Reflection: Exit Tickets Representing Fraction Multiplication Day 2 - Section 4: Closure and Ticket to Go


I collected the tickets to go to see what students understood about fraction multiplication and what gaps in understanding they had.  I corrected the tickets to go and grouped them in the following way:

Novice: Unit 4.8 Novice.jpg

These students were able to accurately use the shortcut for fraction multiplication.  They struggled to create rectangular models for these problems.  This tells me that although they know the procedure, they do not really understand what is going on when you multiply fractions.  This particular student looks like he created the models after he figured out the answer.  Instead of shading the factors (one vertical and one horizontal) he creates 30ths and shades three rows.  For problem 2, he was able to shade 2/3 and create columns of sevenths, but he did not shade 2/7.  He needs more practice and instruction on how to create rectangular models and how they connect to multiplication problems.

Approaching Mastery: Unit 4.8 Approaching Mastery.jpg

These students were able to use the shortcut to multiply the fractions.  They also created models to show the fraction multiplication.  These students made at least one mistake with their model.  This student in particular created a model of ½ x 2/5, instead of ½ x 3/5.  Her answer is 3/10, which shows me that she can use the shortcut, but that she didn’t check to make sure that her model showed the same answer. These students were also able to identify that problem 4 represents ¾ x 1/3 = 3/12 or ¼.

Proficient: Unit 4.8 Proficient.jpg

These students were able to create accurate rectangular models of the fraction multiplication problems.  They were also able to use the shortcut to verify their answer.  For problem 4, these students were able to recognize that the rectangle showed 1/3 x ¾ = 3/12 or ¼. 

For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work.  Nearly all of the students were able to accurately use the shortcut.  Most students were able to create accurate models using rectangles.  I plan on returning these ticket to gos to students to that they can compare and analyze their work.  I plan on showing students rectangular models and asking them to determine the factors and the product.  I also want students to be able to come up with a word problem that matches the situation.  For example, if my model shows ½ x ¾, a story could be that I took home ½ of the math quizzes to grade over the weekend.  Over the weekend I only graded ¾ of the quizzes I had.  What fraction of all of the quizzes did I grade?  This will help the Novice and Approaching Mastery students to develop understanding about what is going on and how to model it.

  Exit Tickets: Modeling Fraction Multiplication
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Representing Fraction Multiplication Day 2

Unit 4: Fraction Operations
Lesson 9 of 19

Objective: SWBAT: • Create an estimate of a fraction multiplication problem. • Multiply fractions using visual models. • Develop a strategy for multiplying fractions without a diagram.

Big Idea: What does it mean when you multiply fractions? How can you multiply fractions without drawing a diagram? Students build on their skills for multiplying fractions and they work to develop an algorithm.

  Print Lesson
Math, Number Sense and Operations, multiplying fractions, 6th grade, master teacher project, area model
  60 minutes
unit 4 8 image
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