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Section 3.3. Algorithms for Addition and Subtraction. Mathematics for Elementary School Teachers - 4th Edition. O’DAFFER, CHARLES, COONEY, DOSSEY, SCHIELACK. Developing Algorithms for Addition: Using Models as a Foundation.

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## Section 3.3

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**Section 3.3**Algorithms for Addition and Subtraction Mathematics for Elementary School Teachers - 4th Edition O’DAFFER, CHARLES, COONEY, DOSSEY, SCHIELACK**Developing Algorithms for Addition: Using Models as a**Foundation • Base-ten blocks can be used to find a sum and provide models that help explain the addition algorithms. • Recall that addition can be defined as the number of elements in the union of two disjoint sets. Think of the base-ten blocks representing numbers to be added as the elements in disjoint sets; the union of these sets is found by joining the two sets of blocks, combining and regrouping as necessary.**Using the Base-Ten Blocks Model for Addition**278 + 146 = ?**Using the Base-Ten Blocks Model for Addition**278 + 146 = ?**Using the Base-Ten Blocks Model for Addition**278 + 146 = ?**Using the Base-Ten Blocks Model for Addition**278 + 146 = ?**Using the Base-Ten Blocks Model for Addition**278 + 146 = 424 278 + 146 = ?**Developing Algorithms for Addition: Using Paper-and-Pencil**• The values of each place are added first and later combined. • The order in which the numbers with a given place value are added doesn’t matter because all partial sums are recorded.**Developing Algorithms for Addition: Using Paper-and-Pencil**• Start with the ones and proceed to add, with regrouping, from right to left.**Example: 562 + 783**• Standard algorithm:Add the ones, then add the tens and regroup. Add the hundreds: 13 hundreds are 1 thousand and 3 hundreds. • Expanded algorithm:Add the ones, then the tens, then the hundreds, writing partial sums. Add the partial sums.**Developing Algorithms for Subtraction: Using Models as a**Foundation • Using base-ten blocks for modeling subtraction embraces the take-away interpretation of subtraction rather than building directly from the definition of subtraction of whole numbers. • There may be more than one way to use base-ten blocks to model a subtraction problem.**Developing Algorithms for Subtraction: Using Models as a**Foundation • One way to solve 245 – 18 using models: • Trade 1 ten for 10 ones, then take away 8 ones, leaving 7 ones. • Take away 1 ten, leaving 2 tens.**Using the Base-Ten Blocks Model for Addition**245 – 18 = ? 245 – 18 = 227**Developing Algorithms for Subtraction: Using**Paper-and-Pencil • Expanded algorithm for subtraction:Start with the greatest number and repeatedly take away as much as possible mentally before moving from left to right.**Developing Algorithms for Subtraction: Using**Paper-and-Pencil • Standard algorithm for subtraction:Start with the ones and proceed to subtract, with regrouping, from right to left.**Example: 635 – 248**• Standard algorithm: • Expanded algorithm:**The End**Section 3.3 Linda Roper

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