# Help ME Learn Fractions

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I just don't understand fraction math well enough to teach it.  Fortunately I have some time before we have to dig in, but I'd like to deepen my understanding in order to be a competent teacher.  I don't mind a resource aimed at elementary students.  I have Key to Fractions, which is fine for reviewing the procedures but didn't help deepen my understanding.  I have Life of Fred Fractions which is... bad.  Other suggestions?

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Look at Math Mammoth dark blue. I've used it for other math subjects with success.

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I've learned a lot from Elementary Mathematics for Teachers.

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I liked Cuisenaire rods for this.

Education Unboxed videos were good to start.

I like the NZmaths pages for more depth and examples - particularly for demonstrating multiplication and division with fractions.

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I havent used this, but maybe Hands on Fractions? I  really like HOE, so if the quality is equal, it should be good.

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I have liked Education Unboxed a lot for fractions.

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On 5/8/2020 at 6:22 PM, medawyn said:

I just don't understand fraction math well enough to teach it.  Fortunately I have some time before we have to dig in, but I'd like to deepen my understanding in order to be a competent teacher.  I don't mind a resource aimed at elementary students.  I have Key to Fractions, which is fine for reviewing the procedures but didn't help deepen my understanding.  I have Life of Fred Fractions which is... bad.  Other suggestions?

I would be happy to help, if you'd like to ask any questions :-).

Fractions are actually just... division. So, something like 2/3 is just 2 divided into 3 parts. I don't know if that helps right now, but that's the basics you should start with.

Do you have any specific questions?

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Along square's answer, I teach my kids fractions, ratios, percentages, and decimals all interconnect. If you think of how you can manipulate the numbers back and forth, it helps to demystify them and how numbers relate to each other.  The / line simply represents the division symbol. Percentages are a number representation of a decimal or a number divided by 100, etc. Thinking big picture and working into details might help clarify things for you.

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Posted (edited)
21 hours ago, 8FillTheHeart said:

Along square's answer, I teach my kids fractions, ratios, percentages, and decimals all interconnect. If you think of how you can manipulate the numbers back and forth, it helps to demystify them and how numbers relate to each other.  The / line simply represents the division symbol. Percentages are a number representation of a decimal or a number divided by 100, etc. Thinking big picture and working into details might help clarify things for you.

This is so true! I was taught math very procedurally as a kid, but needed to see the big picture. When I studied and relearned to be able to teach my kids the light bulb lit up as everuthing connected and it was so exciting!

Edited by ScoutTN
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Posted (edited)

I would get Elementary Mathematics for Teachers, read it, and do the suggested problems (from Singapore math).  I recommend doing all of it because it all interrelates (in other words, don't just do the fraction parts).

(If you can, you might want to keep going through Algebra 1 using a text that deals with algebraic fractions (Jacobs and Lial do), because that is a good way to really cement things, and it will make you an even better teacher of elementary math.)

Edited by EKS
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The chapters on fractions in Liping Ma's "Knowing and Teaching Elementary Mathematics" are surprisingly clear -- terrific explanations of fractional division, for example. The book wasn't really written to teach math, rather contrasting the Chinese and American approach, but I certainly learned something here.

Key to Fractions is good as far as giving a large number of different exercises, and does an OK job explaining most things, but it completely fails to explain what fractional division means - telling you how to do it, but nothing about why or when you would do it.

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Posted (edited)

I really understood fractions after working through (with my DD) this out-of-print book: Everything's Coming Up Fractions with Cuisenaire Rods by John Bradford.

I bought another used copy when my youngest was a toddler just to have around for future use. That future is now! She just finished 5th grade, so she knows how to handle fractions procedurally, but this will help her see/understand what they really mean. She’s a kid who needs things to be done in that order— learn to do it first and understand it later. I think her anxiety/ADHD contribute to this. She’s stressed out by having to ‘discover’ anything or intuit via models.

Edited by fourisenough
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Posted (edited)

This can help: RightStart Fractions

ETA: Here's a video:

Edited by ChrisB

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Posted (edited)
On 5/13/2020 at 7:58 AM, fourisenough said:

She’s stressed out by having to ‘discover’ anything or intuit via models.

For kids who do NOT like banging their heads against the wall, the "discovery method" works best when it doesn't actually involve discovering anything. Perhaps we need to relabel it the "exploring" method -- it's not that you need to invent or discover anything, per se, it's just that you need to have the freedom to study things at the same time as you're learning to calculate them.

For instance, if you know that 4*5 just means that you're taking four 5's, then you don't need to do any actual "discovery" to figure out 4*5 -- you just need to apply the definition. However, if you do this a few times, and someone points out that if you already know that two 5s makes a ten and that this may help you shorten your calculations... congratulations, you're on your way to "discovering" the distributive and associative properties.

Note that the important part is the exploring, not the discovering. However you add up those four 5's, you'll still be learning your multiplication tables. However, with some guidance, you'll discover things along the way, whenever it is that you're ready to discover them.

Edited by square_25
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Posted (edited)
On 5/13/2020 at 1:16 AM, jboo said:

The chapters on fractions in Liping Ma's "Knowing and Teaching Elementary Mathematics" are surprisingly clear -- terrific explanations of fractional division, for example. The book wasn't really written to teach math, rather contrasting the Chinese and American approach, but I certainly learned something here.

Key to Fractions is good as far as giving a large number of different exercises, and does an OK job explaining most things, but it completely fails to explain what fractional division means - telling you how to do it, but nothing about why or when you would do it.

I've posted this before, but when I read that book, I realized that I didn't have a good partitive model of fraction division! For anyone interested, the partitive model is "splitting between people": that is, 63/9 means "If we have 63 things and we split them between 9 people, how many things does each person get?" The quotative model is "how many copies of the denominator fit into the numerator?": that is, 63/9 means "How many copies of 9 make a 63?" or if you want something more analogous to the example with people, "If each person has 9 things, how many people do we have?"

Anyway, I understood the quotative model of fraction division: that is, 2 divided by 2/3 is "How many copies of 2/3 fit into 2?" But I actually didn't have a good partitive model. I had to really think about it to make sense of the partitive models that the Chinese teachers favored as models for fraction division in her book. Since I taught DD7 the partitive model for integer division, I WANTED to have an analogous partitive model for fraction division... so I actually taught myself the partitive model before teaching it to her. (If anyone wants to know, in the partitive model of fraction division, 2 divided by 2/3 means "If 2/3 of a jar contains 2 quarts, then how many quarts does 1 jar contain?" -- it took me some thought to realize that this is the same model as "splitting between people" or in this case, between jars.)

By the way, I have a fancy-schmancy math PhD and all... there's really no shame in realizing you have some conceptual gaps and rectifying them!!

Edited by square_25