Reflection: Exit Tickets Dividing Whole Numbers by Fractions - Section 5: Closure and Ticket to Go


I collected the tickets to go to see what students dividing whole numbers by fractions.  I corrected the tickets to go and grouped them in the following way:

Novice: Unit 4.12 TTG Novice.jpg

These students struggled to show the connection between multiplication and division.  Also, they struggled to model the division problem in number 2.  This particular student wrote that 3 times 1/6 equals 18 and 3 times ¼ equals 12.  This shows me that she is incorrectly applying a procedure and does not really understand the question.  If 3 times 6 equals 18, than 3 times 1/6 cannot also equal 18.  On problem 2, the model correctly shows the answer of 6, but her number sentences do not match.  I am not sure where the answer of 24 came from.  Perhaps she again incorrectly applied a procedure and multiplied 4 times 3 and then multiplied 12 by 2.  Another common mistake was to solve the problem 4 divided by 1/3 and get 12, rather than solving 4 divided by 2/3. 

This shows me that she is trying to perform shortcuts and lacks understanding of the relationship between multiplication, division, and models.

Approaching Mastery: Unit 4.12 TTG Approaching Mastery.jpg

These students have an adequate understanding of using models and the connection between multiplication and division but they made a careless mistake.  This student solved the problem 4 divided by ¼ rather than 3 divided by ¼.  She drew a model and split 4 wholes into fourths.  

Proficient: Unit 4.12 TTG Proficient.jpg

These students were able to use models and demonstrate the connection between multiplication and division. 


For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work.   Almost all students were proficient on this ticket to go.  A few students were in the approaching mastery and novice categories.  I will pass these tickets to go back so students can correct their mistakes.  I will also check in with the novice students during the next lesson.

  Exit Tickets: Connecting Multiplication and Division
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Dividing Whole Numbers by Fractions

Unit 4: Fraction Operations
Lesson 13 of 19

Objective: SWBAT: • Demonstrate the relationship between multiplication and division involving fractions. • Use visual models to divide whole numbers by fractions. • Develop strategies for dividing a whole number by a fraction.

Big Idea: What do you get when you divide 6 by 2/3? How can you connect this problem to multiplication? Students continue to make connections between multiplication and division and work to develop strategies for dividing whole numbers by fractions.

  Print Lesson
Math, Number Sense and Operations, multiplying fractions, 6th grade, master teacher project, dividing fractions
  60 minutes
unit 4 12 image
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