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 unit fraction by a whole number.
  • Communicate how they solved the problem using pictures, models, words, and numbers.
  • Make connections between visual representations and writing division equations.
  • 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:

  • Review the partitive division model of division with whole numbers requiring students to show their thinking with visual models.
  • Introduce students to division with fractions by starting with word problem situations and visual representations to connect division with whole numbers to division with unit fractions.
  • Provide students with problem situations for students to model dividing a unit fraction by a whole number.
  • Facilitate discussions helping students to make connections between a student’s work and written equations.
  • Highlight patterns found by students in written equations regarding the relationship between multiplication and division of unit fractions by whole numbers.

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Questions to ask students:

  • Is it always, sometimes, or never true that you divide a bigger number by a smaller number? Explain.
    • Sample answer that indicates understanding: This is sometimes true because when dividing a fraction by a whole number, like dividing by 3, results in a quotient of   so it depends on the situations. If the situation is about dividing 12 muffins among 3 people, each person will get 4 muffins. In that case, we divided the greater number by a smaller number.
    • Sample answer that indicates an incomplete understanding or a misconception: It is always true that you divide a bigger number by a smaller number because that’s what I learned about division before.
  • How do you know that the equation you wrote matches this word problem?
    • Sample answer that indicates understanding: The student is able to explain how the model or picture made matches the problem and understands the division of a unit fraction by a whole number.
    • Sample answer that indicates an incomplete understanding or a misconception: The student is unable to adequately explain how the model or picture matches the division problem.
  • How can you check your work to explain why 1/2 divided by 3 equals 1/6 ?
    • Sample answer that indicates understanding: I know that  1/2 ÷ 3 = 1/6   because 3 x 1/6 = 1/2  . Multiplication is the inverse of division.

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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

Assessment Limits: For given fractions in items, denominators are limited to 1‐20.

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

 

Videos:

https://learnzillion.com/lesson_plans/5021-divide-a-unit-fraction-by-a-whole-number

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-div-fractions-word-problems/v/dividing-a-fraction-by-a-whole-number-word-problem

 

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Sample Formative Tasks: (Click to make larger)

 

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

  • Abigail has 1/2 gallon of orange juice. She pours the same amount of the juice into each of 6 glasses. Write an equation to represent the fraction of a gallon of orange juice in each glass.

 

  • Divide of a sandwich among 2 people or share a  quart of milk with 4 friends. Ask how much each person will get. Draw models to support thinking.

(1/2  ÷ 2 = 1/4 sandwich; 1/3  ÷ 4 =  1/4 quart of milk)