. Name one.
Show the answers
  1. −7 < −2
  2. 0 > −4
  3. −10 < 3
  4. −15 > −51
  5. −8, −1, 0, 3
  6. 6, −4, −7, −12
  7. −13°C
  8. −200
  9. −6 or −7

Games to play at home

Integer war

Play the card game War with red cards negative and black cards positive.

Temperature line-up

Look up five cold cities and order their temperatures.

Human number line

Give family members integer cards and ask them to line up in order.

A 5-day plan for comparing integers

Ten minutes a day is enough. Short, regular practice works far better than one long session.

By grade

Grade 6 (Common Core 6.NS.C.7a and 7b) compares and orders integers using the number line, and writes and explains inequality statements in context. Grade 7 compares rational numbers, like −2.5 and −2¼. In India, comparing integers is part of class 6.

More for each grade: Grade 6 math and the CBSE class 6 maths guide.

What comes next

Next, practice reading and plotting on integers on a number line. Compare any two numbers with the integer number line.

Worksheet and more practice

Print a free worksheet with an answer key, or keep practicing online with integer practice.

Printable PDFs: comparing integers · absolute value · adding and subtracting integers · make a fresh integers test

← Absolute valueIntegers on a number line →

More: integers for kids · integer calculator · integer number line · integer practice · multiplying integers · ratios for kids

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Questions parents ask

How do you compare integers?

Picture the number line. The integer further right is greater, so −3 > −8.

Which is greater, −5 or −10?

−5, because it is closer to 0 and further right.

Is a negative number always less than a positive one?

Yes. Every negative number is less than 0, and 0 is less than every positive number.

How do you order integers from least to greatest?

Place them on a number line and read from left to right.

What grade learns comparing integers?

Grade 6 under Common Core 6.NS.C.7. In India, class 6.