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# Chapter 3 - Chapter 3 Algorithms is a systematic step by...

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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 one-digit 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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