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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

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)

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/)

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

● 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/

● 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/

● 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

● 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/

● 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

Everyday Math Algorithms

Everyday Math Free Resources

Multiplication Algorithms

Division Algorithms

Everyday Math Virtual Learning Community