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How can I explain this to a third grader (a math question)

episodic

episodic

Lifer
Helping a relative help a kid with his math homework.

Question:
If you have an equilateral triangle and one side measures 5 inches, how many similar triangles with a side length of 1 inch will fit inside of it?

WTH for a 3rd grader!

Well I took the triangle and bisected it forming to adjacent right angles, the applied the pythagorean theorm then used the area formula for the big triangle, then did the same for the little triangle and got the answer - but how to I explain that to a kid that barely knows through his 9 times tables?

There was no ruler and no manipulatives available and this was on the kid's test.
 
make shapes

cut out the small triangles and stuff them into the big triangle

then he can take them out and see the relationship

like paper triangles, cut them out of paper
 
Make it a visual thing. If you have to, draw it out for him. Unless he's in some sort of accelerated program, I don't imagine that they're dealing with the pythagorean theorem just yet.
 
Originally posted by: FoBoT
make shapes

cut out the small triangles and stuff them into the big triangle

then he can take them out and see the relationship

like paper triangles, cut them out of paper
Click to expand...

I thought that as well, and probably should have put this in the OP. This question was on the kid's math test, and no manipulatives were available.
 
Originally posted by: otispunkmeyer
you could do it by drawing it to scale

and then drawing the smaller triangles in side and then counting them?
Click to expand...

The kid had no ruler during the test.
 
For a 3rd grader?!? I was still learning cursive in 3rd grade... not geometry! If kids are getting started on HS material in 3rd grade... how are they failing the exit exams?? I don't know how to dumb this down to a 9-year old's level, except for maybe drawing pictures. Draw a big triangle thats 5 units on each side; then pile 1 inch triangles inside it. But from a more advanced view, I realize that it would intuitively be 25 because that's 5 squared. Or triangle'd in this case.
 
Originally posted by: giantpinkbunnyhead
For a 3rd grader?!? I was still learning cursive in 3rd grade... not geometry! If kids are getting started on HS material in 3rd grade... how are they failing the exit exams?? I don't know how to dumb this down to a 9-year old's level, except for maybe drawing pictures. Draw a big triangle thats 5 units on each side; then pile 1 inch triangles inside it. But from a more advanced view, I realize that it would intuitively be 25 because that's 5 squared. Or triangle'd in this case.
Click to expand...

Yea, the answer is 25 - but how to intuit that to a 3rd grader. I'll try drawing pics, but I'm not sure I can draw a triangle to scale without a protractor or ruler.
 
yay for a teacher trying to advance our kids to a more appropiate level for their age 😀 heck if the asian kids could do this by 3rd grade why not ours?
isntead of bitching teach the kid the pythagorean theorum and have him 0wn the teacher next test time 😉
 
Originally posted by: dullard
1+3+5+7+9 = 25.

What is hard to explain about that?
Click to expand...

Sigh, have you dealt with many third graders. There is alot of theory there. There is the assumption you know patterns, odd numbers, properties of triangles, similar figures, etc.

Although, this is a pretty good explantion that may get me by with his parents 🙂

 
Originally posted by: Drakkon
yay for a teacher trying to advance our kids to a more appropiate level for their age 😀 heck if the asian kids could do this by 3rd grade why not ours?
isntead of bitching teach the kid the pythagorean theorum and have him 0wn the teacher next test time 😉
Click to expand...

I started to try and asked him if he knew what squared meant, and he told me doesnt that mean a nerd?
 


That makes no sense--- most 3rd graders aren't even taught what an equilateral triangle is-- much less calculating area.

I think the question you posed is best answered by the teacher who gave this test in the first place-- maybe they have a really good answer for why a 3rd grader would or should know this.

 
Originally posted by: episodic
Sigh, have you dealt with many third graders. There is alot of theory there. There is the assumption you know patterns, odd numbers, properties of triangles, similar figures, etc.

Although, this is a pretty good explantion that may get me by with his parents 🙂
Click to expand...
For me, I was doing independant study math through much of elementary school since my teachers couldn't satisfy my needs (my dad taught me algebra in the summer between 1st and 2nd grade). Thus, maybe I overestimate 3rd graders. I just think far too many of them are underestimated.

I keep drawing bowling pins when thinking of this problem. I was a bowler at that age, and I could draw 1, 2, 3, 4 pins in that pattern. All this problem does is add a 5th row. Then connect the dots and count them up. But maybe that is beyond the typical 3rd grader's ability. Sorry, I cannot help.
 
Originally posted by: dullard
Originally posted by: episodic
Sigh, have you dealt with many third graders. There is alot of theory there. There is the assumption you know patterns, odd numbers, properties of triangles, similar figures, etc.

Although, this is a pretty good explantion that may get me by with his parents 🙂
Click to expand...
For me, I was doing independant study math through much of elementary school since my teachers couldn't satisfy my needs (my dad taught me algebra in the summer between 1st and 2nd grade). Thus, maybe I overestimate 3rd graders. I just think far too many of them are underestimated.

I keep drawing bowling pins when thinking of this problem. I was a bowler at that age, and I could draw 1, 2, 3, 4 pins in that pattern. All this problem does is add a 5th row. Then connect the dots and count them up. But maybe that is beyond the typical 3rd grader's ability. Sorry, I cannot help.
Click to expand...


Actually, that is an excellent idea, and does not require a high level of precision. Thanks! I'm not a creative math genius. I went through calc II before I changed my major to philosophy/minor in computer sci.


 
Originally posted by: NatePo717
damn in 3rd grade I was doing my multiplication tables....
Click to expand...

In this school he goes to, they sent a letter home to parents telling them to teach the kids tables themselves, as they did not have time to teach that.
 
N00bs 😛. I'm homeschooled and I was doing this stuff in about 4th grade. 3rd seems a bit early, but yeah this is what I was doing around that age. (I started a year early too, so when I was in 4th grade, I was about the same age as 3rd graders. I'm in 9th grade now FYI.)

EDIT: And in case you're wondering what I'm doing now in math, I'm finishing up radical equasions. (you know, the ones with the square roots that need divided and stuff 😀). That's not to mention that I have built about 3 computers, and keep up all of the computers in the house, and know c++, and know how to do 3d modeling, and know... 😀
 
Originally posted by: TuxDave
Maybe the teacher was trying to isolate the gifted students with that question?
Click to expand...

Here is the rest of the quiz. . .

1. A right triangle has three angles, one measures 50 degrees, one measures 40 degrees, what does the third angle measure?


2. An angle named "H" is 51 degrees and is vertical to an angle named "G" - what is G's measure?


3. Draw two parralel lines cut by a transversal and shade really dark 2 alternate exterior angles.

4. Draw two adjacent complementary angles, then draw two adjacent supplementary angles.

5. What you've already saw.
 
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