Transcript Division, Part 3

An alternative method of division
Division using manipulatives
Use the base 6 blocks to find:
2436 ÷ 56
Division Algorithms
Compare the scaffolding algorithm
with the standard algorithm.
13 5799
Meaning of Division
9 ÷ 2 = 4 R1 means
2∙4+1=9
Mathematical language
a, b W , (b  0)q, r W  a  b  q  r ,0  r  b
For any whole numbers a and b, except that
b cannot be equal to zero, there exist two
whole numbers q and r such that a is equal
to b times q plus r, where r is less than b
and could possibly be equal to zero.
a, b  W , (b  0)q, r  W  a  b  q  r ,0  r  b
Mental Division
• Some are easier to do in our heads than
others:
6000/30
• How about 152 divided by 8?
Simplify
4  6  2 1
Rules for order of operations
•
•
•
•
•
•
Please
excuse
my
Dear
Aunt
Sally
parentheses from inside out
exponents
multiplication and
division from left to right
addition and
subtraction from left to right
Rules for order of operations
• Why do we have the rules?
• Where did the rules come from?
Order of operations
10  6  3
24  2  3
Simplify
4  6  2 1
Rules for order of operations
• Please
• excuse
• my Dear
• Aunt Sally
parentheses from inside out
exponents
multiplication and
division from left to right
addition and
subtraction from left to right
Rules for order of operations
• Why do we have the rules?
• Where did the rules come from?
Order of operations
10  6  3
24  2  3
Connections
• Addition and Multiplication
• Subtraction and Division
Connections
• Addition and Subtraction
Inverse Operations
• Addition and subtraction
Number line representations
Inverse Operations
• Multiplication and Division
number line representation
For Thursday, March 11th
• Finish pages 5 - 15 in your class notes packet.
• This will count as a project grade, not a
homework grade.
• 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 is
important; it is the quality of the explanation.