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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
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.
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.
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.
Missing Factor Model of Division
28 ÷ 4 =
Can be thought of as 4 X ? = 28
Terminology
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b ÷ n = a iff a∙n = 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.
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.
What Properties Hold for Division?
Dividing by Zero
No calculators!
Do the following division problem
159 ÷ 13
Division
• Can you divide without using the Long
Division Algorithm?
• Hint: the answer is YES!
• Let’s see what students do.
Strategies
• Amelinda and Alosha both used repeated
subtraction.
• Elaine and Thomas used a combination of
repeated subtraction and something else.
Describe this.
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!!!