November 29, 2013
High Low Difference POW
Problem Statement: The POW starts off with the random 3-digit number 473 and number the problem says to arrange the digits from largest to smallest, which is 743. Then arrange the digits from smallest to largest, which is 347. The arrangement of the digits from least to greatest is subtracted from the arrangement of those same digits from greatest to least. The problem we ultimately end up doing is 473-347 and the difference is 396. The problem asks the students to continue the process of choosing a number, arranging its digits so the lowest arrangement of the digits is subtracted from the highest arrangement of the digits. The problem also asks the readers to test out the steps using 3, 4, 5, 6 and so forth and explain what they discover. Process/Solution: To start this POW I continued the steps with the given number 473. Continuing with the steps I noticed that the digits 9, 4, and 5 repeating. I tried a different 3 digit number and the same digits kept repeating. I continued with 4, 5, 6, 7 digit numbers to see if I could find other patterns. For 4 digit numbers 1, 4, 6, and 7 continued to repeat. In 5 digit numbers, 3, 4, 5, 6, and 9 repeated. For 6 digits, 0, 2, 4, 6, 7 and 8 repeated. And lastly for 7 digits, 2, 2, 4,5,6,8 and 9 repeated. I found that all of the repeating digits for 4 added up to 18, for 5 digit numbers the repeating numbers added up to 27 and for 7 digits the numbers repeating at up to 36. I saw that a pattern occurred with the sum of the digits because the sum increased by 9.18+9 is 27 and 27+9 is 36. We can infer that the sum of the 8 digits will be 45 based on the pattern. Extension: Another similar problem could be if multiplication was used instead of subtraction, but keeping the same steps of arranging the numbers from largest to smallest and then multiplying them and seeing what patterns we find. Evaluation: This POW was interesting. It was...
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