A brief history of me:
So, usually I teach older students -- freshmen in high school through college kids. That's worked out really well for me, during the school year when lots of college students needed help. Unfortunately, it's summer now. My main job working as a backstage tech at the Chandler Center for the Arts had no calls for me to work, so I was dead broke, needing to pay rent and be able to eat. That's when I really started to use my good star rating to my advantage. :)
I ended up contacting somewhere around thirty students who asked for tutoring! Right now I tutor six students (seems like more to me xD ) and spend as much time tutoring as I do driving to meet those who I tutor. Anyway! So whilst student 1, student 2, and student 3 needed help in GRE prep, Geometry (HS), and College Anatomy respectively, students 4, 5, and 6 were a bit of a scene change. They needed help with elementary math.
Students 4 and 5 are both girls in the fifth grade, unfortunately for me, it seems that neither of them know how to do fractions.
I tried these methods already:
Okay, so we sat down looking at learning how to simplify fractions, how to change fractions to decimals and back, and how to multiply by decimals. Here's how the lesson went:
1. Prime factorization method -- Look for all of the numbers that multiply to get the top of the fraction and the bottom of the fraction (so, 125 = 5*5*5, and 1000 = 2*2*2*5*5*5). Then, look at what is the same on the top and the bottom, you can cross those out. So 125/1000 (5*5*5/5*5*5*2*2*2) could be simplified down to 1/8 (1/2*2*2). This method will always work with big numbers. So, you get how to do it, but you don't understand why it does that nor why something like 25/100 would be 1/4.
2. Chocolate bar method -- if this chocolate bar has ten pieces and one extra piece. The whole chocolate bar is one, and the extra piece is one tenth because it's one piece out of ten pieces to get to the whole chocolate bar. Okay, getting closer, but not quite there yet; still having trouble understanding how to look at different number of fractions like 2/10 or 3/10, not even close to understanding why 2/10 = 1/5.
3. Pie method -- so, say you have a pie, cut into four slices. You see how if you take two slices, you have taken half the pie? Maybe kinda sorta, still not getting it.
4. Paper method -- This has a lot of sub-steps; this is what I suggested you do with her at home with 1/3 as a starting base.
A. You see this piece of paper, this is a whole.
B. -tear paper in half hamburger style- okay, so what fraction is this. It's one half, so you need two halves -demonstrate- to make a whole, right?
C. -tear one of the one half papers in half- so what fraction is this? It's one forth, so you can see -demonstrate- it takes two fourths to make one half. How many fourths does it take to make a whole?
D. -tear one of the one fourth papers in half- repeat questions with 1/8 to make 1/4, 1/2, 3/4, and 1 whole.
E. -tear one of the one eighth papers in half- repeat questions with 1/16 to make 1/8, 1/4, 1/2, 3/4, and 1 whole.
F. -tear one of the one sixteenth papers in half- repeat questions with 1/32 to make 1/16, 1/8, 1/4, 1/2, 3/4, and 1 whole.
G. Need to change up the fractions that I did it with, including parts of fractions like how many 32nds does it take to make 3/16ths.
She seemed to understand that well...
5. The number line -- from there, we took all of the fraction pieces (1/32, 1/16, 1/8, 1/4, 1/2, and 1 whole [I also made a 1/5 and a 1/10]) and arranged them from biggest to smallest. Then drew a line on down the middle of the paper with one half for fractions and one half for decimals. I wrote down the fractions in order leading up to one, then I had her use the calculator to find the corresponding decimal. Next time, I think I'm going to have her find the corresponding decimals by hand, that way she can see why it works (I hope).
Does anyone else have a better suggestion? aka HELP :(