Subtracting Mixed Numbers

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Students will be able to use models and computational skills to subtract mixed numbers.

Big Idea

Given a set of mixed fractions students will be able to subtract the fractional parts and then subtract the whole number parts.


10 minutes

Material: Fraction strips.pdf

Fraction Pad

I use an interactive pad to demonstrate. 

Generally when students enter into the room there is a review question posted on the board.  However, today I want to focus on subtracting mixed numbers.

We have already been working on the concept of relationships between addition and subtraction using whole numbers.

I start this lesson by having them subtract fractions with the same denominator.

For example:  I ask students to subtract 5/6 from 17/6

As students hurry to be the first one to answer the given problem, I circle the room to see if students are using various ways to solve the given problem.  For instance, one student compute the sums of whole numbers and fractions, by representing the whole number as an equivalent fraction with the same denominator as the fraction.    Another student add mixed numbers with like denominators by converting a mixed number to a fraction. Some students may need to see and feel how wholes are different from fractions. I use fraction strips to show the whole verses a fraction. Then I write two mixed fractions on the board and ask student volunteers to represent the mixed fraction using the fraction strips. Visual support is very important , so that students can examine the structure of a given fraction.

 I tell students it does not matter how they solve a problem, as long as they can determine how and why they got their answer.   

Mathematical Practices:

 MP.2. Reason abstractly and quantitatively.

MP.5. Use appropriate tools strategically.

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

Model and Guide

20 minutes

Because I am moving students forward in understanding how to subtract mixed numbers, I want them to focus on how to formulate a method for subtracting mixed numbers on their own.  To do this, I ask students how you can subtract mixed numbers.  I want to see if they can problem solve on their own, however, it is not necessary for them to do so at this point in the lesson.  I just want to know that they know so far.

I tell students we know how to add mixed numbers.  Today we are going to apply what we have learned so far to learn how to subtract mixed numbers. 

Connecting to real experiences:

If students can think of a ways they might have used subtracting mix numbers it makes it easier for them to understand, so I ask students can you think of a way you may use subtracting mixed numbers everyday. 

Some students say when comparing amounts.

Because it is essential for students to have real world experience integrated into their lessons, I pose this question.

I ask students to move into their assigned groups. They were given fraction model strips, scissors, paper, pencil, and crayons to perform the given task.


Paula is walking 2 1/8 miles to her sister’s house.  She has already walked 6/8 miles.  How much father does she have to go?

Students were given about 10 minutes to solve their equation using mathematical models.  As students where working I ask them how is adding and subtracting mixed numbers similar. How is it different?

I provide struggling students with colored fraction rods and graph paper. It is easier for them to use the line on graph paper to illustrate the given fraction, or use fraction rods.

Color Fraction Rods.pdf  graph paper.pdf

Students tend to add or subtract the whole numbers first and then work with the fractions using the same strategies they have applied to problems that contained only fractions.   Because it is essential for students to have numerous experiences with adding and subtracting mixed numbers.  It is important for them to practice on converting mixed numbers so that the numerator is equal to or greater than the denominator. At this point I want students to work with this skill until they are comfortable enough to explain how and why they got their answer.  If the desire goal is not met I will repeat this step by modeling and explaining.

Independent Closing

20 minutes

I ask students to return to their assigned seats to begin working on subtracting mixed numbers on their own.  I call students' attention to how visual learning allows them to see the process of subtracting mixed numbers. 

Because students have explored several types of models, I want to see if the number line would be something additional they can use to support them in their learning.

I tell students they can use a number line to replace mixed numbers with the nearest one-half or whole unit.  I demonstrate the use of the number line and allow the students to choose whatever model they feel comfortable with to help them solve the given set of equations.  I remind them that renaming whole numbers with equivalent fractions should be done when subtracting larger fractions from smaller fractions.  I try to make sure they understand that when you begin to experience difficulty determining your answer, you can try breaking the problem down into smaller steps.  I also, tell students to check for reasonableness.

As students are working, I circle the room to check understanding. For instance I ask the following questions:

 How would you describe the problem in your own words?

Can you explain what you have done so far?

What did you notice?

Does this make sense? Explain?

 Students offer up several ways to solve. They are also beginning to explain their own thinking for they solution they found.

I give students about twenty minutes or so to solve the given set of equations.  After that, I invite student volunteers to share with the class how and why they solved their given set of equations.

Student Sample