Review 7: Painting Tables - Dividing with Fractions

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SWBAT use models to represent dividing whole numbers by fraction, use models to represent dividing mixed numbers by fractions, determine how to interpret a remainder when dividing a whole number by a fraction.

Big Idea

How do you visually represent dividing with fractions? When you have a remainder, what does it actually mean? Students look for patterns and create algorithms for dividing with fractions.

Do Now

5 minutes

Part of my class routine is a do now at the beginning of every class.  Students walk into class and pick up the packet for the day.  They get to work quickly on the problems.  Often, I create do nows that have problems that connect to the task that students will be working on that day.  During this review unit, I have selected multiple choice questions that cover as variety of topics. 

To check the do now, I display ask a student to share what thermometers read at each city.  Then I take a poll to see who thinks that City A is colder vs. City B.  Some students may be able to correctly read the thermometers but may get confused to whether negative 3 degrees is warmer or colder than -7 degrees.  I ask a couple students to explain their thinking and push students to see that when trying to find the colder temperature, you are comparing the two temperatures.  Since -7 degrees is less than -3 degrees, City A is colder.  I go through a similar process of sharing out and explaining for #2.

I ask students to share out one thing that they wrote down on their do now that will help make today a productive math class.  I find that students enjoy sharing out these goals – it is a way for them to be held accountable by their teacher and peers.

Dividing with Fractions Review

5 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will be connecting their knowledge fractions and division to create models of division problems.  We will be working to show what to do with a remainder when we are dividing with fractions.

I have students work in partners to complete the problems on page 2.  Students can check in with the partner if they have a question, and check in and compare answers when they have completed the five questions.  I walk around to see how students are drawing the problems and whether then can identify the dividend, divisor, and quotient.  After about 5 minutes I call on students to share their thinking and answers.

I clarify any questions students have about the divisor, the dividend, and the quotient.  I explain that dividing with fractions is still finding how many of a certain-sized group (the divisor) there are within the original group (dividend).  The answer is the quotient.  I also have a couple students share and explain their pictures for the problems.  

Painting Tables

35 minutes

Closure, Ticket to Go, and Homework

15 minutes

I ask students to flip to #6 on page 5.  I ask students to share how they created the model and how they interpreted the remainder.  During the work time I selected 2 students who I want to present their work (1 student who used the common denominators method and one student who used the multiplication method.).  I have each of these students share how they wrote their number sentence and how their algorithm works.  I ask the class what each student has done well, how the student could improve their answer, and if they have any questions for the student.  See the Closure  video in my Strategy Folder for more details.

The goal is that at the end of the lesson students have the use of models, partitioning, grouping, and algorithms to make sense of their answers from visual models as well as check these answers for accuracy.  They will need more opportunities to explore different situations and continue to develop their skills in creating and interpreting models as well as using the algorithms.  Through continued exposure paired with discussions about why the model represents the problem and why the process works, students will be able to develop a deep understanding of dividing with fractions.

If you have time, have students complete the ticket to go.  See the Ticket to Go video in my Strategy Folder.  If you run out of time, collect students’ work to analyze their success with the task.