05-06-2012, 01:16 PM
An Introduction to Various Multiplication Strategies
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Multiplication is one of the four basic operations of elementary arithmetic and is commonly defined as repeated addition. However, while this definition applies to whole number multiplication, some math researchers argue that it falls short for multiplication of fractions and other kinds of numbers. These mathematicians prefer to define multiplication as the scaling of one number by another, or as the process by which the product of two numbers is computed (Princeton University Wordnet, 2010). Despite the controversy, multiplication, by any definition, is an essential skill to students preparing for life in the mathematical world of the 21st century. It is an important tool in solving real-life problems and builds a firm foundation for proportional reasoning, algebraic thinking, and higher-level math.
Finger Multiplication
Some of the oldest methods of multiplication involved finger calculations. One such method is believed to have come out of Italy and was widely used throughout medieval Europe (Rouse Ball, 1960 p. 189). The algorithm is fairly simple and can be used to calculate the product of two single digit numbers between five and nine. In order to use this method, one must understand that the closed fist represents five, and each raised finger adds one to that value.
Area Model of Multiplication
All students need to be able to make connections between mathematical ideas and previously learned concepts in order to build new understandings. The area model of multiplication is an algorithm that uses multiple representations to explain the multiplication process, and can help students make connections to algebra and algebraic thinking.
Lattice Multiplication
Lattice multiplication, also known as sieve multiplication or the jalousia (gelosia) method, dates back to 10th century India and was introduced into Europe by Fibonacci in the 14th century (Carroll & Porter, 1998).
Circle/Radius Multiplication
Another graphic multiplication algorithm, involves the drawing of concentric circles to represent the multiplier along with the drawing of radii to represent the multiplicand. For example, to multiply 3 × 4, first draw three concentric circles to model the multiplier three, and then add four radii to model the multiplicand four. Then count the number of separate pieces created within the circle. Since 12 pieces are created, 3 × 4 = 12.
[attachment=116]
Multiplication is one of the four basic operations of elementary arithmetic and is commonly defined as repeated addition. However, while this definition applies to whole number multiplication, some math researchers argue that it falls short for multiplication of fractions and other kinds of numbers. These mathematicians prefer to define multiplication as the scaling of one number by another, or as the process by which the product of two numbers is computed (Princeton University Wordnet, 2010). Despite the controversy, multiplication, by any definition, is an essential skill to students preparing for life in the mathematical world of the 21st century. It is an important tool in solving real-life problems and builds a firm foundation for proportional reasoning, algebraic thinking, and higher-level math.
Finger Multiplication
Some of the oldest methods of multiplication involved finger calculations. One such method is believed to have come out of Italy and was widely used throughout medieval Europe (Rouse Ball, 1960 p. 189). The algorithm is fairly simple and can be used to calculate the product of two single digit numbers between five and nine. In order to use this method, one must understand that the closed fist represents five, and each raised finger adds one to that value.
Area Model of Multiplication
All students need to be able to make connections between mathematical ideas and previously learned concepts in order to build new understandings. The area model of multiplication is an algorithm that uses multiple representations to explain the multiplication process, and can help students make connections to algebra and algebraic thinking.
Lattice Multiplication
Lattice multiplication, also known as sieve multiplication or the jalousia (gelosia) method, dates back to 10th century India and was introduced into Europe by Fibonacci in the 14th century (Carroll & Porter, 1998).
Circle/Radius Multiplication
Another graphic multiplication algorithm, involves the drawing of concentric circles to represent the multiplier along with the drawing of radii to represent the multiplicand. For example, to multiply 3 × 4, first draw three concentric circles to model the multiplier three, and then add four radii to model the multiplicand four. Then count the number of separate pieces created within the circle. Since 12 pieces are created, 3 × 4 = 12.