# Subtracting Across Zeros

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## Objective

SWBAT subtract numbers with zeros.

#### Big Idea

Subtracting with zeros requires regrouping.

## Opener

5 minutes

In this video, I explain the objective for the lesson today:  Introductory Video for Subtracting Across Zeros.

This lesson is on a skill that's somewhat difficult for students.  It is very important to teach the students how to subtract across zeros because this is a skill that they will use in their every day lives.  This lesson aligns with 4.NBT.B4 because the students fluently subtract multi-digit whole numbers using the standard algorithm.

I begin the lesson by setting up a scenario for the students to solve.  "Mr. Reed owns 500 books.  He donates 217 books to the school library.  How many books does Mr. Reed have left?"  I give the students a minute to think about the question.  "What operation will we use to solve this problem?"  The students tell me that we will subtract because Mr. Reed is giving something away.  "Let's work together to find the answer."

## Direct Instruction

10 minutes

I call my students to the carpet as we work on this lesson.  I like for my students to be in close range of me as I am teaching from the Smart board.  This gives me a chance to make sure that they are staying focused and participating in the lesson.

The word problem is written on the board.

Mr. Reed owns 500 books.  He donates 217 books to the school library.  How many books does Mr. Reed have left?

I remind the students of why this is a subtraction problem.  Mr. Reed is giving something away and it is not a repeating number, therfore, we subtract.  Also, I remind the students that when we subtract, we line the numbers up according to place value.

Because we have worked in previous lessons using place value blocks, the students should understand the concept of regrouping.

I explain to the students that they have to regroup from the hundreds place because the ones place and tens place both have zero.  The hundreds place becomes a 4, and the tens place now becomes 10.  There is still nothing in the ones place.  Now, we can regroup from the tens place.  The 10 becomes a 9 and the ones place becomes a 10.  I ask the students to explain why there is a 10 in the ones place instead of a 1.  They should be able to tell me that the 1 was worth 10 because each place is 10 times larger the place to the right.  Subtract the problem on the board for the students to see.

10 ones - 7 ones = 3 ones.

9 tens - 1 tens = 8 tens

4 hundreds - 2 hundreds = 2 hundreds

The answer to this subtraction problem is 283.  Check the subtraction problem with the inverse operation of addition.

Possible Misconceptions:

1.  Regrouping without taking 1 away from the number to the left

2.  Subtracting from the bottom when the top number is smaller

Guiding questions to help with misconceptions:

1.  How did your number go up by 10?  Where did you get the 10?  Did you cross out the number to the left before you added the 10?

2.  Which place do we start with when we subtract?  Do we subtract from the top number from the bottom number or bottom number from the top number?  How did you subtract your problem?

## Group or Partner Activity

20 minutes

To give the students practice, I let them work as pairs.  This keeps the group small enough so that all students will be heard.  In order to make the lesson more interesting, the students pull numbers from a bag in order to create their subtraction problems.  The students take turns pulling two numbers from the bag to subtract.  It would be easy to write out the numbers for the students, but this gives the students a feeling of playing a game.  Students love to play games in math.  This is a link to the Subtract Across Zeros Number Pieces used in the activity.

Once the students have their subtraction problem, they can begin to solve it.  After they have worked the problem and checked it with addition, their partner should check their work to make sure it is correct.  The students switch roles to give the other person a chance to solve a problem.

I walk around to monitor the activity.  Guiding questions are asked to help lead the students through the process of the skill.  Students having difficulty by the end of the lesson are identified for remediation. The next day, I pull those students in a small group at the beginning of class while the other students are working on their "do now."

## Independent Activity

10 minutes

After the students complete their activity in pairs, I give them an independent assignment.  This allows me to monitor all students to see if they have mastered the skill.  The students use paper and pencil to solve this problem.

The following problem is displayed on the Smart Board (Independent Assignment Subtracting Across Zeros):

400 students attended our school last year.  This year there are 123 fewer students at our school.  How many students are at our school this year?

Findings:

Subtracting across zeros is a difficult skill for students.  I was not surprised that some of the students struggled with the skill.  This is evident in this sample of student work that is not correct:  Incorrect Answer for Student Work - Subtracting Across Zeros.  This student did not regroup correctly.  Therefore, the answer is incorrect.  Any students making similar mistakes will be grouped together for more practice.  The place value blocks will be used to give them that conceptual understanding of exchanging hundreds for tens, and tens for ones.

## Closure

10 minutes

To close the lesson, I bring all the students back together as a whole to discuss the problem.  I have a student share his/her answer.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the student's work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during student independent and partner sharing will be addressed whole class.