FINALE: T3 CONSECUTIVE NUMBERS
Note:
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This is a serious investigation requiring some serious, sustained work!
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Your write-up should not be all the work you really did, but an afterwards, refined and polished product,
using writing as communication to explain the logic and validity of your reasoning, i.e. justifying your logical
conclusion, and to convince the reader that your reasoning and conclusion is correct.
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Submission by e-mail: 29 October, midnight
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Marks: 40
Activity : Sums of Consecutive Whole Numbers
Some numbers can be written as the sum of two or more
consecutive positive whole numbers, e.g.
12 = 3 + 4 + 5 (the sum of 3 consecutive numbers)
13 = 6 + 7 (the sum of 2 consecutive numbers)
14 = 2 + 3 + 4 + 5 (the sum of 4 consecutive numbers)
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Understand the problem! Make a plan! Polya Execute the plan! Looking back Is it right? Is there another way?
Some numbers can be written as the sum of consecutive whole numbers in more than one way, e.g.
15 = 7 + 8 (the sum of 2 consecutive numbers)
 Resources – what knowledge can I bring? 15 = 4 + 5 + 6 (the sum of 3 consecutive numbers)
 Heuristics – what problem solving strategies?
15 = 1 + 2 + 3 + 4 + 5 (the sum of 5 consecutive numbers)
 Control – am I on the right track? Schoenfeld
Some numbers cannot be written as the sum of consecutive
whole numbers – try writing 16 as the sum of consecutive numbers …
Investigate: Which numbers can and which numbers cannot be written as the sum of consecutive positive
whole numbers? Which numbers can be written in more than one way? How many ways?
Develop enough mathematics so that you can easily:
 decide if any given number can be written as the sum of consecutive numbers or not
 find all the different ways the number can be written as the sum of consecutives.
Finally, implement your mathematics and write the following as the sum of consecutive numbers.
Needless to say, provide all the possibilities. Needles to say, prove that it is all the possibilities!
(1) 105
(2) 128
(3) 144
(4) 1430
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(5) 1764
(6) 3582
Do something! Make a plan, and do it! May I ? Is it right, is it true? Control! Looking back Does it help? Is this going somewhere? Control! Olivier 