Grade by Grade
B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Comparing and Ordering Numbers to 10 000

B1.2 A1About 35 minutes
Learning goals
  • I can compare two numbers up to 10 000 using place value.
  • I can use the symbols >, < and =.
  • I can order numbers from least to greatest and from greatest to least.
  • I can use a number line to show which number is greater.

Words to know

compare
Decide which number is greater, which is less, or if they are equal.
greater than (>)
Has more. 5200 > 5100.
less than (<)
Has fewer. 3999 < 4000.
order
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 3

In Grade 3 you compared numbers to 1000 by looking at the hundreds first, then the tens, then the ones. You used > (greater than) and < (less than). The open side of the sign always faces the greater number. The same method works up to 10 000. We just start one place earlier: the thousands.

Let's start with a story

Two classes are counting steps for a fitness challenge. Class A walked 4372 steps around the track. Class B walked 4327. Which class walked more?

Both numbers have 4 thousands and 3 hundreds. Look at the tens: Class A has 7 tens and Class B has 2 tens. 7 tens is more, so 4372 > 4327. Class A walked more.

How to compare two numbers

  1. Count the digits. A number with more digits is greater. 10 000 is greater than any four-digit number.
  2. If they have the same number of digits, line up the places and compare from the left: thousands first.
  3. If those digits are the same, move one place to the right. Keep going until the digits are different.
  4. The number with the greater digit in that place is the greater number.
ThousandsHundredsTensOnes
Class A4372
Class B4327
Lined up: the thousands are the same, the hundreds are the same, and the tens are different. 7 tens > 2 tens, so 4372 > 4327.
Worked example

Example 1: Compare using place value

Compare 6185 and 6815. Use > or <.

  1. Thousands: 6 and 6. Same.
  2. Hundreds: 1 and 8. Different! 1 hundred is less than 8 hundreds.

6185 < 6815

Start at the leftThHTO61856815samedifferent!6 = 61 < 86185 < 6815The hundreds decide.No need to look at tens or ones.
Line up the places and compare from the left. The thousands match, so move right. The hundreds are different, and 1 hundred < 8 hundreds.
Worked example

Example 2: Different numbers of digits

Compare 985 and 1002.

  1. 985 has 3 digits. 1002 has 4 digits.
  2. Any four-digit number is at least 1000, which is more than any three-digit number.
  3. Don't be fooled by the big 9 in 985!

985 < 1002

50005500600065007000
5096, 5609, 5960 and 6590 on a number line. Numbers farther to the right are greater.
Worked example

Example 3: Order four numbers

Order from least to greatest: 5960, 5096, 6590, 5609

  1. Thousands: three numbers have 5 thousands. 6590 has 6 thousands, so it is the greatest.
  2. Compare the hundreds of the others: 5960 has 9, 5096 has 0, 5609 has 6.
  3. 0 < 6 < 9, so the order is 5096, 5609, 5960.

5096, 5609, 5960, 6590

Worked example

Example 4: Missing digit

Which digits could go in the box? 3□45 > 3745

  1. The thousands are both 3.
  2. The tens and ones (45) are the same in both numbers, so the hundreds digit decides.
  3. If the box is 7, we get 3745, which is equal, not greater. So 7 does not work.
  4. 8 or 9 work: 3845 > 3745 and 3945 > 3745.

8 or 9

Check your thinking

Before you decide, check your answer another way: picture both numbers on a number line, or ask "Which is closer to 10 000?" Checking your work is a habit strong math thinkers have.

Just for fun

Some people picture < and > as a hungry crocodile's mouth. The crocodile always chomps the greater number, so in 4372 > 4327 it picked the snack with more tens. Smart croc!

Hands-on activity

Greatest number game

You need: 10 small pieces of paper with the digits 0 to 9 (one digit on each), a bowl, paper and a pencil. Play with a grown-up or a sibling.

  1. Each player draws 4 boxes on paper: □□□□ (thousands, hundreds, tens, ones).
  2. One person pulls a digit from the bowl and reads it out. Each player writes it in one of their boxes. Once a digit is written, it can't move! Put the paper back in the bowl.
  3. Repeat until all four boxes are full.
  4. Read your numbers aloud and compare them with > or <. The greatest number wins the round.
  5. Play again, but this time the least number wins.

Math talk: "Where did you put the 9? Why?" Be a good sport: congratulate the winner, and talk about what you'd do differently next time.

Your turn

1

Compare with > or <: 2459 □ 2495

2

Compare with > or <: 8103 □ 7999

3

Compare with > or <: 999 □ 1000

4

Compare with >, < or =: 4000 + 60 □ 4060

5

Order from least to greatest: 3201, 3012, 3210, 3120

6

Order from greatest to least: 7450, 7045, 7504, 7054

7

A ski hill has two trails: 2850 m and 2580 m long. Which is longer?

More practice: warm-up

1

Which is greater: 5000 or 4999?

2

Compare: 6300 □ 6400

3

Compare: 10 000 □ 9876

4

Which is less: 1234 or 1243?

5

Order from least to greatest: 2000, 9000, 5000

More practice: on your own

1

Order from least to greatest: 4089, 4890, 4809, 4098

2

Write a number between 6990 and 7010.

3

Which digits make this true? 58□2 < 5832

4

Use the digits 2, 7, 0, 9 once each. Make the greatest and the least four-digit numbers.

5

Three towns had snowfall totals of 2140 mm, 2410 mm and 2104 mm over ten years. Order them from greatest to least.

Challenge

1

Ava says 3999 > 4001 because 3999 has more 9s. Explain her mistake.

2

I am a four-digit number. I am greater than 8500 and less than 8600. My tens digit is 9 and my ones digit is 2 less than my tens digit. What number am I?

3

How many whole numbers are greater than 9990 and less than 10 000?

Check your understanding

Quiz

1.

Which is true?

2.

Which number is the greatest?

3.

Which list is in order from least to greatest?

4.

Which digit can go in the box? 7□19 > 7619

5.

Which is less than 1000?

6.

Compare: 6000 + 500 □ 6050

For parents and teachers

Big idea: B1.2 asks Grade 4 students to compare and order whole numbers up to 10 000 in various contexts. The key is place value: compare from the greatest place (on the left) to the right.

Common difficulties:

  • Being fooled by big digits (thinking 985 > 1002 because 9 is big). Ask "How many digits? Which place matters most?"
  • Mixing up > and <. Remind your child the wide, open side faces the greater number.
  • Starting from the ones instead of the thousands.

How to help: Compare real numbers: prices of two used bikes in a flyer, distances on road signs, page counts of two books. Play the greatest number game; talk about where to place big and small digits. Strand A: model being a good sport and checking work another way.