Comparing Multi-Digit Whole Numbers

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SWBAT compare whole numbers based on place value of the digits, using >, <, or = to record the comparison.

Big Idea

In this lesson, students use a place value chart as a tool for comparing large numbers.

Warm Up

10 minutes

I start this warm up by replaying this counting by fours song because my students like the videos so much.  This song also reinforces factors and multiples in a fun and engaging way. 




After the video, I then direct students to complete the multiplication by 4 sprint.

Click here for the Multiplication by 4 sprints and the Sprint directions. 

Next, I direct my students to count by 4 tens.  Students should say  4 tens, 8 tens, 12 tens. I have students stop and I ask them what 12 tens is in standard form.  Students should respond with 120.  Then I direct students to continue. I stop their counting again at 24 tens, and 36 tens. I ask students what the number is in standard form.

I repeat this same procedure counting by 3 tens and stopping at various numbers.

Concept development

35 minutes

I begin this lesson by activating students prior knowledge and review the previous days work by writing this 5 digit number on the board:


I ask students what the value of the 8 is.  Students respond with 8,000.  Next, I ask students to state the value of each number.  I do this very quickly and my expectation is that student are answering orally in unison. 

Then I draw a place value chart to millions on the board. I direct students to draw a place value chart on their personal white boards.  

(Included in the resources is a pre-made blank place value chart. I use this with some students who need this scaffold.)

Next, I write two, four digit numbers on the side of the place value chart.  e.g. 5,231 and 6,487

Students copy the numbers on their white boards.  Next, I direct students to model the numbers on the place value chart by using a proof drawing or visual representation. I also draw both numbers on the place value chart using a proof drawing. 

I encourage students to model each digit with number dots in the corresponding place. I find this helpful. Most of my students come to fourth grade with a solid understanding that they can represent ones with dots, tens with straight lines or tallies, hundreds with squares, and thousands with cubes. I have found that students are able to work with dots for all place values, which is much easier to draw and model for large numbers. 


Next I explain to students that a place value chart can be a useful tool when comparing numbers. I  ask students what the greatest unit is.  Students respond with thousands.  Then I ask how many thousands are in each number. I lead a brief discussion centered around the fact that 5 thousands is less than 6 thousands. I remind students that the number with more of the largest unit is greater.  Next, I remind students that we say that 6,487 is greater than 5,231 because there are more thousands in the number 6,487 and thousands is the largest unit.

I repeat this process with other four digit numbers until students are comfortable modeling numbers with the place value chart. As students model numbers, I circulate around the room and check for misunderstandings through guided questioning.

Next I display the numbers 37,257 and 32,641.  Again, I ask students what the largest unit is. Students respond with ten thousand.  I direct students to identify how many ten thousands are in each number.  I explain to students that when the digit in the largest unit is equal, they can compare the next largest unit; the thousands in this example. Students see that 7 thousands is more than 2 thousands thus 37,257 is greater than 32,641.  I write the mathematical expression for greater than and less than on the board for students to see.

37,257 ˃ 32,641  and 32,641 ˂ 37,257

I repeat this same process with one more 5 digit number to give students practice with modeling and comparing numbers to ten thousands.

I then show students how a place value chart can be helpful when comparing three or more numbers that have several digits and units equal. I show the numbers 56,841 and 56,589, and 56,481.  By lining up the ten thousands, thousands, hundreds, etc with the three numbers in a vertical column, students can see that 56,481 is the smallest number because it has the least number of hundreds.

I really wanted to focus on Math Practice Standard 3 and 6 in this lesson. As I develop a safe and caring classroom culture, it is very important that students are able to construct viable arguments. As we discussed the value of digits in this lesson, students were able to practice talking about math. Students making conjectures and talking about mathematical concepts is an area that must be nurtured. One way I begin by creating this environment is by having them begin to talk about their thinking. I have various talk prompts that I use.  The one students were encouraged to use today was "I think ______, because___________"  Each time I catch students saying the phrase, I pay them with a gold ticket.  Each week I have a phrase that pays for students to incorporate into their math talk.

This was very effective today.  I love when students catch each other or tell each other to use the phrase that pays. Not only are they using math language and working on MP.3, they are really building our classroom climate that we are all learners and that we can all learn from each other.

Near the end of this lesson students complete the practice sheet- Comparing Numbers Practice.  Students that do not finish take it home as homework.


Student debrief - Wrap up

10 minutes

To end this lesson I collect students finished work and direct them to complete the exit ticket - comparing number exit ticket.

This is a photo of how I store my exit tickets. I have a pocket chart I hang on the classroom door.  Students place their exit tickets in their numbered slot as they leave for the day. (All students in my class are assigned a number) 

I use the exit tickets for re-teaching and to identify misconceptions.  I like to use quick checks for understanding often in order to provide rich and meaningful lessons for all students.  After students complete the exit tickets, I can quickly look at each ticket and group the papers according to proficiency level.