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K03 • Lesson 15 of 105

Comparing and Ordering Numbers

Students learn to compare two- and three-digit numbers using place value reasoning. Starting with base-10 block comparisons, they progress to using greater than, less than, and equal to symbols. They practice ordering sets of numbers from least to greatest and greatest to least, and locate numbers on a number line to build number sense.

K-2 Foundations • K-2

Prerequisites: E01, K01, K02

Key Concepts

  • greater than, less than, equal to symbols
  • comparing by place value from left to right
  • ordering numbers on a number line
  • reasoning about magnitude using hundreds, tens, and ones

Comparing and Ordering Numbers

Which is more: 47 or 74? To answer questions like this, we need to compare numbers. We look at the digits place by place, starting from the left.

The Comparison Symbols

SymbolMeaningExample
>is greater than8 > 3
<is less than2 < 9
=is equal to5 = 5

Helpful Trick

The symbol always opens wide toward the bigger number, like a hungry mouth eating the larger amount. The pointy end points to the smaller number.

BIG > small      small < BIG

How to Compare Two Numbers

  1. Count the digits. A number with more digits is always greater. (245 > 98 because three digits beats two digits.)
  2. Same number of digits? Compare the leftmost place first.
  3. If those digits match, move one place to the right and compare again.
  4. Keep going until you find digits that differ.

Worked Example 1: Comparing Two-Digit Numbers

Compare 56 and 52.

  1. Both have 2 digits.
  2. Tens place: 5 and 5 -- they are the same.
  3. Ones place: 6 and 2 -- 6 is greater than 2.
  4. So 56 > 52.

Worked Example 2: Comparing Three-Digit Numbers

Compare 384 and 391.

  1. Both have 3 digits.
  2. Hundreds place: 3 and 3 -- the same.
  3. Tens place: 8 and 9 -- 8 is less than 9.
  4. We stop here! 384 < 391.

Ordering Numbers

To put numbers in order, compare them two at a time:

Worked Example 3: Ordering from Least to Greatest

Order these numbers: 78, 42, 85, 41

  1. Compare tens digits: 42 and 41 start with 4; 78 starts with 7; 85 starts with 8.
  2. The 4-tens group is smallest. Between 42 and 41: 41 < 42.
  3. Next is the 7-tens: 78.
  4. Largest is 85.
41, 42, 78, 85

The Number Line

A number line shows numbers in order from left to right. Smaller numbers are on the left. Bigger numbers are on the right.

0 ------- 25 ------- 50 ------- 75 ------- 100

To place a number on a number line, find where it belongs between the labeled marks.

Watch Out!

Do not just look at the ones digit! The number 19 is less than 21 even though 9 is bigger than 1. Always start comparing from the leftmost digit.

Real-World Connection

When you check the temperature, you compare numbers. If Monday is 72 degrees and Tuesday is 68 degrees, you know Monday was warmer because 72 > 68.

Practice Problems

1. Write >, <, or = between: 63 ___ 67

Show Answer

63 < 67. Same tens digit (6), but 3 < 7 in the ones place.

2. Write >, <, or = between: 450 ___ 405

Show Answer

450 > 405. Same hundreds (4), but 5 > 0 in the tens place.

3. Order from least to greatest: 88, 38, 83

Show Answer

38, 83, 88. The tens digits are 3, 8, 8. Among the two 8-tens numbers, 83 < 88.

4. Which is greater: 199 or 200?

Show Answer

200 is greater. Both have 3 digits, and in the hundreds place, 2 > 1. So 200 > 199.

5. Place these on a number line: 30, 75, 10, 50

Show Answer

From left to right: 10, 30, 50, 75. Smaller numbers go to the left.

Lesson Summary

Overview