Subtracting Across Zeros

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SWBAT subtract across zeros (i.e: 100-57=____).

Big Idea

Students use place value blocks to accurately subtract across zeros.


10 minutes

I have a subtraction problem for you.  Work on your white board to solve this problem:

200 – 54 = 

I allow students 3-4 minutes to solve the problem, noticing common mistakes and strategies that students use.  Some students might solve this problem using an open number line or by breaking the problem down (200-50 = 150, 150-4 =146),  others might draw hundreds, tens, and ones to represent the problem.  Students in my class have not seen a problem where they are required to subtract across zeros but they can make use of the structure of hundreds, tens, and ones and the tools they know to solve this problem to the best of their ability. (MP6) 

Turn and talk: How did you solve this problem?  

Introduction to New Material

10 minutes

To start the introduction to new material, I have students who successfully solved the problem share their strategies.  Some students may have drawn hundreds, tens, and ones.  Other students might know how to  regroup across zeros.

Let’s look at this problem using base ten blocks.

I have 2 hundreds and I want to subtract 54.  

I need to start with taking away 4 ones but I can’t do that because I don’t have any ones or tens.  So, I go to the neighbor.  My neighbor also is a zero!  I  then take one of my hundreds and turn it into ten tens.  Now, I can turn one of these tens into ten ones and I can solve the problem.

As I model this problem, I notate how I am solving this problem using regrouping (i.e: turn the 200 into a 100, the 0 in the tens place into 9, and the 0 in the ones place into a 9).

If time permits, I pose another problem and have students come and model using the base ten blocks. 

Guided Practice

10 minutes

We are going to work in pairs to solve some problems.  You can use base ten blocks if you want. As you solve the problem, draw the base ten blocks to help you solve the problem accurately.

I divide students into heterogeneous pairs so that students can support each other and have them work on the problems.  As students work, I circulate to determine any common misconceptions and support students who are struggling. 

When finished, have  I have students come back together and share their work—I also use this time to address any common misconceptions or problems.

Independent Practice

10 minutes

Independent Practice is differentiated based on student understanding of this concept.  Students can solve these problems using whatever strategy is best for them (open number lines, hundreds/tens/ones chart or blocks, etc.) 

Group A: In need of intervention

Students will work with the teacher to solve subtracting across zero problems using place value blocks (if they want) and will have a hundreds/ tens/ ones chart available to them. 

Group B: Right on track!

Students will work independently or with a partner to solve subtracting across zero problems. This group will have place value blocks and a Hundreds/Tens/Ones chart available to them.

Group C: Extension

Students will work independently to solve subtracting across zero problems.  

This group will have place value blocks and a Hundreds/Tens/Ones chart available to them.


5 minutes

Now that we have worked independently to solve these problems, I want two or three students to  share their work with the class, explaining how you solved the problem and how you regrouped.  

When students share, I have them come to the board and solve their problem, explaining the steps that they took to get the answer.