Multiplication and Division

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Multiplication and Division

• In mathematics, we say that addition and
  subtraction are inverse operations. This is why
  there are related facts
• 3 4 7 7 - 4 3 7 - 3 4
• In this same way, multiplication and division are
  inverse operations
• 3 4 12 12 4 3 12 3 4

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Exploration 3.15

• Make up a story problem for 15 3.
• Share them with your group.
• Sort them into two or more piles. Select one
  from each pile, and read it to the class.

3
Different Word Problems

• In any division problem
• Dividend Divisor Quotient.
• In word problems, we usually have a rate as part
  of the problem (apples per person). Where the
  rate appears determines the type of word problem.

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Models for Division

• Carlos has 24 apples. If it takes 4 apples per
  pie, how many pies can he make? This is repeated
  subtraction.
• Carlos has 24 apples. If he wants to make 4
  pies, how many apples will be in each pie? This
  is partitioning.

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Missing Factor Model of Division

• 28 4
• Can be thought of as 4 X ? 28

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Terminology

• b n a iff an b
• b is the dividend
• n is the divisor
• a is the quotient
• a and n are the factors of b and b is a multiple
  of a and n.

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The number line!

• We use the number line with multiplication when
  we think about continuous models, or
  multiplication as repeated addition.
• We can use the number line here to show division
  as repeated subtraction.

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What Properties Hold for Division?
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Dividing by Zero
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No calculators!

• Do the following division problem
• 159 13

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Division

• Can you divide without using the Long Division
  Algorithm?
• Hint the answer is YES!
• Lets see what students do.

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Strategies

• Amelinda and Alosha both used repeated
  subtraction.
• Elaine and Thomas used a combination of repeated
  subtraction and something else. Describe this.

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For this weekend

• You will finish pages 1 - 15 in your packet.
• This will count as a project grade, not a
  homework grade--there are 41 total questions that
  need to be answered. A total of 40 points.
• For each question, be sure to explain both how
  the student answered the question, and why the
  mathematics is appropriate.
• The length of the answer is not what will get you
  a good grade!!!

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