Comparing Numbers Written in Expanded Form

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SWBAT compare numbers written in expanded form

Big Idea

Students take their understanding of place value to the next level when they compare numbers written in expanded form.


10 minutes

Using place value blocks, I build 310 and 301 on the carpet (or under the document camera). 

I want you to help me decide which number is larger. Before we start, let’s write these numbers in expanded form. 

I ask students to volunteer what each number is in expanded form. 

Now, turn and tell your partner which number is larger and WHY that number is larger.

I ask 2-3 students to share why 310 is larger. 

Make sure that students are able to articulate why it is larger and are using place value language (i.e: I know 310 is larger because a ten is larger than a one and 310 has one ten while 301 has 0 tens). 

Introduction to New Material

10 minutes

Now, we are going to do another practice problem.  Let’s read this problem together:

Is this statement TRUE or FALSE? 

3 hundreds and 2 ones >  3 hundreds and 1 ten

Turn and talk:  What should I do first to decide whether this statement is true or false? 

I ask 2-3 students to share. Students may discuss changing the number to standard form or drawing out the place ten blocks. 

Turn and talk: Is the statement true or false?   How do you know?

I ask 2-3 students to share out about why  310 is larger.  Make sure that students are able to articulate why it is larger and are using place value language . If students are struggling, encourage them to draw out the numbers using place value blocks so they can see clearly which is greater. 

Depending on time, I may go over another practice problem. 

NOTE: Throughout this lesson I  have chosen to use numbers that have zeros in them during this practice because it challenges students to compare tens and ones and to internalize that 1 ten is always larger than 0-9 ones. 



Guided Practice

10 minutes

Now, you are going to work in a group of two or three to solve your own problem. If you choose to, you can use place value blocks.  Make sure that you are explaining why each number is larger using your place value vocabulary.

Our problem is:

Is this statement TRUE or FALSE?

 3 hundreds and 9 ones <  3 hundreds and 6 tens 

I send students out to work on guided practice problems (on attached worksheet)  and circulate to determine mastery and ask guiding questions:  Why is this one larger?  How do you know that 3 hundreds and 9 ones is smaller than 3 hundreds and 6 tens when 9 is larger than 6?  

I also encourage students to use place value blocks for two reasons: (1)It helps student internalize the difference in value between tens and ones, and (2) it normalizes use of manipulatives and helps build a positive class culture where all students feel comfortable and confident using manipulatives to help clarify their thinking. 

When finished, I have students come back together.  

I want you to tell me how you solved this problem.  Turn to your partner and explain how you solved this problem and what answer you got. 
I ask students to share their responses and select an exemplary student to share his or her explanation. 

Independent Practice

15 minutes

Now that we have practiced as a group and in partners, we are going to practice alone. Use your place value blocks to help you solve the problems on your worksheet.  

As students work, I circulate to help students who are struggling and to check for understanding. 


5 minutes

Today we have taken what we know about expanded form and what we know about comparing numbers to work on comparing numbers written in expanded form.  Now that we have practiced this skill, I want you to turn to a partner and share whether the following statement is true or false?

 3 hundreds and 2 ones > 3 hundreds and 1 ten.

 I allow students time to talk and then call on 2-3 students to share their answers.