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Multiplication and Division

- Learning progressions
- Word problems
- Online resources

CCSS

- 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

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.

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?

- Chad had 5 bags of candy with 7 pieces of candy

in each bag. How many pieces of candy did Chad

have? - 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? - Lee collects stamps. He has 45 stamps. If he

sticks 9 stamps on each page, how many pages

would he fill with stamps? - 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? - 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? - 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

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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

Online Resources

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