Hangman DivisionDecomposing numbers to simplify “long” division

CarieAnn Morrissey-PulversJ.H. Gunn Elementary

December 2008

Making Sense of Division

The standard algorithm for dividing by a 2- or 3-digit divisor requires students to estimate, guess and check, then follow a series of steps that they memorize, but often don’t understand. Can your students explain why they “bring down” the next number in the dividend?

“Hangman” division allows students to remove chunks of the dividend, using numbers that make sense to them.

Doubles, Fives, and Tens

The student starts by listing the products of two, five, and ten times the divisor.

This example problem is 854 divided by 37.

37 8541 x =

2 x =

5 x =

10 x =

74

185

370

Taking Away ChunksThe student takes the biggest possible “chunk” out of the dividend (in this case it’s possible to take a

chunk of ten) and subtracts it from the dividend. Write 10 to the right of the problem to remind us what we have taken. Keep taking (and recording) your chunks until you can’t take any more away.

37 854

-370 10

484

-370 10

114

- 74 2

40

-37 1

3

1 x =

2 x =

5 x =

10 x =

74

185

370

Add ‘Em UpThis solution is also a reminder to students that division is repeated subtraction!

37 854

-370 10

484

-370 10

114

- 74 2

40

-37 1

3

1 x =

2 x =

5 x =

10 x =

74

185

370

= 23

Add up the number of “chunks”---this is the quotient.

The number remaining under the “hangman” bar is the remainder.

Practical Applications

Start with graph paper, to help students keep their places lined up for subtraction. After they are comfortable with the method, help them transition to regular paper.

Students can use whatever size “chunks” they are comfortable with---but they learn very quickly that the larger the chunks, the less work they have to do!

This method works extremely well when dividing across zeroes in the dividend.

Resources and Links

www.doubledivision.org http://www.math.nyu.edu/~braams/links/em-arith.html

***this site has alternate methods for all 4 operations from the University of Chicago Everyday Math program***