WASL 4TH GRADE SORTING PROBLEMS FROM HELL
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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.