Carla Seeger AF Amistad Academy Middle School, NEW HAVEN, CT
6th Grade Math : Unit #1 - Number Sense : Lesson #15

Adding and Subtracting Decimals

Objective: SWBAT add and subtract decimal numbers using the standard algorithm.
Standards: 6.NS.B.3 MP1 MP2 MP4 MP5 MP6
Subject(s): Math
60 minutes
1 Think About It - 7 minutes

To start the lesson, I ask students to share where they've seen decimals in the real world.  Students might say shopping at the store, measuring precisely, distances on road signs, etc.

Students then complete the Think About It problem with their partners.  Students previously worked with decimals in 5th grade (5.NBT.B.7), so they are able to quickly make sense of and complete this problem. 

2 Intro to New Material - 15 minutes

To begin the Intro to new Material section, I guide students to complete the notes at the bottom of the Think About It problem page: To add and subtract decimals, we line up the numbers by place value, just like we do with whole numbers. 

We then work through the examples together.  In addition to practicing adding and subtracting decimal numbers, this lesson gives students an opportunity to strengthen their skills with annotation and representing problems using bar models (these exemplars for the exit ticket illustrate all of components of completed problems).

The steps that students follow to solve problems:

1)      Read and annotate the problem.

2)      If necessary, represent the problem using a bar model.

3)      Decide the operation and write out the number sentence.

4)      Estimate the sum or difference by rewriting the numbers to the side, rounding, and then adding or subtracting.

5)      Line up both numbers by place value. 

6)      If necessary, annex 0’s.

7)      Add or subtract.  Write answer using units. 

8)      Check by comparing to the estimate. 


3 Partner Practice - 15 minutes

Students work in pairs on the Partner Practice problem set.  As they work, I circulate around the room and check in with each group.  I am looking for:

  • Are students explaining their thinking to their partner?
  • Are students annotating the problems?
  • Are students estimating first?
  • Are students representing the problems with bar models?
  • Are students lining up numbers correctly by place value?
  • Are students answering the problems in complete sentences?


I am asking:

  • Explain you determined this answer. 
  • Explain your bar model.
  • How did you know how to line up the numbers to subtract? 
  • How did you check your answer with estimation? 


After 10 minutes of partner practice time, I ask a student to present his/her work to the class on the problem of his/her choice.

Students then complete the check for understanding problem independently. 


4 Independent Practice - 15 minutes

Students work on the Independent Practice problem set.  While they're working, the Steps for Finding Sums and Differences of Decimals are displayed on the document camera, for students' reference.

As students work, I am circulating around the room and making sure that students have not only found the correct sums or differences, but also have annotated the problems, created accurate bar models, and have answered the questions with full sentences.  

Tracking Independent Work
Organizational Systems

During independent practice, I carry around my Circulation Tracker to help me keep track of information that's important to me.  

Each day, I make note of the standard that is the focus of the lesson.  I save the trackers, and writing the standard makes it easy for me to file and reference later, as I am thinking about review and reteach.

I pick a problem from the independent practice to focus on during my circulation.  At the bottom of this sheet, I make myself notes about what to look for. This list contains what I want all students to do (annotation, line up the decimals, etc) and also common errors that I want to keep in the forefront of my mind.  

In the left hand column are the names of my classes (Fairfield, Miami, UConn) - I use the same sheet all day.

I keep quick tally marks for whether or not each student completed the problem correctly.  I can compare this with exit ticket data to get a sense of how student mastery progressed over the course of the lesson.

The next section is for exemplary work.  I make note of problems that look great, so that I can show the student work on doc cam for the class to see.  This gives me a chance to recognize great work, and also allows the rest of the class to see examples of exemplary work.

The 'Cycle Back' column is where I make quick notes about students who need to re-do a problem or who made a mistake that I want to be sure gets fixed (ex - in this lesson, if a student isn't lining up the decimals, I'll help them fix the mistake, and then I want to be sure that I check to see that this error isn't happening when I come back a second time).

Finally, I make note of students who are working with urgency.  This is something I've been focusing on in my classroom, and I am giving lots of praise and feedback to kids about it.  This last column can change throughout the year, if there is a focus area I want to track or gather data on.

5 Closing and Exit Ticket - 8 minutes

After independent work time, I have students turn to their partners and share their answers to Problem 5 with one another.  They adjust their responses based on their conversation.

Students then complete the Exit Ticket independently to close the lesson.  This exemplar illustrates what student work can look like.