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Multiplication of Fractions

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Multiplication of Fractions WMC Annual Conference May 2012 Astrid Fossum, Milwaukee Public Schools Paige Richards, School District of South Milwaukee – PowerPoint PPT presentation

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Title: Multiplication of Fractions


1
Multiplication of Fractions
  • WMC Annual Conference
  • May 2012
  • Astrid Fossum, Milwaukee Public Schools
  • Paige Richards, School District of South
    Milwaukee

Isnt this everything I need to know?
2
Current Connections to Fractions
  • Thinking about your current grade level of
    instructiontalk to a shoulder partner
  • Concepts you currently teach around fractions
  • Roadblocks that you encounter when you try to
    work with fractions with your students.

3
Learning Intentions
  • We are learning to
  • Develop strategies related to multiplying
    fractions.
  • Understand how estimation should be an integral
    part of fraction computation development.
  • Read and interpret the cluster of CCSS standards
    related to multiplication of fractions.
  • We will know we are successful when we can
  • Justify our thinking when multiplying fractions
    using concrete models and estimation strategies.
  • Clearly explain and provide examples for specific
    CCSS standards

4
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5
Domain-Cluster-Standards
  • Domain Number and Operations Fractions
  • Cluster Apply and extend previous understandings
    of multiplication and division to multiply and
    divide fractions.
  • Standard 5.NF.6
  • Solve real world problems involving
    multiplication of fractions and mixed numbers,
    e.g., by using visual fraction models or
    equations to represent the problem.

6
Big Ideas for Multiplication and Division of
Fractions
  • Multiplication and division of fractions are
    among the most complicated fraction concepts that
    elementary students encounter.
  • Instructional opportunities that students
    encounter should include the meaning of
    multiplication and division on a range of
    situations and build procedural fluency with
    understanding.

7
Launch Building on What We Know
  • What do you know about multiplication and
    division of whole numbers?
  • As a table group, make a list of what students
    have learned as they interact with multiplication
    and division problems.
  • Are they all true for fractions?

8
The Importance of Models
  • Researchers indicate that teachers need knowledge
    of concrete models to help students transition
    from multiplication of whole numbers to
    multiplication of fractions. (Fendel, 2000)

9
Thinking in Whole Numbers
  • 3 X 4 12
  • Write a word problem for this equation.
  • What does each number mean?

10
Multiplication of Fraction Standards
  • 4.NF.4a, 4.NF.4b, 4.NF.4c, 5.NF.4, 5.NF.5,
    5.NF.6
  • On your Standards Interpretation Sheet we will
    rephrase these standards and provide examples.

11
Some Stories
  • Solve these problems. Use a visual model to
    record and then discuss your thinking with the
    group. Then write an equation.
  • There are 15 cars in Dereks toy car collection.
    Two-thirds of the cars are red. How many red cars
    does Derek have?
  • Tia has 11 cookies. She wants to share them with
    her three friends. How many cookies will Tia and
    each of her friends get, if they share them
    equally?
  • Jason filled 5 glasses with 1/3 liter of soda in
    each glass. How much soda did Jason use?

12
Unpacking 4.NF.4
  • 4. Apply and extend previous understandings of
    multiplication to multiply a fraction by a whole
    number.
  • a. Interpret the product (a/b) q as a parts of
    a partition of q into b equal parts
    equivalently, as the result of a sequence of
    operations a q b. For example, use a visual
    fraction model to show (2/3) 4 8/3, and
    create a story context for this equation. Do the
    same with (2/3) (4/5) 8/15. (In general,
    (a/b) (c/d) ac/bd.)
  • b. Understand a multiple of a/b as a multiple of
    1/b, and use this understanding to multiply a
    fraction by a whole number. For example, use a
    visual fraction model to express 3 (2/5) as 6
    (1/5), recognizing this product as 6/5. (In
    general, n (a/b) (n a)/b.)
  • c. Solve word problems involving multiplication
    of a fraction by a whole number, e.g., by using
    visual fraction models and equations to represent
    the problem. For example, if each person at a
    party will eat 3/8 of a pound of roast beef, and
    there will be 5 people at the party, how many
    pounds of roast beef will be needed? Between what
    two whole numbers does your answer lie?

13
More Stories
  • Solve these problems. Use a model to record and
    then discuss your thinking with your group. Write
    an equation for each problem.
  • You have of a pizza left. If you give of
    the left-over pizza to your brother, how much of
    a whole pizza will your brother get?
  • Frankie had 2/3 of the lawn left to cut. After
    lunch, she cut 3/ 4 of the lawn she had left. How
    much of the whole lawn did Frankie cut after
    lunch?

14
Unpacking 5.NF.4a
  • 4. Apply and extend previous understandings of
    multiplication to multiply a fraction or whole
    number by a fraction.
  • a. Interpret the product (a/b) q as a parts of
    a partition of q into b equal parts
    equivalently, as the result of a sequence of
    operations a q b. For example, use a visual
    fraction model to show (2/3) 4 8/3, and
    create a story context for this equation. Do the
    same with (2/3) (4/5) 8/15. (In general,
    (a/b) (c/d) ac/bd.)

15
Multiplying with Mixed Numbers
  • Determine the solution to these problems. Do not
    use a computational algorithm.
  • 6 ½ x 4
  • 2 ½ x 5 ¾

16
Unpacking 5.NF.6
  • 6. Solve real world problems involving
    multiplication of fractions and mixed numbers,
    e.g., by using visual fraction models or
    equations to represent the problem.

17
Revisiting Word Problems
  • Examine the five problems on the handout.
  • Which are story problems for 2/3 x 1/ 4 and which
    are not? Why?

18
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19
Standards Interpretation Summing It All Up
  • As a teacher of mathematics
  • What message are you walking away with regarding
    the CCSSM domain of fractions?
  • As a leader of mathematics
  • What message will you be taking back to teachers
    in your school/district?

20
Thank you!
  • Astrid Fossum, Milwaukee Public Schools
  • fossumag_at_milwaukee.k12.wi.us
  • Paige Richards, School District of South
    Milwaukee
  • prichards_at_sdsm.k12.wi.us
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