Representing Fraction Multiplication

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Objective

SWBAT: • Multiply fractions using visual models.

Big Idea

Riley has only completed one-third of her part of the mural. How can you find 1/3 of 1/2? Students extend their understanding of multiplication to fractions and area models.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to remember the work that they did creating equivalent expressions and area models.  They will be using area models to model fraction multiplication. 

Students participate in a Think Pair Share.  I call on students to share out their thinking. I put a couple students’ work under the document camera to show how they approached the problem.  Some students may have written a version of 3 x 4 + 3 x 5.  Other students may have written a version of 3 (4 + 5).  Another possibility is that students first added 4 + 5 and then multiplied 9 x 3 to get 27 square units.

Mural Madness

25 minutes

Notes:

  • I use the data from the ticket to go from the Fractions Pretest to Create Homogeneous Groups  Students will work in groups of 2-3.
  • Each student will need a Mural Madness Resource Page.  I have extra copies ready for students who want to start over.

I have students move to their groups.  I ask students to share out what they know about murals and what they think the benefit is for creating them.  I have a volunteer read the information on the page.  I review expectations and I tell students that their first job is to talk together to make sure they understand the task.  Group members participate in a Group Members ConsultOnce all group members understand the task, a group member raises his/her hand.  I come to the group and ask a student of my choosing to explain the task.  If this group member successfully describes the task, I give them the Group Work Rubric and copies of the Mural Madness Resource Page.  If the student cannot adequately explain the task, I tell them to continue to talk and make sure everyone is familiar with the task and I tell them I will come back.

As students work I walk around and monitor student progress and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP5: Use appropriate tools strategically.

I encourage students to draw their ideas on their own paper to help them communicate with their group members.  I ask groups, “How many parts can we break the whole mural into so that we can easily show each person’s portion?”  I want students to recognize that they can create fractions with the common denominator of 6 to show each student’s portion. 

Some students may try counting the parts out of 324, since the grid is 18 units by 18 units.  If I see this, I ask them to flip over their resource page and make a quick sketch of Riley’s portion.  Then I ask them to quickly sketch a separate diagram for Morgan and Reggie’s portions.   I ask, “How can we show all of these portions on one drawing?”

If groups successfully complete the task, I have them play “Score the Difference”.  Students need copies of the directions, worksheet, and dice.

With about 8 minutes remaining, we come together as a class.  I have one person from each group come to the document camera and explain their group’s strategy.  I emphasize that students must use precise language to describe their thinking (MP6: Attend to precision).  I give students the opportunity to give feedback, make connections, or ask questions about each other’s work.  I want students to see the various models and how they helped students answer the questions.

Practice

20 minutes

I pass out colored pencils to students.  Each student needs two colored pencils.  We work on problems 1 and 2 together.  I want students to connect finding a portion of a portion to finding the area of a portion that has dimensions that are less than 1 unit.

If students struggle with problem 1, I may ask:

  • What represents the whole in the diagram?
  • What does the lightly shaded portion represent?
  • What does the darkly shaded portion represent?
  • Look back at the Mural Madness problem, whose work does this diagram represent?  How do you know?
  • What is the multiplication problem that is represented? 
  • What is the product?  Can you simplify your answer?

For the different parts of problem 2, I create word problems that match the situation.  I ask students which square would help us model the problem.  We create the model and talk about what the product is telling us.  I ask questions about how the product relates to each of the factors and whether or not that makes sense.

Then I ask groups to talk about how our models in problem 2 could help them with the mural problem.  For the rest of the time, students work with their groups on the mural problem.

If students successfully complete their work, they can play “Score the Difference”.

 

Closure and Ticket to Go

10 minutes

 For Closure I show students the closure diagram and I ask them what problem this represents.  Students participate in Think Pair Share.  I call on students to share and support their ideas.  I ask students, “What is the product?”  Some students may say two-twelfths, while other students may say one-sixth.  I ask students, “Which answer is correct?”  I want students to recognize that the answers are equivalent, and therefore both are correct.  I encourage students to simplify their answers when they can.

I pass out the Ticket to Go.  Then I pass out the HW Representing Fraction Multiplication.