##
* *Reflection: Developing a Conceptual Understanding
Subtracting Across Zeros - Section 2: Introduction to New Material

When I have taught subtracting across zeros in the past, I have taught a trick: "borrow from the hundreds, turn the tens and ones place into nines and solve." In teaching this trick, my students did not develop a conceptual understanding and did not have to understand WHY they were changing the tens place into a 9, etc.

This year, I modeled subtracting across zeros using place value blocks and I was surprised how many students could clearly explain how to subtract across zeros. Student accuracy was also higher because students understood the process more deeply. Allowing students to use place value blocks during their guided and independent practice further helped them develop this conceptual understanding.

*Don't teach tricks!*

*Developing a Conceptual Understanding: Don't teach tricks!*

# Subtracting Across Zeros

Lesson 13 of 13

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

*45 minutes*

#### Introduction/Hook

*10 min*

*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? **

*expand content*

#### Introduction to New Material

*10 min*

**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.

*expand content*

#### Guided Practice

*10 min*

*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.

*expand content*

#### Independent Practice

*10 min*

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.

*expand content*

#### Closing

*5 min*

*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.

*expand content*

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- LESSON 1: What is One Hundred More? What is One Hundred Less?
- LESSON 2: Adding Three-Digit Numbers Without Regrouping
- LESSON 3: Adding Three-Digit Numbers with Regrouping
- LESSON 4: Adding Four Three-Digit Numbers
- LESSON 5: Our Strategies for Result Unknown Problems
- LESSON 6: Two-Step Word Problems (Result Unknown)
- LESSON 7: Solving Result Unknown Problems with Three-digit Numbers.
- LESSON 8: Introduction to Change Unknown Problems
- LESSON 9: How do I solve a change unknown word problem?
- LESSON 10: Acting out Change Unknown Problems
- LESSON 11: Change Unknown Word Problems
- LESSON 12: Change Unknown Word Problems with Number Lines
- LESSON 13: Subtracting Across Zeros