Teaching Division to Elementary Students

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Teaching Division to Elementary Students

• Math Methods
• Spring 2006

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Constructing Meaning for Division

• Division and Multiplication are so closely
  related, division doesnt have to start from
  scratch.
• When we do division problems, we use
  multiplication to think division.

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Thinking Division

• a x 9 63
• a number of bags of oranges
• (or number of sets)
• 9 is the number of oranges in each bag
• (number in each set)
• 63 is the total number of oranges
• (total number of objects)

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Interpretations for Division

• SUBTRACTIVE
• DISTRIBUTIVE

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Subtractive Division

• The easiest for children to grasp.
• We know the total number of objects and the
  number of objects in each set. We need to find
  the number of sets.

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Subtractive Division Examples

• If 6 crackers come in a package, how many
  packages will it take to get 30 crackers?
• If hot dogs come in packages of 8, how many
  packages will 56 hot dogs make?
• There are 7 days in a week. How many weeks are
  there in 49 days?

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Subtractive Division (contd)

• To solve these types of problems, give the
  students counters and containers to work through
  the problem.
• For example, with the cracker problem, the
  containers would represent the packages and the
  students would place 6 counters in containers
  until the counters are gone. The number of
  containers used would be the number of packages
  the answer!

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Subtractive Division (contd)

• The Number Sentence would be
• ____ x 6 30

Total number of crackers
Number of packages
Number of crackers in each package
So, ______ 5
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Subtractive Division (contd)

• If there had been 32 crackers, the Number
  Sentence would be
• (_____ x 6) 2 32

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Subtractive Division (contd)

• Repeated Subtraction is a part of Sub. Div.
• Students will be able to use this once they have
  worked with the manipulatives and understand
  these problems.

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Subtractive Division (contd)

• REPEATED SUBTRACTION
• 22
• -5
• 17
• -5
• 12
• -5
• 7
• -5
• 2

4 groups of 5
Will not make a set of 5.
Number Sentence (4 x 5) 2 22
Number of boxes of items in boxes of
remaining total number of items
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Activity using Subtractive Division

• Materials worksheet showing a table like the
  one here plastic links large, colored paper
  clips
• Directions Make small chains as indicated by
  this table. Use what you find to fill in the
  blanks. Be sure to measure and count carefully.
  Write number sentences after you have completed
  the table.

Use the big chain that is this long Make as many smaller chains as possible that are this many links How many new small chains do you have? How many links are left?
35 cm 9 cm
52 cm 6 cm
(etc) (etc)
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Distributive Division

• In these types of problems, we know the total
  number of objects and the number of sets. The
  goal is to find the greatest number of objects
  that can be placed in each set if the objects are
  distributed equally among the sets.

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Distributive Division Examples

• There are 42 marbles. There are 6 children. How
  many for each child?
• There are 27 chocolate kisses. There are 9
  children. How many kisses for each child?
• There are 35 cat treats. There are 7 cats. How
  many treats for each cat?

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Distributive Division (contd)

• The strategy used for Dist. Div. is different
  than the Sub. Div.
• Instead of removing sets of equal numbers from
  the total number of objects, the total number of
  objects is distributed equally among a given
  number of sets until there are not enough objects
  to go around again. If there are leftovers,
  they are the remainder.

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Distributive Division MARBLE PROBLEM

• Lets solve the marble problem.
• Give the students 42 counters (for marbles) and 6
  containers (for children).
• Have the students distribute the marbles among
  the containers, keeping the number of counters in
  the containers equal, until there arent enough
  to go around again.

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Distributive Division MARBLE PROBLEM (contd)

• Then have the students draw pictures to show
  what happened and write a number sentence to
  describe their findings.
• Number Sentence
• 6 x _____ 42

of children
of marbles in all
Marbles for each child
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When you divide, you dont always get a WHOLE
number

• Once students understand that division is derived
  from multiplication, it is time to introduce the
  division sign.
• Sometimes the idea of fractions needs to be
  introduced before or during division to explain a
  problem such as 11 divided by 5. There is no
  whole number answer. But using multiplication
  and addition helps.

(2 x 5) 1 11
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When you divide, you dont always get a WHOLE
number

• Then explain it as a division problem and that
  there is 1 leftover.
• That is the remainder.

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Division by Zero

• What if one of the factors is 0 and the product
  given is not a 0?
• 0 x ____ 10 or ____ x 0 10
• Is this possible?
• Why or why not?

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Division by Zero

• If we have 0x___0 or ___x00, then what
  replacements can we find for ______?
• Would 0 work? How about 1? How about 4? How
  about 10?
• Why?

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Division by Zero

• It is not possible to divide by zero!

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Review of all 4 Basic Operations

• For every addition fact, there are 2 related
  subtraction facts.
• For every multiplication fact, there are 2
  related division facts (except where 0 is
  involved).
• Addition is an associative and commutative
  operation.
• Multiplication is an associative and commutative
  operation.
• Multiplication can be thought of as repeated
  addition.
• Division can be thought of as repeated
  subtraction.