Fractions Divided by Whole Numbers Using Models

Students work in pairs on the Think About It problem.  After three minutes of work time, I bring the class together for a conversation.

It's likely that students are able to come up with the number sentence for this problem.  The visual model might be more difficult for students, and that's okay!  This problem is intended to get kids thinking about the content of this lesson.

I ask students to articulate what information we know from this problem, and what information we're being asked to find.  I also ask students if they expect each person's share to be more than or less than 1/2.  This is a key question in this conversation - I want students anticipating  the quotient size before they determine the answer.  

In this lesson, we'll use visual models to find the quotients, when dividing fractions by whole numbers.

To start the Intro to New Material section, I ask students to read the first problem and identify what we know and what we're being asked to find out. For this problem, I have students construct a rectangle model.

In this short video, I model how to construct  a rectangle model to represent fractions divided by whole numbers:

For Problem B, I have students construct a number line model.  You can see the process in this short clip:

 Throughout the lesson, students have access to these Model Steps.   I project the steps on the document camera as students work in partners and independently later in the lesson.  I project it on the document camera, and it can also be given to students in hard copy.

Students work in pairs on the Partner Practice problem set.

At this point in the year, students are still learning the many different ways they can work in partners.  For this partner practice, I set a timer for 5 minutes.  During this first 5 minutes, students work independently on the start of the partner practice set.  When the timer goes off, they turn to their partner.  They can compare answers, ask questions, and give feedback on the work product.  They can then decide whether to work independently on the next problem(s) or work together in real-time.  I want students to have choice around the work style that will work best for them as learners.  

As students work together, I circulate around the room and check in with each group.  I am looking for: 

• Are students drawing a visual model that represents the problem?
• Is the model neat and organized?
• Are students trying to use both number line and rectangle models?
• Are students writing a number sentence to solve the problem?
• Are students finding the correct quotient? 
• Are students checking using multiplication? 

I'm asking:

• How did you know to draw the visual like this?
• What does your quotient mean?  Why did the denominator change?
• (before the problem is done) Will your quotient be bigger or smaller than the dividend?  Why? 
• Can you show this using the (other) visual?
• How did you know how many groups to split the quotient into? 

Students work on the Independent Practice problem set.

Much like in the previous lesson, if I notice a student is using all of one type of visual representation, I'll ask her to try the other model for the next problem.  I want students to be fluent in both rectangle and number line models.  

After about 5 minutes of independent work time, I'll display one student's work on the document camera for the class to see.  I don't stop the class from working, but I'll highlight something about the displayed work.  I might say something like 'I see many of you are using rectangle models.  If you want to check out a strong number line model, look at XX's model for problem number 2.'  The resource will be there for students to reference.  Then, as I continue to circulate, I can reference the model myself.  If I see a student make a mistake, I'll ask him/her to compare his/her model with the one of the board.  Or, I can use it to encourage students to try the number line model.

After independent work time, I bring the class back together for a discussion about the work.  First, I ask students to turn to their partners and share out the real world scenarios they wrote for Problem 9.  I'll ask the class to raise a hand if their partner had a great scenario, and then will have 2-3 students share their problems out with the class.  Asking partners to volunteer their peers' strong work helps to build community.

I will then cold call on a student, using my popscicle sticks, to share his/her model for problem 10.  I'll also ask for a volunteer to share the other model with the class (so, if the cold-called student used a number line, I'll ask for a volunteer to share the rectangle model and vice versa).

Students then work on the Exit Ticket independently to close the lesson.