WASL 4TH GRADE SORTING PROBLEMS FROM HELL \doc\web\99\02\block.txt How many of your 4th graders can solve this sorting problem? Do you want your 4th grader held back because he doesn't meet the "standard" of what "he should know and be able to do"? Do you want your kid's diploma denied because you couldn't pass an equally hard 10th grade test? This is exactly what states like Texas and New York are threatening to do, we could be next. Can you solve it? How long did it take? Is this the sort of problem you want on a test where you have to finish 30 other problems in one day? Do you want your kids wasting an entire week trying to solve problems like this when a standardized test only takes a couple of hours on one day, and costs only $2 not $40 to score? See the math benchmarks for Washington State's EALR at http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html BTW, Terry Bergeson claims somebody HAS done a 2nd review of problems and pronounce them fully compliant and reasonable within the goal of 80% passing once everybody starts teaching to the new EALRs. Do YOU agree? Sorting problems: problem 17 page 70 "Scales and Blocks" (sorting) The pictures below show the results when some boxes are placed on a balance: 1---- T J 2---- L X 3---- R W 4---- J W 5---- R L 6---- X T 7---- T W --- Name two boxes that are heavier than Box X. Write the number of the picture or pictures you used to find each of your answers _______________________________ Tell whether box R is lighter or heavier than Box X. Write the number of the picture or pictures you used to find your answer _________________________________ List the 6 boxes in order from heaviest to lightest: 1. 2. 3. 4. 5. 6. Comment - there is nothing in the benchmarks that specifies being able to sort 6 boxes based on 7 inequalities, except "problem solving". There are likely no textbooks that give a solution to this problem. Most adults can't do this problem, I doubt more than a few percent of 4th graders can do this, even after being shown a solution algorithm. This problem is not even appropriate for most 12th graders unless that have taken an algorithms course that includes format sorting algorithms. 4th Benchmark: identify, compare, and order whole numbers and simple fractions. Nowhere is sorting of a list of numbers or items mentioned, even at grades 7 or 10 This problem is not just ordering two numbers, it is sorting a list of unknown values, and asking for a solution as to their order. A benchmark to match this problem would be to "sort a list of six items given 7 inequalities between different pairs of items". Grade level appropriate problem Block A 100 lb Block B 75 lb Block C 200 lb Block D 115 lb Arrange these blocks in order of increasing weight. Grade level benchmark: "Sort a list of 4 3 digit integers". SPOILER***SPOILER*****SOLUTION FOLLOWS***************** One Solution, based on insertion sorting algorithm 1. T, J. 6 shows T is heavier than X, 1 shows J is heavier than T, which is also heavier than X. 2. based on following sort order, R is lighter than X 3. from heavy to light: W J T X L R reverse this result: RLXTJW Letters to sort JTLWRX-6 blocks total # is sorting list * write heavier from left to right * add a letter to left or right if it is definitely to the left or right of what we already have. * try out each letter in sequence * stop when we have all 6 letters Look for J TJ sequence #TJ JW, put W at right end sequence #TJW done J!T!LW!RX Look for T XT put X at left end sequence #XTJW done J!T!LW!RX! Look for W RW? R would be in the middle, wait Look for R RW RL Still in the middle Look for L, lighter than lightest LX Put L at left sequence #LXTJW done J!T!L!W!RX! Next L RL Put R at left again sequence #RLXTJW done J!T!L!W!R!X! All letters complete, stop Problem 35 p.90 In 1991, the five states below had the greatest number of people visit their state parks and recreation areas. The states are listed in alphabetical order Visitors (in thousands) ------------------------ California 70,444 New York 60,744 Ohio 67,222 Oregon 39,479 Washington 46,813 How does washington rank in terms of total number of visitors? A. third largest B. fourth largest C. fifth largest Solution 1. Count how many states are greater (3), then add one for washington's position, answer is fourth. 2. Sort the list, find washington on the list (4 from top) This involves rewriting the list, or writing numbers beside each line without getting confused. Note that sorting a list is NOT a 4th grade required skill. This problem can figured out by many fourth graders, but it is still much more complex than simply "ordering whole numbers". The answer is not directly taught, but must be "figured out", which means that you cannot expect all children to master this problem unless they are either "smart" or have been coached on these particular kinds of problems. Whenever you test for the ability to solve a problem for which there is no known or taught solution, you are testing for cognitive ability, or IQ, which cannot be taught or assessed directly, and the advantage goes to kids with highest IQ and out-of-school resources and exposure.