Thursday, October 8, 2009

Math problems of the week: Systems of Equations in CPM vs. 1900's math

1. The only systems of equations that students are required to solve algebraically in the CPM (College Preparatory Mathematics) Algebra Connections "Systems of Equations" chapter (published in 2006):

y = 1160 + 22x
y = 1900 - 15x

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y = 6 + 1.5x
y = 2x

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y = 2x -3
y = -x + 3

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y = 2x -3
y = 4x + 1

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y = 2x - 5
y = -4x - 2

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y = -x + 8
y = x -2

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y = -3x
y = -4x + 2

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y = 2x - 3
y = 2x + 1

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y = -4x -3
y = -4x + 1

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2. A subset of the over one hundred systems of equations in the Wentworth's New School Algebra "Simple Systems of Equations" chapter (published in 1898):

5x + 2y = 39
2x - y = 3

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x/3 + y/2 = 4/3
x/2 + y/3 = 7/6

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x + y - 8 = 0
y + z - 28 = 0
y + z - 14 = 0

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6x - 2y + 5z = 53
5x + 3y + 7 = 33
x + y + z = 5

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2x + 3y + 1 = 31
x - y + 3z = 13
10y + 5x - 2z = 48

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1/x + 2/y - 3/z = 1
5/x + 4/y + 6/z = 24
7/x - 8/y + 9/z = 14

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2/x - 3/y + 4/z = 2.9
5/x - 6/y - 7/x = -10.4
9/y + 10/z - 8/x = 14.9

3. Extra Credit:

(a) Discuss why CPM, but not New School Algebra, has to stipulate that the simultaneous equations be solved algebraically (rather than graphically or by "guess and check").

(b) Discuss the arithmetic and algebraic skills required by each problem set.

(c) Relate your answer in (b) to the final assignment in CPM's "Simultaneous Equations" chapter, the TEAM BRAINSTORM:

With your team, brainstorm a list for the following topics. Be as detailed as you can. How long can you make your list? Challenge yourselves. Be prepared to share you team's ideas with the class.

Topics: What have you studied in this chapter? What ideas and words were important in what you learned? Remember to be as detailed as you can.

3 comments:

Marcy said...

Is "guess and check" really what is going on now? I ask because math pegagogy is still new to me as a parent and my 9 year old (with the taste for human flesh) has been coming home lately with division problems to do, but no apparent instruction in how to solve them.
It looks to me like the children are being asked to figure out how to divide on their own, before they get instruction. "Guess and check" is a good description of what I think is going on.

Katharine Beals said...

Marcy, Unfortunately, I think your impressions are probably correct, and your 9-year-old will probably need after-school math "enrichment" to learn long division and other strategies. I've been using Singapore Math at home with all three of my kids to make up for what they're not learning at school.

Marcy said...

Ah...obviously I meant pedagogy.

Though maybe pegagogy is the fitting of round peg children into square hole math...

I brought the "division" problem up to my son's aide and another 4th grader said "No, it's multiplication, not division!" But it looked to me that it was only guessing at a multiple, not actual multiplication.
I started that night to teach my son long division, but I think I'll look into Singapore math.
Thank you.