Monday, January 21, 2008

Washington's New 2nd Grade Algebra and Long Division standard

From Math Standards Revision Process Overview and Discussion
Wednesday, January 16, 1:30 - 3:00 p.m.
This appears to be the new 2nd grade problem solving sample.

2.2.d ProblemSolving/Reasoning/ Communication Solve a variety of addition and subtraction problems and justify the solutions.

Including take away, missing addend, and comparison.

Example of Comparison: Hazel and Kimmy each have stamp collections. Kimmy’s collection has 7 more stamps than Hazel’s collection. Altogether, they have 20 stamps. How many stamps are in Hazel’s collection

Solution: 20 - 7 kimmy = 13 hazel , with drawing.

This solution is not correct because 13 - 7 = 6, not 7.=======================================================

How would a grown up solve this problem? Let x = Hazel and x + 7 = Kimmy. x + x + 7 = 20. Simplify 2x + 7 = 20. Subtract 7 from both sides gives 2x = 13, divide both sides by 2 gives x = 6.5, so Hazel has 6.5, and Kimmy has seven more, or 13.5. Together they have 20 stamps. Do they have fractional ownership of a stamp, of half-stamps?

To check, 6.5 + 6.5 + 7 = 20.

None of the 2nd grade textbooks that I have (and I have several) have a solve for the unknown like this one. Their solution evidently relies on guess and check, but this is another classic example of a upper grade problem (solve an equation of the form ax + b = c) to be solved without a proper solution method.

Also note that most graduates of Core Plus probably don't know enough algebra to solve this problem either since this basic level of algebra isn't taught at high school level, and I don't think it's covered by connected mathematics either (can somebody verify that?) The college prep SAT does NOT require knowledge of algebra and does not contain problems like this! It WOULD be appropriate for the 10th grade WASL, but that's only if we assume algebra is required for all students.

They still have the 2nd grade long division problem, though it has been changed so that they have to compute the total of the change, and it still says "struggling students" (those that can't do long division?) can count objects. This entire sample must be tossed, as well as the language "struggling" 38 cents divided by 3 is solved by long division with a remainder, which isn't covered in the curriculum until grade 5. The previous version of this mentioned that the students would encounter a remainder.

Example: Suzy, Ben, and Pedro have found a quarter, a dime and 4 pennies under the sofa. Their mother says they can keep the money if they can tell her what coins they need to share it equally. How can they do this?
• It has multiple entry points: — struggling students can count out objects and move them around.— children at different levels of number facility can combine and separate the values using their skills.
• This problem is understandable to some children through using models, to others by drawing a picture or by using numbers to make a list.
• This problem addresses important grade two mathematics such as place value, grouping, sharing, and money concepts.
• Children can easily verify whether their solution works.

Come on folks, this is total garbage, I shouldn't have been the first one to spot this.

********* ARGH ************

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