How to Teach Comparing and Ordering Numbers

Are your students learning to compare and order numbers?  In fourth grade, our objective is to read, write, compare, and order numbers up to 999,999.  Here is how you can organize your lesson sequence for place value with numbers in the hundred thousands. 

Assess Prior Knowledge of Place Value

Students should know place value up to the amount you are asking them to compare.  In other words, if you want your fourth graders to compare and order numbers in the hundred thousands place, but they can’t read numbers higher than 9,999, practice finding the value of the digits in numbers such as 12,345 and 234,567.  I have a fun, differentiated game called Codebreaker to help them practice applying this skill. 

Students who can’t read numbers as high as your goal can still practice the skill of comparing and ordering numbers.  Start them with numbers that have fewer places (in other words, numbers to 9, then numbers to 99 before delving in to numbers in the hundreds and beyond).  As you introduce the skill of comparing, nearly all your students can participate as long as you differentiate the numbers you are using.  Then during small group instruction you can provide intervention with the place value of higher numbers. 

Provide Direct Instruction for Comparing Numbers

When we compare numbers, we start from left to right because digits on the left have a greater value than those on the right.  In the number 1,234,567 the number with the greatest value is 1.  That’s because it’s in the millions place so it’s not worth just one; it’s worth 1 million.  Use the place value when explaining.  The 7 is in the ones place so it’s not worth as much as any of the other digits. 

When we compare numbers with a different number of digits, the number with the most digits is greater.  In other words, 100 is more than 99 because it has 3 digits but 99 only has 2 digits.

When we compare numbers with the same number of digits, compare numbers starting on the left because they have the greater value.  For example, 876,543 is greater than 765,432 because 8 hundred thousand is greater than 7 hundred thousand.  Again, name the place value when explaining.   

When we compare numbers with the same number of digits and the numbers on the left match, move one space to the right on both numbers to compare (as many times as necessary).  For example, 999,991 and 999,992 have identical numbers until you get all the way to the right.  The numbers 543,210 and 546,789 have identical numbers starting on the left, and in the next place over, but we find a different number in the thousands place.

Provide Opportunities to Practice Comparing and Ordering Numbers in Context

Now students have the math knowledge they need to compare and order numbers.  But your work is not done!  Teach the associated vocabulary and provide and model a variety of contexts for applying this skill.  For example:

  •        Which number is greater?
  •        Which number is less?
  •        If I have this many and my friend has that many, who has more?  Who has fewer?
  •     Fill in the blank:  123,456 is __________ 123,210.
  •        Order these 3 (or more) numbers from least to greatest.
  •        Order these 3 (or more) numbers from greatest to least.

If you’d like a fun activity for your students to practice comparing and ordering numbers, I have a fun task cards activity: Compare and Order Peppers.  And yes, it includes a paper version as well as a Google Slides version.  It was inspired by some of my fourth graders who were very interested in spicy foods, bringing in spicy Doritos and arguing which is the hottest.  Some watch the One Chip Challenge videos on YouTube to see people’s reactions to eating spicy food.  My husband (also a fan of spicy foods) introduced me to the Scoville rating system and I realized the potential connection to math! 

Or, if your students have mastered comparing and ordering numbers in context, start planning your lesson sequence for estimating.  You can get more teaching tips specifically about estimating here on my blog.

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