B. Number · Number Sense: Numbers to 1000 and Fractions

Comparing and Ordering Numbers to 1000

B1.2 A1About 35 minutes

Learning goals

I can compare two numbers to 1000 by looking at hundreds, then tens, then ones.
I can use the words greater than and less than, and the symbols > and <.
I can order numbers from least to greatest and from greatest to least.
I can use a number line to compare numbers.

Words to know

compare
To decide which number is greater, which is less, or if they are equal.

greater than (>)
More than. 486 > 468 means 486 is greater than 468.

less than (<)
Fewer than. 468 < 486 means 468 is less than 486.

order
To put numbers in a line from least to greatest, or greatest to least.

least / greatest
The smallest number / the biggest number in a group.

Remember from Grade 2

In Grade 2 you compared numbers to 200 by looking at the hundreds first, then the tens, then the ones. The same steps work for numbers all the way to 1000!

The can drive

Three classes collected cans for the food bank:

Room 12: 486 cans
Room 14: 468 cans
Room 15: 512 cans

Which class collected the most? Which collected the least?

Number	Hundreds	Tens	Ones
486	4	8	6
468	4	6	8
512	5	1	2

Line up the digits by place. Start with the hundreds.

Three steps to compare

Look at the hundreds. More hundreds means a greater number.
If the hundreds are the same, look at the tens.
If the tens are the same too, look at the ones.

512 has 5 hundreds. The others have only 4 hundreds, so 512 is the greatest. 486 and 468 both have 4 hundreds, so look at the tens: 8 tens is more than 6 tens. 486 is greater than 468.

Worked example

Example 1: The can drive

Order the cans from greatest to least: 486, 468, 512.

Hundreds: 512 has 5 hundreds. It is the greatest.
486 and 468 both have 4 hundreds. Tens: 8 tens > 6 tens, so 486 is greater.
468 is the least.

512, 486, 468. Room 15 collected the most and Room 14 collected the least.

Using symbols

Math has short ways to write "greater than" and "less than":

> means is greater than: 486 > 468
< means is less than: 468 < 486
= means is equal to: 500 = 500

The wide-open side of the symbol faces the greater number. The point faces the smaller number.

The wide-open side of > faces the greater number, 486. The point faces the smaller number, 468.

On a number line, numbers get greater as you move right. 468 is left of 486, and 512 is farthest right.

Worked example

Example 2: Different number of digits

Which is greater, 98 or 108?

98 has 0 hundreds. 108 has 1 hundred.
Any three-digit number is greater than any two-digit number.

108 > 98. Don't be fooled because 9 is bigger than 1!

Worked example

Example 3: Order the numbers

Order from least to greatest: 307, 370, 73, 703.

73 has only two digits, so it is the least.
307 and 370 both have 3 hundreds. Tens: 0 tens < 7 tens, so 307 comes before 370.
703 has 7 hundreds. It is the greatest.

73, 307, 370, 703

Worked example

Example 4: The missing digit

Which digits can go in the box to make this true? 4□7 > 462

Both numbers have 4 hundreds. Compare the tens.
If □ is 7, 8 or 9, the tens are greater than 6, so it works.
If □ is 6, the tens are the same. Then compare ones: 7 > 2. So 467 > 462. It works too!
If □ is 0 to 5, the tens are less than 6, so it doesn't work.

The box can be 6, 7, 8 or 9.

Feeling stuck?

If you feel mixed up, slow down. Write the numbers one under the other so the hundreds, tens and ones line up. Then check with a number line. Mistakes help us learn, so it's fine to try again!

Just for fun

Why was 6 afraid of 7?

Because 7 8 9! (Seven ate nine.) Luckily, in 486 > 468, the 8 tens and 6 tens get along just fine.

Hands-on activity

Greatest number card game

You need: a deck of playing cards (use Ace as 1, and cards 2 to 9; take out the 10s and face cards) or 10 paper cards with the digits 0 to 9. Play with a grown-up or a friend.

Each player takes 3 cards.
Arrange your cards to make the greatest three-digit number you can.
Say your number out loud. Compare: "754 is greater than 632." Write it with a symbol: 754 > 632.
The greater number wins a point. Put the cards back, shuffle and play again.
After 5 rounds, write all the numbers and put them in order from least to greatest.

Variation: try to make the least number instead!

Your turn

Which is greater: 529 or 592?

Write < or >: 806 ___ 860

Which is less: 399 or 401?

Order from least to greatest: 615, 156, 561, 651

Order from greatest to least: 909, 990, 99, 900

Maple Public School has 438 students. Pine Ridge School has 483 students. Which school has more students?

Name a number between 745 and 755.

More practice: warm-up

Which is greater: 300 or 200?

Which is greater: 450 or 540?

Which is less: 1000 or 999?

True or false: 87 > 102

Write <, > or =: 712 ___ 712

More practice: on your own

Tia says 95 > 159 because 9 is bigger than 1. Is she right?

Bags of apples weigh 850 g, 805 g, 580 g and 508 g. Order them from least to greatest.

Which digits can go in the box? 6□3 < 635

Use the digits 2, 7 and 5 once each. Make the greatest and the least three-digit numbers.

Which is closer to 500: 480 or 530?

Challenge

Use the digits 0, 4 and 9 once each. Make the greatest and the least three-digit numbers.

How many whole numbers are between 990 and 1000?

Guess my number: I am between 600 and 700. My tens digit is 8. My ones digit is odd and less than 3.

Check your understanding

Quiz

Which number is the greatest?

Which is true?

Which list is in order from least to greatest?

Which number is less than 500?

Library A has 615 books. Library B has 651 books. Which has more?

Which digit makes 7□4 > 785 true?

For parents and teachers

Big idea: To compare whole numbers, start with the greatest place value. The curriculum (B1.2) asks Grade 3 students to compare and order whole numbers to 1000 in various contexts.

Common difficulties:

Comparing the first digits they see (thinking 95 > 159). Write the numbers one under the other, lined up on the right.
Mixing up > and <. Remind them the open side faces the greater number. Always read the sentence out loud: "806 is less than 860."
Forgetting to check the ones when hundreds and tens are the same.
Including the end numbers for "between".

How to help: Compare real numbers: prices in flyers, page counts of books, kilometres on road signs, scores in a game. Play the card game. If your child gets frustrated, encourage them to slow down and line up the digits (managing frustration is part of Strand A).