View Full Version : HELP! Fractions!?!?

02-21-2014, 06:01 PM
Alright mathies...

I am having a really hard time with Tyler (ds12) and his fractions.

He is having most trouble with mixed numbers and turning those into improper fractions and vise verse. He can do his math facts just fine and can do more complicated things like order of operations (long ones in his head!) and I think he's pretty good at geometry type problems, but for some reason, fractions totally stump him.

He's a whiz at all other math (except for word problems, but that's a comprehension issue), but not fractions, we've been working on it forever. I'll show him, he's like "oh, ok, I get it" will do a few things correct, then the next day totally forget how.

I've got cheat sheets printed to jog his memory, but he still needs me to show him all the time. Any tips/tricks/thoughts on this?? He seems to do better with the math tiles I have, so I'm wondering if I should get more manipulatives so he can "see" the fraction and not just the numbers.

Is there a curriculum out there that is great with fractions for visual and/or kinesthetic learners? I don't mind getting a whole one just for the fractions. Video's online? Anything! We use TT which is great and right now I have him doing mobymax, but for the last year, we can't get the fractions to stick!

02-21-2014, 06:11 PM
I drew pies, lots and lots of pies. Or chocolate bars. Over and over again. For every question. Then we counted the little sections one by one. (e.g. 13/6 is 2 whole pies -of 6 pieces each- and one extra piece, etc...) When I'm absolutely certain that they understand exactly what the fractions mean, then I can show them the faster "steps." For my niece, I wrote down the steps for every type of problem.

02-21-2014, 07:16 PM
Similar to Avalon, we did paper plate pizzas cut into different fractions (halves, thirds, fourths, etc.), then we worked the first few problems using the plate pieces. It didn't take too long (a few problems) for it to click w/DD. She's definitely a visual/kinesthetic learner. There are also books that use food to demonstrate the fraction concepts, and the Sir Cumference books. If he's into videos, has he tried Khan Academy? I just peeked over there and it looks like he's still got the elementary maths broken down by grade level. Ah, and we also used measuring cups (1, 1/2, 1/3, & 1/4) to do some fraction work.

02-21-2014, 07:33 PM
It can't just be converting between mixed numbers and improper fractions? I mean, the algorithm is pretty simple and it's really obvious if you understand what fractions *are* so I'm thinking he has a problem with the fundamentals of fractions.

Math Mammoth and the Key to series both have individual fraction books if you want to try a different resource and program. Both are solid programs. If you have C-rods, there's a lot of good stuff you can do with C-rods for fractions (http://www.educationunboxed.com/fractions.html). And Let's Play Math has some good posts about fractions (http://letsplaymath.net/tag/fractions/).

I think if it were me, I'd try to back up and really go through and play around with fractions again for awhile.

02-21-2014, 08:03 PM
I've seen a lot of photos floating around of people using lego bricks to show fractions. I know it's super simplistic fractions, but maybe there is something similar that you could get to work for you guys?

Using LEGO to Build Math Concepts | Scholastic.com (http://www.scholastic.com/teachers/top-teaching/2013/12/using-lego-build-math-concepts)

02-21-2014, 08:32 PM
My 12 year old "gets" fractions. She can totally tell you 1/4 of 20, but it is BECAUSE she is so visual. For her, the issues come up when she has to do the ones that she can't easily visualize.
I have had to just put the conversion into a mantra that I just repeat verbatim every time she forgets.
"Multiply the whole number times the denominator, add in the numerator, put it all over the denominator"
I had to do the same thing for my son with long division. It was really just cementing the multi-steps into their brains. :p
She did the Life of Fred Fraction book. She started it once before and was really stuck almost immediately, so we put it aside for about 3 months, then went back to it. This time it was easier, she understood the concepts, but I had to remind her of steps.
She is dyslexic and tends to have some issues with math also.

02-21-2014, 08:54 PM
I'm now convinced the biggest friend to fractions is really *getting* the identity property. If you get that, then working operations with different denominators and dealing with mixed numbers is trivial. At least that's what my 10yo says now.

Here's the punch line: the Identity property simply states that any number times 1 is that number, so x * 1 = x

How does that help? Well, 1 = 2/2 = 3/3 = 4/4 = ....

If you ALWAYS treat fraction problems with the identity property, you will get the common denominator quickly.

1) 5/7 - 3/8 = (5/7)*1 - (3/8)*1 = (5/7)*(8/8) - (3/8)*(7/7) =
[now everything is over the same denominator]
(5*8 - 3*7)/7*8 = (40-21)/56 = 19/56.

2) 2 2/3 = 2*1 + 2/3 = 2*(3/3) + 2/3 = (6 + 2)/3 = 8/3

If they really get that 3/3 = 1, then work towards wholes greater than 1, like 1 + 1 = 3/3 + 3/3 = 6/3 = 2.

Nailing the common fractions thru 1/12, and getting these principles based on the identity property is critical. No point pushing forward until they get this. :)

HTHs and good luck!

02-22-2014, 06:11 AM
I really like Key To which is extremely basic, and really breaks fractions down in little pamphlet type books (super cheap too!). These were recommended by someone as either something that works with remediated students or young students working above their level.

I'm wondering how solid his foundation is, and this could help strengthen that foundation.

02-24-2014, 07:01 AM
I and my DD are visual thinkers, and fractions as a set of rules to follow, never helped me (sounds like your son is the same way) but conceptualizing did. Believe it or not, I think Khan Academy does a good job of explaining the concepts with good visuals on their videos, for that.

Manipulatives sound like the way to go, if they work for your son. Here's a page (http://www.mathsisfun.com/mixed-fractions.html) on mixed fractions on "Math is Fun" with spatial, visual demonstrations of what each one means, and how 1 3/4 IS 7/4, with sliced pizzas for the pictures. Hoping this is helpful, because it's free.

02-24-2014, 11:56 AM
I taught fractions at least 5 times and Kearnan didn't get it. We tried every method I could think of, Khan, Saxon, the little foam fraction circles, fraction rods, legos. Life of Fred finally worked for him, he did the Fraction and Decimals and finally "got it." He is 12 and high functioning ASD. For what it is worth he really liked Khan and it has worked for almost everything else for him, but not fractions or decimals (he gets decimals just not how percents and fractions are related).

06-21-2014, 12:36 PM
Cool on the Life of Fred! We've borrowed some of that series from a friend in exchange for something of equal value we could lend them, and I like the constructivist approach much better than the algorithm approach, myself.

Another source I was tipped off about was "Young Mathematicians At Work" by Catherine Twomey Fosnot...it's a series, with one volume subtitled "Constructing Fractions, Decimals, and Percents" and I just got those in from interlibrary loan, and am looking forward to a few weeks of delving into methods for successfully supporting mathematical construction in students along the lines of Life of Fred (first needing the concept for some practical purpose, then inventing or discovering the math as a tool to solve the problem at hand, rather than being told an algorithm and then applying it until it is memorized).

We're having similar troubles with fractions making absolutely no sense, when presented algorithmically on a page.

06-21-2014, 01:52 PM
Have you tried doing the mixed fractions with adding, rather than the shortcut?

Does he understand that 2 3/4 could be written as 4/4 + 4/4+ 3/4? This concept was key to my daughter finally remembering the shortcut (multiply the whole number by the denominator and add the numerator). Once we used fraction tiles to show this concept a couple of times, and she saw that she got the same answer either way (adding it out or using the shortcut), it clicked for her.

Hope that helps.

06-21-2014, 03:01 PM
I'm going to suggest "keys to fractions" too. The keys to decimals really helped my dyscalculia son understand decimals and he had no clue before. I would have no issue buying fractions WHEN he gets there.

06-21-2014, 03:57 PM
Again, we've had success with Key To Fractions. 4 mini books breaking it down into the different operations.

06-22-2014, 05:32 AM
Math U See is good for VSLs and kinaesthetic learners, but is a whole program rather than a supplemental. DS, who is rather visual-spatial, has never had a problem understanding the concepts of fractions and how they relate to percentages and decimals, or vice-versa, but he DOES need to picture things in his mind when doing conversions. DH is not a VSL, and just *knows*, so it goes to show how different people work the same problem out in different ways, and come up with the same answer.

Sort of links back to the threads here in SHS regarding working out mathematical problems and what is "correct working out" (and indeed whether "correct working out" is necessary, so long as the working out is consistent and the answers are right).


Complete Math Curriculum for Homeschool and Small Group Learning | Math-U-See | Complete K-12 Math Curriculum (http://www.mathusee.com)

06-22-2014, 05:52 PM
Bit of a tangent, but we had an interesting journey with fractions this week. I accidentally gave DS1 simplifying fractions to do, without realising that he'd never done them before (and his division is weak, so it was a double challenge). Ended up scrapping the worksheets and doing the verbal approach ("Come and ask me when you want a chocolate biscuit and I will give you a sum to do in your head"). He still struggled, so I said "OK let's not simplify, let's complexify the fractions." He liked this because his multiplication is stronger, so he is happy to do 1/2 into 4/8 in his head etc. This week we will work on division again, then go back to simplifying fractions again. I was really interested that it was possible to break it down into small steps like this, and it made me realise how many small steps are often necessary to understand a new mathematical concept properly (rather than just rotelearning and parroting)

06-23-2014, 02:32 AM
I am also thinking going back and doing more hands on concrete fractions work with manipulatives. Maybe you can make it fun! My hunch is it would most likely be a lack of understanding a more basic concept of what fractions represent than a problem simply converting them. Good luck!

06-29-2014, 10:59 PM
Tiles sound like a great option to me. You could have one color for the top and a different for the bottom. How many groups of the bottom can you make with the top (the whole number) ....and the remainder goes on the top of the problem.

The answer is probably yes....but does he understand that fractions are just another way of showing division? It may help him if he understands this. He can set up improper fractions like a division problem...in fact if he doesn't quiet get this I would have him just convert improper factions to division. Do a page or so until he gets that it is division. He doesn't have to solve them...just set them up as division. Be sure to put that remainder "R" there too. Once he understands this, then try solving some. Or, give him some worked problems and have him set them up as a mixed fraction - a whole page if needed. You can go to this page to do this: http://themathworksheetsite.com/long_division.html Pick problems with remainders, and then print out the answer key. Have him convert them into mixed fractions. If he really understands division, he should "get" this in pretty short order.

07-22-2014, 09:33 PM
We use Math Mammoth for most things, but my daughter just was not getting fractions from MM last year. I searched around and finally found Funny Fraction Stories from Scholastic Teacher Express (I got the digital copy for $1 from their Dollar Days sale, too!). For some reason, seeing the fractions used to answer questions about the story that begins each lesson really did the trick. We ended up working through the whole book last year and she not only got it, she actually began to enjoy it.