# Best resource for *understanding* fractions?

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I'd like some suggestions for resources for having a good understanding of fractions. My dd does really well with pictorial examples and hands on when it comes to really grasping a concept. I'm having a hard time explaining the whys of fractions. They are finding it easy to solve the problems, but having a hard time understanding why it works. For example 1/2 of 8 = 1 x 8 over 2 = 4. They can get the correct answer no problem, but can't understand why that works.

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Lakeshore Learning has great sets of fraction, decimal, and percentage bars that are color coded to match each other and have equivalent and proportional sizes. They are very helpful with conversions and with addition and subtraction.

For multiplication and division, "of" always means 'times' in fractions. Always. Multiplication goes straight across, top and bottom. And you never divide, you invert and multiply. That's all you need to know for those.

You can demonstrate this more easily with measuring cups--1/8 cup, 1/2 cup, and 1/4 cup.

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The first thing is long division. Gotta have that down - we did Saxon 5/4, 6/5, and part of 7/6 and got really good at long division. My dd also did LoF Fractions and MM Fractions from the dark blue series over the summer. MM Fractions has good pictorial and textual explanations. We did a MM geometry that also used lots of fractions which my dd enjoyed. Kitchen Table Math ( I forget which volume it is covered in) will give you a good explanation for different parts of fraction understanding and how it relates to other parts of math.

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visualfractions.com

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I love the fraction towers and fraction circles. I picked up mine at ETA Cusienaire when they had their big sale going on.

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Lakeshore Learning has great sets of fraction, decimal, and percentage bars that are color coded to match each other and have equivalent and proportional sizes. They are very helpful with conversions and with addition and subtraction.

For multiplication and division, "of" always means 'times' in fractions. Always. Multiplication goes straight across, top and bottom. And you never divide, you invert and multiply. That's all you need to know for those.

You can demonstrate this more easily with measuring cups--1/8 cup, 1/2 cup, and 1/4 cup.

I'll look into those. :)

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The first thing is long division. Gotta have that down - we did Saxon 5/4, 6/5, and part of 7/6 and got really good at long division. My dd also did LoF Fractions and MM Fractions from the dark blue series over the summer. MM Fractions has good pictorial and textual explanations. We did a MM geometry that also used lots of fractions which my dd enjoyed. Kitchen Table Math ( I forget which volume it is covered in) will give you a good explanation for different parts of fraction understanding and how it relates to other parts of math.

They have done long division, but we are just starting MM division to review. I do have LOF Fractions (they're on ch 3) and MM fractions. So maybe I should have them do MM division and then MM fractions and LOF Fractions, or MM division and MM fractions simultaneously, the LOF Fractions? I'll see if my library has Kitchen Table Math.

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visualfractions.com

I like this :)

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I love the fraction towers and fraction circles. I picked up mine at ETA Cusienaire when they had their big sale going on.

I do have the fraction circles, but I'm not sure how to make them useful?

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Lakeshore Learning has great sets of fraction, decimal, and percentage bars that are color coded to match each other and have equivalent and proportional sizes. They are very helpful with conversions and with addition and subtraction.

This sounds sort of like the Math-U-See

that I've heard really good things about. (Is it Cathy Duffy who really liked them?) I'm not sure how you'd use them, though--we're not there yet!
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I do have the fraction circles, but I'm not sure how to make them useful?

I was just quickly looking online to see if anything popped up. For my fraction towers I picked up this neat deck of cards that have games to play with the towers. I was hoping that the circles had some similar instruction or game options. I'll keep looking though.... something is bound to come up.

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Pizza!

for reals, it finally sunk in.

I offered them 1/3 of the pizza or they could have 1/8 of the pizza

at first they wanted 1/8

once the realized the bottom was how many pieces...and that 8 parts of 8 is still one pizza

it was fun...and we can now just draw the picture of the pizza to reinforce...

we kept at it, then moved to measuring cups.

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For hands-on we use the RS Fractions chart.

For worksheets we have used MM Fractions 1 and Key To Fractions (along w/ work in our regular math programs).

I think the best way to learn fractions is to work with them intensely for a few months. We did a 'fractions camp' this summer and dd8 had them mastered after focused study. She loves LOF Fractions. Reads it constantly.

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Excellent: Guide to Everything Fractions

I did notice a typo, p.9 (and where there's one, there may be more), but this is a very thorough set of lessons to help you really understand fractions -- and you can't beat the price!

Also extremely good: Division of Fractions

Starts with a review of dividing whole numbers, and then applies this to understanding why fractions work the way they do.

Test your understanding: The Frustrating Fractions Quiz

If you can explain the answers to these questions, then you truly understand fraction math. (Answers are in the comments below the post.)

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Thanks for those links, letsplaymath. Oldest boy needed a little boost in fraction land today...:)

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Pizza!

for reals, it finally sunk in.

I offered them 1/3 of the pizza or they could have 1/8 of the pizza

at first they wanted 1/8

once the realized the bottom was how many pieces...and that 8 parts of 8 is still one pizza

it was fun...and we can now just draw the picture of the pizza to reinforce...

we kept at it, then moved to measuring cups.

I was going to suggest apples :)

I think there's something about dividing a real whole into parts that helps.

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Do you have the Singapore 4A Standards edition Home Instructor Guide? Is has a great explanation and several physical examples, I liked how they had your student cut up pies and give them out.

Edited by ElizabethB
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visualfractions.com

thanks! That's a good one!

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Do you have the Singapore 4A Standards edition Home Instructor Guide? Is has a great explanation and several physical examples, I liked how they had your student cut up pies and give them out.

:iagree:

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