B. Number · Number Sense: Numbers to One Million, Integers, Decimals and Fractions

Comparing and Ordering Integers

B1.3 B1.2 A1About 35 minutes

Learning goals

I can compare two integers using >, < and =.
I can put a set of integers in order from least to greatest or greatest to least.
I can use a number line to explain why −8 is less than −3.

Words to know

greater than (>)
Farther right on a horizontal number line, or higher on a vertical one.

less than (<)
Farther left on a horizontal number line, or lower on a vertical one.

ascending order
From least to greatest.

descending order
From greatest to least.

Which town was colder?

On one January morning, the weather report gives these temperatures for four Ontario places (made-up numbers for this lesson). Look at the table below.

Which town was the coldest? Which was the warmest? Is −8 colder than −3?

Place	Temperature
Town A	−8 °C
Town B	−3 °C
Town C	2 °C
Town D	−15 °C

Morning temperatures (made-up data).

The number line rule

On a horizontal number line, numbers get greater as you move right and less as you move left.

On a vertical number line, numbers get greater as you go up and less as you go down, just like a thermometer.

That means:

Every positive integer is greater than 0.
Every negative integer is less than 0.
Every negative integer is less than every positive integer.
For two negative integers, the one closer to zero is greater. −3 is closer to zero than −8, so −3 > −8. (It's warmer!)

The four temperatures on a number line: −15, −8, −3 and 2. Left is less; right is greater.

Worked example

Example 1: Compare two negative integers

Which is greater: −8 or −3?

Find both on a number line. −3 is to the right of −8.
Numbers to the right are greater.
Check with temperature: −3 °C is warmer than −8 °C.

−3 > −8 (or −8 < −3).

Worked example

Example 2: Order the temperatures

Order the four temperatures from coldest to warmest (least to greatest): −8, −3, 2, −15.

Negative numbers come before positive ones. The only positive one is 2, so it is last.
Of the negatives, the one farthest from zero is least: −15, then −8, then −3.

−15, −8, −3, 2. Town D was coldest; Town C was warmest.

Worked example

Example 3: Watch out for the trap

Sam says −12 > −2 because 12 is bigger than 2. Is Sam right?

On a number line, −12 is 10 steps farther left than −2.
In temperature, −12 °C is much colder than −2 °C.

No. −12 < −2. For negative integers, the bigger the number after the sign, the less the integer is.

−12 is 10 steps lower than −2 on the thermometer, so −12 °C is colder: −12 < −2. Lower is less.

Be a good sport

In the card game below, sometimes you'll flip a big negative card and lose the round. That's part of the game! Take a breath, say "Next round!" and keep playing. Staying calm helps you think clearly.

Just for fun

Funny but true: the coldest temperature ever recorded in Canada was about −63 °C, at Snag, Yukon, in 1947. Compared with that, a −15 °C morning is practically beach weather!

Hands-on activity

Integer war

You need: a deck of playing cards with the face cards (J, Q, K) removed. Ace = 1. In this game, black cards (spades ♠ and clubs ♣) are positive and red cards (hearts ♥ and diamonds ♦) are negative. So a red 7 is −7 and a black 4 is +4.

Share the cards between two players, face down.
Each player flips a card. Say both integers aloud: "negative seven, positive four".
The player with the greater integer takes both cards. Say the comparison with "is greater than" or "is less than".
If the cards are equal, each flips another card; the greater one takes them all.
Play for 10 minutes. The player with more cards wins.

Variation: Each player flips three cards and puts them in order from least to greatest. Check each other's order!

Your turn

Use >, < or =: −5 ___ 3

Use >, < or =: −9 ___ −4

Use >, < or =: 0 ___ −11

Order from least to greatest: 4, −6, 0, −1, 7

Order from greatest to least: −20, 15, −2, −13

Which is colder: −17 °C or −7 °C?

More practice: warm-up

Use >, < or =: 2 ___ −2

Use >, < or =: −1 ___ 0

Which is greater: −3 or −30?

Order from least to greatest: −4, 4, 0

Which is lower on a vertical number line: −6 or −5?

More practice: on your own

Order from least to greatest: −8, 12, −15, 0, 3, −1

A golf score of −4 means 4 strokes under par. In golf, the lowest score wins. Who wins: Amira with −4, Ben with +1 or Chloe with −6?

Write an integer that is between −10 and −6.

Max says "−25 is greater than −5 because 25 > 5." Explain why Max is wrong.

The temperatures at noon for 5 days were: −2, −9, 1, −5, −12 (in °C). Which day was warmest? Order them from coldest to warmest.

Challenge

Find all integers that are greater than −4 and less than 2.

I am an integer. I am less than 0. My opposite is between 6 and 9, and I am odd. What could I be?

A submarine stops at three depths: Stop A at −35 m, Stop B at −50 m and Stop C at −20 m. Which stop is deepest? Which is closest to the surface? Order them from deepest to highest.

Check your understanding

Quiz

Which is true?

Which list is in order from least to greatest?

Which temperature is the warmest?

Which integer is between −3 and 1?

On a vertical number line, a greater integer is...

Which is the least integer?

For parents and teachers

Big idea: B1.3 asks students to compare and order integers, decimals and fractions. This lesson focuses on integers, using the number lines from B1.2.

Common difficulties:

Treating negatives like positives. Many children think −12 > −2 because 12 > 2. Use a thermometer: −12 °C is colder, so it is less.
Mixing up "farther from zero" with "greater". For negative numbers, farther from zero means less.

How to help: Play Integer war with a deck of cards. Ask "How do you know?" after each round and listen for number line reasoning. Notice and praise calm, good-sport behaviour when your child loses a round; this is part of the social-emotional learning in Strand A.