Multiplying Mixed Numbers

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SWBAT solving problems involving the multiplication of mixed numbers.

Big Idea

Students apply many skills as solving problems with fractions become more complex.

Small group warm-up

15 minutes

Students work in small groups to solve three word problems from the book.  These word problems involve both adding and multiplying mixed numbers.  Students have worked with multiplying fractions and also mixed numbers, but they have not yet multiplied mixed numbers.  Without prior instruction, students work to make sense of these problems and persevere in solving them (MP1).  

I have selected these problems because they incorporate multiple operations, are multiple step, and are relevant to students' lives.

Before they get started, I post a list (from a previous lesson) of fraction skills they have already learned. Together, we review the list and the idea that these skills build on one another.  Many skills are often needed to solve one problem.

I intentionally did not directly instruct students to change mixed numbers into improper fractions before solving a multiplication problem.  I want them to discover that this is the most effective and efficient way, but that it is not the only way.  I also want students to learn from their mistakes.

Note: Many groups will multiply whole numbers then multiply fractions and add them together.  It is important to be prepared to show them how/why this doesn't work.  (They are only finding two of the partial products.)  Connecting this to whole numbers can help make this clear.

Group Share

5 minutes

Students share their strategies for solving the warm-up challenges using the focus question:

• What strategy did you use? And why did you choose to solve the problem this way?

Some students will use what they know to solve this problem.  They will change mixed numbers into improper fractions and then solve by multiplying fractions.

Other students will create their own approach.  It is likely that they will multiply the whole numbers and then multiply the fractions.  This will result in a correct partial product, but not the correct product.  For me, at this point in the lesson, it is ok for students to make this mistake.  I will use this mistake as a teaching tool to help students understand how to use multiplication to get the correct answer.  

It will be my goal to have students choose the strategy of making improper fractions then multiplying, however, if they choose to find all partial products and add, that is ok too.

Skill Based Practice

15 minutes

Students practice solving problems involving multiplying fractions.  They may choose 2/3 of six problems in the text book.  To solve with a partner and then check their work. 

Note:  When multiplying mixed numbers, the problems can get very large.  This becomes an exercise in multiplication and division too.  For students who have trouble with solving problems when there are many steps.  It is important to keep this in mind.  After this point, revisiting "simplify before you solve" might be beneficial because students will have more motivation to try.

Ticket Out

5 minutes

You're the teacher, correct my work.

For this ticket out, I put a problem on the board and solve it incorrectly.  I ask students to correct my work.  I use this ticket out to group students for intervention groups at the start of class tomorrow.

See screen capture of ticket out and student work.