Transcript Division, Part 1

Exploration 3.15
• Make up a story problem for 15 ÷ 3.
• Share them with your group.
• Compare the problems and discuss
whether they are similar or if there are
different types. Choose two of the
problems. Then pair up and write each of
the two problems on a white board.
What’s wrong?
49 • 12
49 + 1 is 50, so do 50 • 12,
which is 600, and then
subtract 1, and get 599.
Find the following products in Base 8:
258
× 138
578
×648
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
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.
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 used repeated subtraction.
• Alosha added up, which is a variation of
repeated subtraction.
• Elaine also added up but she used a
“landmark” number to help her find the
answer faster.
• Thomas used partitioning. He also used a
“landmark” or “friendly” number to help him
to the quotient.
What Properties Hold for Division?
Dividing by Zero