Multiplying Fractions to Find Area

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SWBAT find area of various rectangles with sides having fractional measurements.

Big Idea

Students practice multiplying mixed numbers for the purpose of finding area.


10 minutes

Today's lesson continues practice of multiplying mixed numbers.  To add variety, context, and purpose, this lesson asks students to find the area of rectangles (when the side lengths are mixed numbers).  

Students use rulers to estimate the area of their desks to the nearest whole inch.  I ask the students to estimate because the purpose of the warm-up is to review the concept of area (not measuring to a fraction of an inch).  

Student share their measurements and a few possible estimates are recorded on the board.  

After the warm-up, students are presented with the question of the day: 

How would we find the area of the desk if we were not estimating?

During the lesson, students practice finding area of various rectangles with side lengths that are mixed numbers. 

Guided Practice

15 minutes

Students have worked with multiplying mixed numbers.  It is important to allow time for additional practice because there are many steps to solve just one mixed number multiplication problem.  Although the students have developed strong fraction stills throughout the unit, they need time to practice linking these skills together to solve problems involving the multiplication of mixed numbers.  Today, I encourage students to simplify before solving so they can work with smaller numbers when converting fractions to mixed numbers.

We solve two problems together (I choose easy numbers) that demonstrate various situations where simplifying before solving (cross canceling) can be modeled:

• 2 and 1/2 x 2/3

• 35/4 x 2/5 

For students who struggle with the many steps to solving a multiplication with mixed numbers problem, I allow a calculator for converting.  I ask them to earn this tool by showing they can do one problem without it.  Then I let them use the calculator so they can practice solving more problems and develop automaticity. 

Independent Practice

30 minutes

Students work in pairs to find the area of various rectangles.  This resource came from the text book as an enrichment activity.  The text book lesson for finding area had rectangles with side lengths that were less than one.  To increase the rigor of the lesson and add challenge for the students, I used the enrichment portion of the lesson.  

This provides students with additional practice of multiplying mixed numbers as well as a review of finding area.  I communicate to students that although the publishers of the text book believe this is an enrichment activity, I know all students in this class are more than capable.  Maintaining high expectations for all students increases motivation and effort.  

I circulate from group to group answering questions and checking student progress.  Attached are some clips of common errors that students made.  Working in pairs can surface these errors more quickly than when students work alone.  

Ticket Out

5 minutes

To wrap up todays' lesson I post the actual dimensions of the students' desks on the board. Students work to find the area.  

In this case, since the numbers are not controlled, the problem is more challenging because the numbers are larger.  I encourage students to persevere and give it a try.