Subtracting Mixed Numbers

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SWBAT subtract mixed numbers by drawing models and thinking about the relationship between addition and subtraction.

Big Idea

Students can use models to validate their answers to their subtraction problems of mixed numbers with like denominators.

Whole Class Discussion

15 minutes

In today's lesson, the students learn to subtract mixed numbers with like denominators.  This relates to 4.NF.B3c because the students subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

To begin the lesson, I remind the students that yesterday we learned to add mixed numbers with like denominators.  Today, we will learn to subtract mixed numbers with like denominators.  We talked about a mixed number.  I ask for someone to remind of the definition of a mixed number.  Student response:  A mixed number has a whole number and a fraction.  Together, I have the students repeat the definition of a mixed number.  (By having all of the students do a choral response, it ensures me that the students are all paying attention to this important information.)  We are working with like denominators again today.  I ask, "What are like denominators?"  Student response:  When the denominators are the same number.  

On the Smartboard, I display a problem:

A container can hold 8 3/10 cups of sugar.  There are 4 1/10 cups of sugar already in the container.  How much more sugar can fit into the container?

 After I read the problem aloud to the students, I ask the students to tell me what operation we are going to use to solve this problem.  Student response:  subtraction.  I like for all of my students to be able to justify their answers.  Therefore, I ask this student to tell me how he knows that the operation is subtraction. He tells me that the problem says "how much more."  

The students work through this problem on their own paper, as I work it out on the board.  8 3/10 - 4 1/10.  Because we have like denominators, we can go ahead and subtract. I tell the students to begin subtracting the fractions.  3/10 - 1/10 = 2/10.  Next, we subtract 8 - 4 = 4.  Our mixed number is 4 2/10.  I remind the students to simplify their answers.  To simplify, the students list the factors of 2 and 10.  The factors of 2 are 1 and 2.  The factors of 10 are 1, 2, 5, and 10.  The students know that we should divide by 2/2.  The simplfied answer is 4 1/5.   

To give the students a visual (a more conceptual understanding), they draw out the top fraction of 8 3/10.  (I model this on the board, as the students draw the mixed number on their paper.)  We draw a total of 9 rectangles on the board (8 whole and an additional rectangle for the fraction.)  The students divide each rectangle into 10 pieces to represent the denominator.  (We discuss the fact that 10 is an even number, therefore, the rectangle can be divided in half first.  This makes it easier to divide the shape into 10 even pieces.)  The students shade 8 whole rectangles.  In the last rectangle, they shade 3 out of 10.  

To show that 4 1/10 were subtracted, the students mark out 4 whole rectangles.  Then, the students mark out 1/10 to represent the fraction.  To check the answer, the students count the remaining pieces that were not marked out.  There were 4 2/10 pieces not marked out.  


Skill Building/Exploration

20 minutes

For this activity, I let the students work independently.  I give each student a Subtracting Mixed Numbers with Like Denominators.docx activity sheet.  The students must subtract mixed numbers with like denominators and draw a model to validate their answer (MP4).  

The students work on real-world scenarios to subtract mixed numbers with like denominators.  The students are guided to the conceptual understanding through questioning by me.  As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students.  Any misconceptions are addressed at that point, as well as whole class at the end of the activity.


1. How many pieces will you divide the whole into?

2. Does your model validate your answer? How?

3. Which mixed number represents the total in the problem?

Any student that finishes the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing:

 My Findings:

In today's lesson, the students learned to subtract mixed numbers, then validate their answers by drawing a model.  As I monitored and answered questions from the students, I noticed that a few of the students were drawing models that were connected.  I spoke with those students about drawing models that show separate "wholes."  To make it clear, I used the example of baking cakes.  If I baked 10 cakes, they would not all be connected to each other.  They would be in their own separate pans.  I worked with these students and feel confident that they finally understand. 

 Overall, the students understood how to draw a model for the first mixed number, then "x" out the second mixed number.  They knew that whatever was left was a representation of their answer.


15 minutes

To close the lesson, we review the answers to the problems as a whole class.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' 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 ( Student Work 1 and Student Work 2).  From the Video - Subtracting Mixed Numbers with Like Denominators, you can hear a student explain how she solved a problem.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the activity will be addressed whole class.  


-Drawing models correctly (as stated earlier)