Adding and Subtracting Mixed Numbers

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SWBAT solve problems involving the addition and subtraction of mixed numbers.

Big Idea

Regrouping fractions to whole numbers is not unlike regrouping ones to make a 10. Students use rich language as they learn the procedures for adding and subtracting mixed numbers.


5 minutes

Today's lesson will connect modeling addition and subtraction of mixed numbers with the mathematical procedure.  As a ticket out yesterday, students wrote about the similarities between subtracting mixed numbers and spending money.  They had just a few minutes to get their ideas down.  Today, I have them expand their thinking and support it with models and examples.  It is beneficial to revisit former thinking and then elaborate. 

I use the money tool from the Tools for Math program to demonstrate the connection.


10 minutes

Students solve an addition and subtraction problem that requires regrouping using the standard algorithm, then explain their thinking to a partner.

Two students will be asked to explain the procedure to the group.

This part of the lesson will transition student's thinking from regrouping ones to tens and regrouping fractions to whole numbers and vice versa.

Guided Practice

15 minutes

To start this lesson off, I model an addition and subtraction equation.  I show just the models and ask students to work in small groups to determine the equation that it represents and discuss how they know this.  

These equations model the connection between using fraction tiles to add and subtract mixed numbers and the procedures for manipulating only numbers.

When modeling the connection between the model and procedure for subtraction, I focus on regrouping. I cross out the whole number number and rewrite it as one (in fractional form) to show the regrouping process. 

I expect students to show their thinking in the same way.

Independent Practice

20 minutes

Students work in pairs to practice solving mixed number addition and subtraction problems. While working, they are expected to show their thinking as they regroup whole numbers and fractions. 

For an optional extension, I provide a worksheet from the text book that has more complex problems. These problems have multiple addends, subtrahends, and/or operations. If students choose this option, they must demonstrate an understanding by answering five from the daily assignment.

Group Share

5 minutes

Students share challenges and successes from today's task.