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Multiplication and Division


Multiplication and Division Learning progressions Word problems Online resources – PowerPoint PPT presentation

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Title: Multiplication and Division

Multiplication and Division
  • Learning progressions
  • Word problems
  • Online resources

  • Practice Standards
  • Problem solving
  • Reasoning
  • Modeling
  • Content Standards
  • Critical Areas at each grade

In Grade 4, instructional time should focus on
three critical areas
  • (1) developing understanding and fluency with
    multi-digit multiplication, and developing
    understanding of dividing to find quotients
    involving multi-digit dividends
  • (2) developing an understanding of fraction
    equivalence, addition and subtraction of
    fractions with like denominators, and
    multiplication of fractions by whole numbers
  • (3) understanding that geometric figures can be
    analyzed and classified based on their
    properties, such as having parallel sides,
    perpendicular sides, particular angle measures,
    and symmetry.

In Grade 5, instructional time should focus on
three critical areas
  • (1) extending division to 2-digit divisors,
    integrating decimal fractions into the place
    value system and developing understanding of
    operations with decimals to hundredths, and
    developing fluency with whole number and decimal
  • (2) developing fluency with addition and
    subtraction of fractions, and developing
    understanding of the multiplication of fractions
    and of division of fractions in limited cases
    (unit fractions divided by whole numbers and
    whole numbers divided by unit fractions)
  • (3) developing understanding of volume.

Curriculum Tools
  • C-R-A An instructional approach
  • U-F-G A theory of knowledge
  • Learning progressions
  • Types of problems
  • Visual representations

C-R-A Concrete
  • Solve this with mental math.
  • There are 47 children on the playground. 24 go
    home. How many are left on the playground.
  • 47 24 ____

C-R-A Concrete (objects)
  • Now solve this with mental math.
  • There are 53 children on the playground. 38 go
    home. How many are left on the playground.
  • 53 38 ____
  • You can use counters or a number line.

C-R-A Representational (pictures)
C-R-A Abstract (symbols)
U-F-G Framework
Conceptual Understanding Fluency Generalization
Addition is putting together and adding to, subtraction is taking apart, taking from and comparing.
Problems are solved using objects and drawings to represent situations. Fluency starts with strategies such as counting on, making ten, doubles plus one.
By end of 2nd grade, know all sums from memory. Addition is the foundation for multiplication through skip counting of arrays.
How would children solve these?
  1. Chad had 5 bags of candy with 7 pieces of candy
    in each bag. How many pieces of candy did Chad
  2. At Sallys birthday party there were 15 children
    and 3 blankets. If the same number of children
    sat on each blanket, how many children sat on
    each blanket?
  3. Lee collects stamps. He has 45 stamps. If he
    sticks 9 stamps on each page, how many pages
    would he fill with stamps?
  4. Mr. Wong has 4 children. He wants his children to
    share 12 marbles so that they each get the same
    amount. How many marbles should Mr. Wong give
    each child?
  5. 19 children are going to the circus. 5 children
    can ride in each car. How many cars are needed so
    that all the children can go to the circus?
  6. Maria has 17 fish. If 3 fish can be put into one
    fish bowl, how many bowls does she need to hold
    her fish?

Types of multiplication and division problems
  • Grouping problems
  • (Partitive and measurement division)
  • Rate problems
  • Price problems
  • Multiplicative Comparison problems
  • Array and Area problems

(No Transcript)
Three questions
  • What does it mean to really know multiplication
    and division well?
  • How is multiplication of decimals related to
    multiplication of whole numbers?
  • How can I use these resources in my teaching?
  • C-R-A, U-F-G
  • Types of Problems
  • Learning Progressions
  • Virtual Manipulatives
  • Number Talks

Online Resources
  1. http//
  2. Find Out More About Wiki Spaces
  3. Elementary Math Resources
  4. 4th-5th Grade