Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a.  Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b.  Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c.  Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

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Students are able to… 

  • Use models and pictures when solving problems involving division of a whole number by a unit fraction.
  • Communicate how they solved the problem using pictures, models, words, and numbers.
  • Make connections between visual representations and writing division equations.
  • Ask themselves questions to relate that actions in the problem to the written equation. For example, “How many groups of ¼ can I make out of 2 wholes?”
  • Make connections between multiplication with fractions and division with fractions.
  • Seek patterns and make generalizations regarding the multiplication and division of fractions.

Students are able to…because teachers:

  • Connect the measurement model of division of whole numbers to dividing a whole number by a fraction.
  • Provide students with problem situations for students to model dividing a whole number by a unit fraction.
  • Facilitate discussions helping students to make connections between a student’s work and written equations.
  • Model questions students can ask themselves when solving problems such as “How many groups of ¼ can I make out of 2?” Relate this question to a visual model.
  • Highlight patterns found by students in written equations regarding the relationship between multiplication and division of whole numbers by unit fractions.

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Questions to ask students:

  • Create a story for the problem 4 ÷ ½
    • Sample answer that indicates understanding: I swam 4 laps in a pool. Every ½ lap, I paused to take a big breath. How many times did I pause to take a big breath? I need to find how many groups of ½ are in 4 so I can divide 4 by ½ to get 8.
    • Sample answer that indicates an incomplete understanding or a misconception: I have 4 quarts of juice and divide them in half to share it with my friend.
  • What connections do you see between 3 ÷ ¼ = _____ and ¼ x ____ = 3?
    • Sample answer that indicates understanding: Since multiplication and division are inverse operations, then the quotient of 3 ÷ ¼ will be the factor to multiply by ¼ to equal 3.
    • Sample answer that indicates an incomplete understanding or a misconception: They both have a 3 and a ¼ in them and a missing part.

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FSA Notes

Cognitive Complexity Level: Level 2: Basic Application of Skills & Concepts

Achievement Level Descriptors:

Level 2: Intentionally Left Blank

Level 3: solves real-world or mathematical problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, using visual fraction models and equations to represent the problem

Level 4: creates real-world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions

Level 5: Intentionally Left Blank

Context: Allowable

 

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Additional Resources:

Additional in depth content knowledge:

http://www.katm.org/flipbooks/5%20FlipBook%20Final%20CCSS%202014.pdf#page=57

Video: Divide whole numbers by a unit fraction

https://learnzillion.com/lesson_plans/7994-divide-whole-numbers-by-unit-fractions-using-a-model

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Sample Formative Assessment Tasks: (Click to make task image larger)

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[divider] [/divider] Resources/Tasks to Support Your Child at Home:

 

  • A baker has 6 small bags of flour. Each bag weighs 1 pound. She divides each bag into thirds. How many – pound bags of flour does the baker have?

 

  • Create a story context for 4 ÷ 1/3  and use a visual model to show the quotient.