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Hangman Division Decomposing numbers to simplify “long” division

Hangman Division Decomposing numbers to simplify “long” division. CarieAnn Morrissey-Pulvers J.H. Gunn Elementary December 2008. Making Sense of Division .

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Hangman Division Decomposing numbers to simplify “long” division

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  1. Hangman DivisionDecomposing numbers to simplify “long” division CarieAnn Morrissey-Pulvers J.H. Gunn Elementary December 2008

  2. 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.

  3. 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. 1 x = 2 x = 5 x = 10 x = 37 854 74 185 370

  4. Taking Away Chunks 1 x = 2 x = 5 x = 10 x = 37 • 854 • -370 10 • 484 • -370 10 • 114 • 74 2 • 40 • -37 1 • 3 The 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. 74 185 370

  5. Add ‘Em Up 1 x = 2 x = 5 x = 10 x = 37 • 854 • -370 10 • 484 • -370 10 • 114 • 74 2 • 40 • -37 1 • 3 This solution is also a reminder to students that division is repeated subtraction! 74 185 370 Add up the number of “chunks”---this is the quotient. = 23 The number remaining under the “hangman” bar is the remainder.

  6. 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.

  7. 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***

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