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Where can I go to learn fractions inside-out?


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Dd is just beginning to REALLY work with fractions, and I'm discovering that I don't understand them well myself. Certainly not well enough to explain them to her -- not past walking her through the procedural steps, anyway. I never "got" fractions in school, and looking back, I think that's probably why I struggled in algebra. I want to make sure dd has a better foundation.

 

We use CLE, which is light on conceptual teaching, although there is some, and I've been able to supplement that on my own up to this point. (For other reasons, we don't want to switch curricula right now, although we will be changing in another year or so.)

 

Where can I go to get a crash course in fractions so I can make sure dd understands them? Are there resources that she and I could work through together?

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Key to Fractions starts at the beginning so you might be able to do that with your student.

 

You might also look at MEP. Starting with level 7, each chapter stands on it's own. MEP integrates the math in the primary grades more so it's hard to pick out the fractions. However, as you move along in fraction knowledge, I really like MEP starting with level 7 and up. (It's also free to download).

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This is a teacher resource, not something to work through together, but I highly recommend Van de Walle's "Elementary and Middle School Mathematics: Teaching Developmentally." I don't love every chapter in that book and I disagree with some of his overall recommendations, but the fraction chapters are amazing. There's one on fraction concepts (including the pros and cons of different models, what a fraction is, and equivalent fractions) and one chapter on fraction computation (including estimation and the standard algorithms). The chapter that connects to percents and decimals is really helpful, too. 

 

The most recent editions are very expensive, because they're used as teacher ed textbooks, but the older editions are only a penny on amazon. I've linked a cheap one above. 

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This is a teacher resource, not something to work through together, but I highly recommend Van de Walle's "Elementary and Middle School Mathematics: Teaching Developmentally." I don't love every chapter in that book and I disagree with some of his overall recommendations, but the fraction chapters are amazing. There's one on fraction concepts (including the pros and cons of different models, what a fraction is, and equivalent fractions) and one chapter on fraction computation (including estimation and the standard algorithms). The chapter that connects to percents and decimals is really helpful, too. 

 

The most recent editions are very expensive, because they're used as teacher ed textbooks, but the older editions are only a penny on amazon. I've linked a cheap one above. 

 

Thank you Kate -- this looks like a good place to start! My dd isn't really struggling with her work right now (we just started finding common denominators to add or subtract), but it's hard for me to tell whether she really understands or is just applying the algorithm. Today on her practice sheet she found the correct common denominators but kept the numerators the same. When I pointed out to her that this couldn't be correct (e.g., 1/2 does not equal 1/6), she understood, but I couldn't give her any explanation as to why she should multiply the numerator by the same number as the denominator.

 

I was a decent math student (but a much better English one!), and there is so much that I can do but not explain, if that makes sense. Hopefully this will give me some ideas. Thank you all for your suggestions!

 

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Keys to Decimals. Think of them as fractions.

 

Perhaps something like Lial's BCM for you to reference as needed rather than working through it. You can usually find older editions along with their solutions manual for $10 on Amazon (any edition will do; just make sure the image on the covers matches). It covers all the basic arithmetic one needs to be successful in higher maths.

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Keys to Decimals. Think of them as fractions.

 

Perhaps something like Lial's BCM for you to reference as needed rather than working through it. You can usually find older editions along with their solutions manual for $10 on Amazon (any edition will do; just make sure the image on the covers matches). It covers all the basic arithmetic one needs to be successful in higher maths.

 

Ok, I've got both of these so I will check them out tomorrow. Dh said I had the concepts right and the issue was just miscommunication with ds, so I feel better about the math anyway, but it is nice to know I have them handy.

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I like the free online resource - Khan Academy.  I have been working through the math programs myself to stay ahead of my son.  The videos do a good job of explaining the problems and then when you do the problems, you can ask for hints which show you the next step only...

 

We have also used Key To...series, but the Khan Academy is free!

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My mom says the MUS fractions level is terrific.  I have not used it, though.

 

Definitely Key to Fractions or the MM Topic book on fractions might work well.  

 

FWIW, I love CLE but I do sometimes have to supplement with other things to beef up the conceptual side.

 

Yes, we love CLE too. It enables dd to work more or less independently, and most of the time she does understand both the procedures and the concepts. We've tried a few other things (like BA) that were total flops for both of us, so I think we'll stick with a traditional curriculum when we switch over. We will probably go with Saxon, as the spiral approach seems to be good for her.

 

Just curious which resources you've used to supplement CLE? I think it does a decent job of teaching concepts, but I'm always anxious that we're not getting enough.

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Yes, we love CLE too. It enables dd to work more or less independently, and most of the time she does understand both the procedures and the concepts. We've tried a few other things (like BA) that were total flops for both of us, so I think we'll stick with a traditional curriculum when we switch over. We will probably go with Saxon, as the spiral approach seems to be good for her.

 

Just curious which resources you've used to supplement CLE? I think it does a decent job of teaching concepts, but I'm always anxious that we're not getting enough.

I actually find CLE more appealing than Saxon.  They are both spiral but CLE is just more user friendly for my kids.  And I mostly like how they cover the topics through Algebra 1, as well as how they review math facts all the way through 5th grade.  CLE has worked so much better for us than other math programs.  Most concepts seem to be explained well.  Once in a while, though, it makes leaps and I find we need to fill in the blanks, KWIM?  I also have to be flexible and slow down if we run into issues or cut out a lot of review if many things are mastered.

 

My main concerns have been with word problems and some specific conceptual understanding with areas such as fractions and division.  I use Math In Focus word problems to supplement some there.  I have MM plus Math in Focus and the Key to Fractions/Decimals/Percents/Metric workbooks for additional practice or supplementation.  Anything else I usually just looked up youtube videos for supplementing in division and fractions.  

 

We also use Khan Academy periodically and Beast Academy.  Best Academy we do together, as a family.  Also, the AoPS Pre-Algebra book is something DS has found interesting.  We do that on the side, also together.  He likes the thinking side of math.  He just can't do all of it on his own.  This type of math keeps him more engaged, though.

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