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Vito Prosciutto: Teaching community college math on the road to a PhD.

Sunday, May 16, 2004

12:30
Sunday Math 

a school yard blog presented the following math problem:
Find the 3 consecutive integers such that the product of the first and second integers is 40 less than the square of the 3rd integer.

Please develop a visual/conceptual model before you go directly to an algebraic generalization.

Here's what I came up with:
The green rectangles have a length equal to the middle number and width of one. The blue rectangle has length and width of the first two numbers. So we put a blue and a green rectangle together to get a square (because they're one apart. Then putting green rectangles on the top and side of the square with a 1x1 red square to complete the big square which has side length of the largest number.

So we take 40, subtract one and we have three greens so the three numbers are 12, 13 and 14.

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