Re: [MATHEDCC] Squares

Bret Taylor (bret@IAG.NET)
Mon, 6 Oct 1997 20:15:32 -0400 (EDT)

At 08:48 AM 10/6/97 +0100, you wrote:
>As a little HW research problem I gave my students in intermediate algebra
>the following: Divide each of the first ten squares by 4, then examine the
>answers. What conclusions can you make about dividing squares by the number
>4?
>
>All the students who responded made the follwing table:
>
>1=F74=3D0.25
>4=F74=3D1
>9=F74=3D2.25
>16=F74=3D4
>25=F74=3D6.25
>36=F74=3D9
>49=F74=3D12.25
>64=F74=3D16
>81=F74=3D20.25
>100=F74=3D25
>
>I haven't read all the answers in detail, but none of the students (out of
>nearly 30) recognized the modulus relationship. Curious.
>
>
>Vince McGarry
>Department of Mathematics
>Austin Community College
>Austin, TX
>(512) 223-3358
>FAX (512) 467-8739

Let's see, every even number can be written as 2k so (2k)^2, ;when divided
by 4 yields a remainder of 0. Every odd number can be written as 2k+1, so
(2k+1)^2, when divided by 4 yields a remainder of 1. Hence, since even and
odd numbers alternate, the remainders will follow the pattern 0,1,0,1,...
regardless of which even number you start with. Probably a little abstract
for the typical intermediate algebra class, but after they understand the
concept of factoring perfect square trinomials and squaring binomials,
maybe.....

Oh no, we are back to the do-students-need-to-know-how-to-factor discussion.=
:-)

Bret
>
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Bret Taylor Lake-Sumter Community College Leesburg FL

"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden

John 3: 3^3 + 3

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