Chapter 3:
Algorithms is a systematic step by step procedure to solve a class of problems. A mathematical
algorithm is a cyclic computation algorithm, which solves problems, is a finite number of steps.
3.1 The Addition Algorithm The addition algorithm is build around a central mathematical fact:
place value allows us to find the sum of any two numbers, however large, by doing a series of
onedigit additions, rebundling when necessary.
Prerequisites
•
Expanded form 300+40+5=345
•
The idea of adding ones, tens, and hundred separately including the mental
math skills. Pg. 60
•
Rebundling, that is “cashing in” ten units of one domination for one unit if
the next larger denomination. Pg. 60
Step one addition without rebundling students add separately the hundreds, tens, and ones
columns.
Step two addition with rebundling this step is commonly referred to as “carrying”.
Complications:
•
3 digit plus a 2 digit with bundling ones
•
Two 3 digit numbers with bundling ones
•
Two 3 digit with bundling tens
•
Double rebundling
Lattice Addition: add columns first and then add down the diagonals. Pg. 62
3.2 The Subtraction Algorithm
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 Spring '10
 Kwon
 Addition, Multiplication, Elementary arithmetic, Range Estimation

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