## Tuesday, November 6, 2012

### Fraction Equivalence

Kal-El continued his fraction equivalent work today.

He discovered all the equivalent fractions for 1/2, 1/3, 1/4, 1/5.  Afterward, I formed some equivalences with the cards, fraction bars, and equal signs and had him solve for a missing numerator on one side or another.  Tomorrow I think he will start recording his work in his fraction notebook.  You can see Me Too hard at work in the background.

I put together a work Me Too has been begging for, spooky cards and counters.  Ideally the counters in this work should all be the same size and color, but when you mastered this work more than a year ago it doesn't matter anymore ;)

I have spent many, many hours this week creating all of the prepared equations for the fraction works.  These are simply not for sale anywhere, except perhaps Nienhuis.  I have finished all the slips for equivalence, addition with like denominators, and subtraction with like denominators.  I WILL be sharing my work when I am finished.  It won't necessarily be pretty, but it will be available.

Can anyone share how their kids record their fraction work?  What kind of paper?  What format?  I would love to see some images if possible.

Also, does anyone have fraction research charts that they can scan and e-mail me?  The ones I've found for sale are \$30.  I don't want to spend that much on three sheets of paper.

Finally, if you have time please vote for me today for the Homeschool Blog Awards.  My category is Best Homeschooling Methods Blog 2012 .

1. If you mean these ones:
http://www.nienhuis.com/en/fraction-equivalent-research-sheets.html

I have never seen them in use - ever ;) But I think the school I visit every Monday might have them (seems like I have seen them there). I can ask about them if no-one finds you anything in the meantime.

This is one area that I did bring in some work-sheet style work for my son just because I couldn't come up with numbers on the spot that particular week - (that's essentially what these charts become anyway, with the pad of 50 of each). After that he made up his own numbers and I just worked with him on the tough ones; OR would say "let's save this one for another day."

I have some of the fraction work in files too - I should have posted those long ago! Oops! Maybe yours look better than mine ;)

2. Jessica,

I was thinking of having one research sheet on hand in their fraction notebooks as a "control chart" or something like that.

I guarantee my files won't look better than yours. They look awful until I got to the last subtraction presentation. (So, all of addition and subtraction look awful and multiplication and division will look pretty good.) Ack. That would have saved me at least four hours of work so far...I guess the six hours cutting and laminating would have still happened.

I only use open office and Google docs for word processing. Open office won't let you size the fractions big enough. Google doc doesn't have columns and the fractions aren't enabled in a spreadsheet. When I was facing typing in the 308ish equations for the last subtraction presentation I realized I could create a table in Google docs. Thank goodness, those 22 pages look pretty good.

Do you have multiplication and division files?

Also, I've only done like denominators and equivalence so if you have the mixed denominator equations I can skip making those from scratch too.

3. http://montessoritrails.blogspot.com/2012/11/fractions-in-lower-elementary.html

Some samples and one file for you :) It is essentially just equation slips like we have for the whole numbers - every possible "simple" combination should be included (should be! let me know if I missed any!).

I really don't feel comfortable at all sharing the elementary file yet, with the mixed equations, because it is THAT sloppy. And I had started to compare it to the main requirements, to be sure all skills were basically covered, but time got away from me. ;)

4. Thanks Jessica!

Now, you brought up my other burning question. You said "every possible 'simple' combination should be included.

I wound up buying the Montessori R&D album for fractions JUST for the pages of prepared equations after each presentation (I know, I have a problem). The LAST presentation for subtraction says "Have prepared slips with all possible equations for each of the following formats (I'll use "x" for the blank spots):

x/5-3/5=2/5
5/5-x/5=2/5
5/5-3/5=x/5
2/5=5/5-x/5
2/5=x/5-3/5
x/5=5/5-3/5

I've already made a file for these. However, I wondered...does the child complete ALL of these equations or does he do enough to demonstrate understanding and move on.

Also, the Cultivating Dharma album has the child reduce fractions right from the beginning of Addition with like denominators. MR&D doesn't introduce it until the second fraction album (after like denominator work for all four operations, but before unlike denominator work for all four operations). Your album doesn't specifically say. It mentions that the equivalence work prepares them for reduction. The fraction charts always end with a reduced fraction. But, the album doesn't seem to specifically say when you start requiring them to reduce the fractions.

I was HOPING that if Kal-El was supposed to do all 308 equations for that one presentation that we could at least speed it up by letting him fill in the blank with a dry erase marker rather than copy the whole equation in his fraction notebook. BUT that will not allow him room to reduce the difference.

BTW, thanks for you post on your blog. Exactly the type of thing I wanted to see. Today Kal-El worked with a notebook I made from 1/2 inch squared paper. I printed a light blue version so that he could put the numerator and denominator in their own boxes (that's how big his handwriting is right now) but I wanted the fraction bars and operators to show up against the grid if you know what I mean. I showed him how to decorate between equations.

5. Yes, the ones you listed are the "elementary" version - with changing up the places and formats. Hence my time slipping away ;)

I don't worry about all of them - enough to master the concept; then there are children who want the challenge!

For writing them out, what I have always done is to have the child work with the material, find some answers; when ready for the writing stage, select 5 (or so) to be written out, with the expectation that more are done. My son would would do 2-4, then choose a "favorite" to write down. Since he had the slips there, he could remember what he had already done. For the elementary version of the slips, I had printed some out, then mostly just made up ones up for him, or had some work-sheet style pages I pulled from the internet (I know - anti-my-own-albums ;) ). He would copy out the ones he wanted to write down. This way, the children are working a lot, still writing some - getting the best of both worlds without having to slow down just TOO much for the writing. He ended up working through everything I had, simple or otherwise, but didn't write it ALL down.

For writing out the equations that need to be reduced --- I would move to larger squared graph paper, so there is plenty of space for writing larger, but still space for the reductions. You can get it 3-hole punched or just punch it at home; then those folders with the three-prongs in them are 15 cents in August at Meijer or similar stores - and work great for storing favorite work. (we put the sheets into the pocket then every couple of weeks (supposed to be every week when we check work plan, but well....) choose which ones to go into the prongs themselves.

Reductions - wherever they make sense to move into. Some children love it right away; others needs to wait a bit. My son discovered it on his own (because he already knew equivalencies) - others you have to ask, "Hm. Does this look equivalent to a fraction that would use fewer pieces?" And yes, that is where the charts come in handy - because they point out concepts that don't have specific presentations - something for the children to discover (sometimes with our fingers pointing to it ;) )

I'll go see if I can clarify that in the albums ;)

6. Thanks! That answered my question!

Yup, I own a comb-binding machine so I made my graph paper pages each half of an 8/5x11 so there is plenty of room for reductions. He loves doing equivalences in his head, so I predict he'll like it (on and off)

7. I guess what I'm hearing you say though is that the child WOULD complete all of the basic equations?

8. Yes - *probably* - but they would not all have to be written down is all. And if they don't all get done but is obvious the concept has been mastered - move on! ;)

I just had an image of Maria Montessori standing over a child with the fraction work, holding a whip. "You must do them ALL! Bwahahaha!" We know that wouldn't happen, so I'm not sure where that came from ;) (sleep deprivation... aha!) ;)

9. Maria with a whip, what are you doing to my mind?

10. Where did you get your fraction circles and did they come with the trays or did you purchase them separately? If separately, which did you order? Thinking of splurging on these as they will get used by both kids eventually and will make learning about fractions much more tactile. I have homemade paper circles, but I don't think it is the same.

11. GWPT,

I hope to post about our fractions materials tomorrow! I know I need to post all about the trays and what's on them. Stay tuned!

12. I love ALL the fraction works your boys doing!! NICE WORK!!! THANKS for share it!!! and of course your wonderful ideas!!