This includes Algorithms that generally involve repeating a series of steps over and over, as in the borrowing and carrying algorithms and in the long multiplication and division.
1. Multiplication and Division Algorithms Information for parents on the multiplication and division algorithms taught in Everyday Math
2. What is an algorithm? An algorithm is a set of rules for solving a math problem which, if done properly, will give a correct answer each time. Algorithms generally involve repeating a series of steps over and over, as in the borrowing and carrying algorithms and in the long multiplication and division (Information from: instruction.aaps.k12.mi.us/EM_parent_hdbk/algorithms.html)
3. Why do we teach multiple algorithms? Researchers working in the 1970s and 1980s showed that U.S. children often learn standard computational algorithms with very little understanding (Brown & Burton, 1978; Van Lehn 1983, 1986). Other researchers found that the traditional approach to teaching computation engenders beliefs about mathematics that impede further learning (Hiebert, 1984; Cobb, 1985; Baroody & Ginsburg, 1986). On the other hand, Kamii and others demonstrated that students are capable of inventing their own effective and meaningful methods for computation (Kamii, 1985; Madell, 1985; Kamii & Joseph, 1988; Cobb & Merkel, 1989; Resnick, Lesgold, & Bill, 1990; Carpenter, Fennema, & Franke, 1992). Furthermore, these experiences were found to improve understanding of place value and enhance estimation and mental computation skills. (Information from: http://everydaymath.uchicago.edu/about/em-history/curriculum-research/)
4. Multiplication - Traditional Method ● Most familiar algorithm to adults ● Multiplies from right-to-left ● Regroup as needed ● Below is a video demonstrating the traditional algorithm for multiplication: https://vlc.uchicago.edu/resources/9697
5. Multiplication - Partial Products Algorithm ● Based on the distributive property of multiplication ● Multiply each digit of one factor with each digit of the other factor ● Then add the products together to get the final answer ● Below is a video demonstrating the Partial Products Algorithm: http://everydaymath. uchicago.edu/teaching-topics/computation/mult-part-prod/
6. Lattice Multiplication ● This method has been used for hundreds of years ● This method is an alternative method for long multiplication ● Using a grid, or lattice, you are able to multiply large numbers easily ● Multiply the top digits by the digits on the side. Then add along the diagonal lines. ● Below is a video demonstrating lattice multiplication: http://everydaymath.uchicago.edu/teaching- topics/computation/mult-lattice/
7. Division - Traditional Algorithm ● Familiar to adults and children ● Place the dividend inside a division bracket, and the divisor outside and to the left of the bracket. ● Make a series of estimates and record the results. Then subtract the result from the number above it. ● If there is a remainder, it is written next to the quotient at the end of the problem. ● Below is a video demonstrating the Traditional Algorithm for Division: https://www.youtube.com/watch?v=pyfn3IeGf7g
8. Division - Partial Quotients ● At each step find a partial answer, or quotient. Once you have found all of the partial quotients, you add them together to find the answer. ● The better the estimates, the fewer the steps it takes to solve the problem. ● Students who struggle with basic facts can find correct answers with this approach. ● Below is a video demonstrating the Partial Quotients Algorithm: http://everydaymath.uchicago.edu/teaching-topics/computation/div-part-quot/
9. Additional Resources Everyday Math Algorithms Everyday Math Free Resources Multiplication Algorithms Division Algorithms Everyday Math Virtual Learning Community
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