Modeling Addition and Subtraction of Mixed Numbers

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Students will be able to use mathematical models to add and subtract mixed numbers.

Big Idea

Given a set of mixed fractions students will be able to show different ways of adding and subtracting mixed numbers using models.


7 minutes

To begin this lesson I display a situation that involves the addition and subtraction of unlike denominators.  I use student names from my class to make it more entertaining.  For example, Nicole bought 5/6 of a pound of chocolate and Tim bought ½ of a pound of fudge.  I record both fractions on the board in large print.  I ask students, "Who bought more chocolate Nicole or Tim? How do you know?"   I students that we are going to figure out how much fudge they have altogether.  I ask them if we would use addition, subtraction, multiplication or division and why?  


Some students may have difficultly understanding this process, so I will show a visual fraction strip that models this concept.

It’s ok if students are not able to answer, however, what I intend to do is basically check to see how much prior knowledge they have on adding and subtracting fractions.


Mathematical Practices:

 MP.1. Make sense of problems and persevere in solving them.

 MP.2. Reason abstractly and quantitatively.

 MP.5. Use appropriate tools strategically.

 MP. 8. Look for and express regularity in repeated reasoning.

Fraction Pad



Modeling and Guiding

20 minutes

Material:   Fraction Pies.pdf

This activity will be done in their assigned groups. 

Because I want students to be able to model adding mixed numbers using illustrations or fraction strips, I focus their attention to the following question: 

How do you use models to add mixed number?

To do this, students are given fraction strips, paper, pencils, and crayons.  


I ask students to describe and explain some of the mathematical models they have used while learning different aspects of fractions. 

 Student’s response may include:

Fraction strips, fraction circles, rectangles divided into equal parts etc… 

After that, I pose the following word problem to see if students can use what they have already learned to add and subtract mixed numbers.  

Shirley is cutting slices of pizza into fourths.  She needs to wrap up 3 ¾ pizzas to take to Kim’s party, and 1 2/4 pizza to the school’s Fall Carnival.  How many pizzas does Shirley need to wrap in all for the party and the Fall Carnival? 

As students are working I ask which strips they will need to model the problem. What should you model first? How can you add mixed numbers without renaming first? 


Some students talk about grouping the whole numbers to perform decomposing. They seem to be pulling from prior experience of grouping like terms.  I allow students to work in their groups for about 7-8 mins.  After that, I ask a couple of student volunteers to share out loud I encourage students to ask questions. Some students are responding well, however, their responses are a bit vague. I decide to model how they should explain their answers mathematically.

Teacher’s Model:

  First, I choose the fractions that display one whole and fourths.

Then, I model each mixed number from the problem.  After that, I find the sum by combining the fourths and combining the ones separately.  I write the new fraction on the board 4 5/4.  I tell students that there should not be a whole number and an improper fraction in a mixed number.  Teacher's Model.

Even though, some students were unable to understand when I gave them a group task, most or all of them gained a deeper understanding after I have modeled/demonstrated how to add mixed fractions.



Interactive Learning!

10 minutes

In this interactive lesson, students are able to see how models are used to add and subtract mixed fractions. I ask students to take notes throughout the video. note taking paper.pdf It is equally important that students are provided various ways to experience new skills. Throughout the lesson I will ask the following questions to check for understanding:

How do you know?

Can you demonstrate for me?

Did anyone come up with another way to solve? Explain?

I want students to explore the structure within each problem and become better mental problem-solvers! 

Student Response:

Students are noticing patterns, and they are using good reasoning skills to explain how they solved the problems.



Independent Closing

20 minutes

I remind students that when adding fractions they may need to trade some fractions for wholes, and for subtracting they may need to trade wholes for fractional pieces.  If students are having a difficult time renaming fractions, I demonstrate how to add.

1 2/5 + 4 1/5, where the fractional part is already in simplest form.  This will help them get a clear understanding of how this process varies depending on the form of the fraction.  

I will continue to remind students that renaming their fractions before writing their final answer is critical to getting the right answer. 

After students have reached a level of understanding, I allow them about 20 minutes or so to work on their assignment.  The students have to model subtraction and addition of mixed numbers. 

Finally, to sum up this entire lesson I invite students to share their work with the entire class.  I ask them to show off their mathematical models and explain how and why they choose to solve the problem with their problem-solving method.

 Student Sample