Grade by Grade
B. Number · Number Sense: Numbers to 100 000, Fractions, Decimals and Percents

Comparing and Ordering Numbers to 100 000

B1.2 A1About 35 minutes
Learning goals
  • I can compare two numbers up to 100 000 using place value.
  • I can use the symbols >, < and =.
  • I can order numbers from least to greatest and from greatest to least.
  • I can show where numbers belong on a number line.

Words to know

compare
Decide which number is greater, which is less, or if they are equal.
greater than (>)
Bigger. 50 000 > 40 000. The open side faces the bigger number.
less than (<)
Smaller. 9999 < 10 000.
order
Put numbers in a list from least to greatest or from greatest to least.
ascending / descending
Ascending means going up (least to greatest). Descending means going down (greatest to least).

Remember from Grade 4

In Grade 4 you compared numbers to 10 000. You lined up the places and compared from the left. The first place where the digits are different tells you which number is greater. The same rule works for numbers to 100 000.

Let's start with a question

Two towns had a reading challenge. Pinecrest read 48 395 pages. Maple Falls read 48 539 pages. Which town read more pages?

The numbers look almost the same! Let's line them up.

Ten thousandsThousandsHundredsTensOnes
Pinecrest48395
Maple Falls48539
Same ten thousands (4). Same thousands (8). The hundreds are different: 3 < 5.

How to compare

  1. Count the digits. A 5-digit number is greater than a 4-digit number.
  2. If they have the same number of digits, line up the places.
  3. Compare from the left. The first place that is different decides.

So 48 395 < 48 539. Maple Falls read more pages. The 9 tens in 48 395 don't matter, because the hundreds already decided!

48 00048 50049 000Pinecrest48 395Maple Falls48 539greater numbers are farther right
Between 48 000 and 49 000, each small tick is 100. 48 539 is to the right of 48 395, so Maple Falls read more pages.
Worked example

Example 1: Different number of digits

Compare 9875 and 10 102.

  1. 9875 has 4 digits. 10 102 has 5 digits.
  2. Any 5-digit number is greater than any 4-digit number. Don't be tricked by the big 9!

9875 < 10 102

Worked example

Example 2: Order a list

Order from least to greatest: 63 208, 63 280, 36 820, 63 028

  1. Ten thousands: 36 820 has only 3. It is the least.
  2. The others all have 63 thousand. Compare hundreds: 63 028 has 0, 63 208 and 63 280 have 2.
  3. Compare the tens of 63 208 and 63 280: 0 < 8.

36 820, 63 028, 63 208, 63 280

20 00022 00024 00026 00028 00030 00021 90023 60026 100
A number line from 20 000 to 30 000. Each tick is 1000. The dots show 21 900, 23 600 and 26 100.
Worked example

Example 3: Use a number line

Which of 21 900, 23 600 and 26 100 is closest to 25 000?

  1. Place each number on the line between 20 000 and 30 000.
  2. 26 100 is 1100 away from 25 000.
  3. 23 600 is 1400 away from 25 000. 21 900 is even farther.

26 100 is closest to 25 000.

Worked example

Example 4: Real life

Three used cars have been driven 45 680 km, 54 680 km and 45 860 km. Which has been driven the least?

  1. Ten thousands: 4, 5, 4. The 54 680 car has driven the most.
  2. Compare 45 680 and 45 860: same 4 and 5, then hundreds 6 < 8.

The car with 45 680 km.

Be a good math partner

When you play a comparing game, sometimes you win and sometimes you lose. A good sport says "good game" either way. Explaining why a number is greater ("the thousands decided") is just as important as winning.

Just for fun

Why wasn't 10 000 worried when 9999 showed up with four big 9s?

Because it had one more digit up its sleeve!

Hands-on activity

Greatest number wins

You need: 20 small paper cards with the digits 0 to 9 written on them (two of each digit), a bag or bowl, and a partner.

  1. Each player takes 5 cards without looking.
  2. Arrange your cards to make the greatest 5-digit number you can. (A 0 can't go first.)
  3. Read your numbers out loud. Write them with >, < or = between them.
  4. The player with the greater number explains which place decided, then wins a point.
  5. Play 5 rounds. Then play again where the least number wins.
  6. At the end, put all the winning numbers in order from least to greatest.

Your turn

1

Use >, < or =: 67 412 ___ 67 241

2

Use >, < or =: 9999 ___ 10 000

3

Use >, < or =: 80 050 ___ 80 500

4

Order from least to greatest: 52 300, 25 300, 53 200

5

Which is greatest: 71 096, 71 960, 71 690?

6

Name a number between 34 500 and 34 600.

7

Three cars have been driven 45 680 km, 54 680 km and 45 860 km. Which one has been driven the most?

More practice: warm-up

1

Use >, < or =: 30 000 ___ 3000

2

Use >, < or =: 45 000 ___ 54 000

3

Use >, < or =: 12 345 ___ 12 345

4

Which is greater: 88 000 or 80 800?

5

Order from greatest to least: 40 000, 100 000, 4000

More practice: on your own

1

Order from least to greatest: 18 097, 18 790, 18 709, 17 980

2

Ella says 9876 > 12 000 because 9 is bigger than 1. Is she right?

3

Birchwood has 23 415 people. Cedar Lake has 23 451 people. Which town has more people?

4

What digit could go in the box? 56 □42 > 56 842

5

Is 49 800 closer to 40 000 or 50 000?

Challenge

1

Use the digits 2, 5, 7, 0, 9 once each. Make the greatest number that is less than 60 000.

2

Order from least to greatest: 70 007, 70 070, 7770, 70 700

3

My number is between 45 000 and 46 000. Its hundreds digit is 9. Its tens and ones digits are the same. Its digits add up to 18. What is it?

Check your understanding

Quiz

1.

Which is true?

2.

Which number is greatest?

3.

Which list is in order from least to greatest?

4.

Which number is between 62 000 and 63 000?

5.

Compare 8754 and 10 004.

6.

Which place decides which is greater: 74 618 or 74 681?

For parents and teachers

Big idea: B1.2 asks Grade 5 students to compare and order whole numbers up to 100 000 in various contexts. The key is place value: line up the places and compare from the left.

Common difficulties:

  • Comparing first digits when numbers have different lengths (thinking 9876 > 12 000). Always count digits first.
  • Looking at the last digits. Once a place on the left is different, the places to the right don't matter.
  • Mixing up > and <. The open side of the symbol faces the greater number.

How to help: Compare real numbers: prices of two cars in a flyer, kilometres on two vehicles, attendance at two games. Play the card game and ask your child to explain which place decided. Strand A (social-emotional learning) is woven in through being a good sport and explaining reasoning.