Dividing Mixed Numbers Algorithm

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Objective

SWBAT develop the algorithm for dividing mixed numbers.

Big Idea

How is this similar to multiplying mixed numbers?

Do Now

15 minutes

Students often have difficulty with word problems and are intimidated by them.  Students have worked on different strategies for solving word problems, such as draw a picture, highlight important information, and work backwards.  For this Do Now problem, I'm introducing a fun way of having students visualize the situation in the problem, acting it out.

I will give one group the Division Problem Acting Out.docx Worksheet and assign them roles.  They should read the problem and discuss how they will act it out.  I will explain to them that they don't have to speak during their "play", they can simply act it out with motions.  They will have 2 - 3 minutes to present their "play" for the class.

When the group is finished presenting, students will be instructed to complete the Do Now problem.

Do Now

Janna brings peanuts to be shared equally by her and her 3 friends.  If they share 1/4 pound of peanuts, how much of a pound will each student get?

After a few minutes, I will ask students to share their reasoning, work, and answers.

Did the presentation help?  How?

What operation did you use? 

Developing an Algorithm

10 minutes

Students have previously developed an algorithm for multiplying mixed numbers and dividing fractions. This lesson will rely heavily on students prior knowledge to develop an algorithm for dividing mixed numbers.

I will introduce the below example to students.

Example 1

20 ½ ¸ 2 2/3 

When we multiplied with mixed numbers, what did we do first?

  • Students should remember that we changed the mixed numbers to improper fractions.

How did we divide fractions?

  • Students have the strategy of Keep, Change, Reciprocal.

This leads us to the Dividing Mixed Numbers Algorithm.png for dividing mixed numbers.  

 I will model another example with students to ensure that they use the algorithm correctly.

Example 2

2 1/3  ¸ 1 1/3

Group Practice

20 minutes

Since students tend to miss a step when dividing mixed numbers, they will work with their group to solve the problems below.  I will encourage discussion among students and emphasize that they should "check in" with their group as they work.  For this lesson students have been grouped by math level, based on a previous assessment.

 

Students will be given 10 minutes to complete the Group Work Problems.png.  As students are working I will circulate, but focus more on the lower level math groups.

After about 10 minutes, I will randomly select students to present their work to the class.

Exit Ticket

5 minutes

To assess students' understanding of dividing mixed numbers, they will complete an exit ticket.  They will have 5 minutes to complete the problem below.  The exit tickets will be used to help me determine student groups and future lessons.

Exit Ticket

83/7 ¸ 14/5