Sunday, January 13, 2013

How To Figure Out How Many Spheres Will Balance One Cube!

OK. There are times when we must divert attention from the really important things in our lives to the things that are going to cause us problems just because they exist. My child has to take a test. While preparing for that test, we went over an online test booklet that had various example problems. Here is the problem.
Kent is using the scale to compare the weight of various solids. How many spheres will balance one cube?
This is an example question on the Washington State Algebra End Of Course exam (also known as the WASL). It seems that a lot of people have struggled with this question, but it really is simple and it doesn't really require much math. In fact, I don't even understand why this question would be on an Algebra high school math test and not a seventh grade math test! So let's do this with almost no math. In the top equation you have this -


TOP EQUATION
SIDE ONE
4 Cubes
2 Triangles
3 Spheres
 
SIDE TWO
3 Cubes
4 Triangles
5 Spheres
 
BOTTOM EQUATION
SIDE ONE
1 Cube
1 Sphere
SIDE TWO
4 Triangles
2 Spheres


TOP EQUATION WITH CANCELLATIONS
4 Cubes leaves 1 Cube
2 Triangles
3 Spheres
 
3 Cubes
4 Triangles leaves 2 Triangles
5 Spheres leaves 2 Spheres
 
BOTTOM EQUATION WITH CANCELLATIONS
1 Cube
1 Sphere
4 Triangles
2 Spheres leaves 1 Sphere

So what does that tell you? With hardly no effort, you have learned that 1 Cube = 2 Spheres and 2 Triangles AND 1 Cube = 1 Sphere and 4 Triangles You found this just by cancelling things out. You can EASILY cancel in this problem because you know that 1 sphere = 1 sphere and 1 triangle = 1 triangle and 1 cube = 1 cube. NOW you just use patterns to find out how many spheres will balance on one cube.


FIND THE NEXT ITEM IN THE PATTERN
1 Cube = 4 Triangles 1 Sphere
1 Cube = 2 Triangles 2 Spheres
1 Cube = 0 Triangles 3 Spheres

So the answer is 3 Spheres (or B) and we did that all without any math. What does that tell you? More importantly, what does that tell me? As a parent, it tells me that the Washington State Math test isn't an accurate predictor of anything! What does this question prove? I solved this question in minutes without any real math. Why is this on an Algebra End Of Course test? Hmmmm.......





5 comments:

Anonymous said...

u r so funny

Anonymous said...

actually, without knowing it you have use algebraic process and critical thinking to solve the problem.
your 1st (2-column) equation
you have:
4 Cubes + 2 Triangles + 3 Spheres
=
second column:
3 Cubes + 4 Triangles + 5 Spheres

and through ("cancellation") you ended up with the equation:
1 Cube = 2 Triangles + 2 Spheres

and so on...

Cheers,
Warshintonian


Kila Morton said...

Hi Warshintonian!

LOL - Actually, if you are finished with your answer, you are wrong.
The answer is 3 Spheres not 2 spheres. The triangles have some weight and since you aren't trying to find out how many triangles are involved, you have to get rid of those. Therefore, you have to determine how many spheres two triangles are equal to. I guess you weren't finished, but if you aren't going to put a correct answer, you shouldn't put anything because someone might see that and assume, without reading, that the answer is two spheres. You did write "...and so on..." so I will give you the benefit and say that you were trying to prove a point and didn't finish answering the question. In any case, the answer is 3 SPHERES - NOT 2 SPHERES! Here is a link to some more of the questions - http://www.k12.wa.us/mathematics/pubdocs/eocsamplebookletanswerkey.pdf.

Now, you could use substitution. The point I was making is that you don't have to. I believe that math problems ON A TEST should actually test a person's MATH skills! Reasoning is one thing, but kids need to know their hardcore math facts and being able to look at a problem like that and figure it out without a lick of math isn't a true test, in my humble opinion.
Thanks,
Kila Morton

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