Multiplication and Division

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Multiplication and Division

• Learning progressions
• Word problems
• Online resources

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CCSS

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

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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.

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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
  operations
• (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.

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Curriculum Tools

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

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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 ____

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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.

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C-R-A Representational (pictures)
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C-R-A Abstract (symbols)
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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.
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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
   have?
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?

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Types of multiplication and division problems

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

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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

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Online Resources

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