Transcript 01-31 3.4 Dividing Whole Numbers

§3.4 Dividing Whole
Numbers
1/30/17
Today We’ll Discuss
What is the definition of the quotient of
two numbers?
How do we use models and algorithms to
divide whole numbers?
~DIVISION~
Division (specifically “long division”) often
gets a reputation for being
hard
stupendously long
torture
“The point at which I gave up on math.”
What can we do to motivate and teach
division effectively?
What is Division?
Division is the inverse operation of
multiplication.
This means we define division in the same
way we started with subtraction: “undo”
the original operation.
So, either we can think of division as
repeated subtraction or as splitting into
groups.
Definition of Division
Definition: The quotient of two whole
numbers a and b (b ≠ 0), denoted a ÷ b, is
the whole number such that
b • (a ÷ b) = a
Divisor
Quotient
Dividend
Missing Factor Method
10 ÷ 5 = 2
5 • 2 = 10
Missing Factor Method
10 ÷ 5 = 2
5 • 2 = 10
Example
Explain how to solve each division problem
using a multiplication problem in the
Missing Factor Method.
a) 12 ÷ 3 =
b) 24 ÷ 4 =
Set (Partition) Method
10 ÷ 5 = 2
Set (Partition) Method
An array is a display of objects in a
rectangular arrangement.
Set (Partition) Method
When the quotient is not a whole number,
we sometimes refer to the remainder. This
is the amount remaining in the dividend
after we have removed all possible whole
number amounts of the divisor.
Example
Use an array to find…
a) 30 ÷ 5
b)
Number Line Model
The number line can be another good tool
for emphasizing division as repeated
subtraction.
Place an arrow the length of the dividend
starting at zero.
Number Line Model
Repeatedly draw arrows back to the left,
each of the size of the divisor.
The number of left divisor arrows it takes
to get as close to zero as possible is the
quotient.
Number Line Model
If it is impossible to reach exactly zero,
then the length remaining is the remainder
of the division problem.
Example
Use the number line to model…
a) 19 ÷ 3
b)
Traditional, Compressed
Algorithm
The traditional algorithm still requires
guess-and-check, as well as a mastery of
multiplication.
However, it attempts to make the process
involve as little writing as possible.
Example
Use the Traditional, Compressed Algorithm
to calculate:
a) 893 ÷ 19
b) 800 divided by 27
c.) 315 ÷ 16
Scaffold Algorithm
The scaffold algorithm makes things even
more “guess-and-checky” by letting you
choose suboptimal guesses for the repeated
subtraction.
At the end, you total how many times you
subtracted the divisor.
Example
Use the Scaffold Algorithm to calculate
a) 2640 ÷ 27
b) 741 divided by 13
c.) 853 ÷ 11
Story Problem Example
On a car trip across the United States, you
drive 2938 miles and use 125 gallons of
gasoline. How many miles per gallon did
your car average?
HW#6 Section §3.4
Pages 114-117
#7, 8, 9, 12, 14, 15, 18, 20, 24, 26