Share your Fraction Interactives

Task Discussion

• 
  Maria Droujkova   Dec. 12, 2011, 8:03 p.m.

  Alex Bogomolny has a lot of material about fractions at Cut the Knot. I think we can talk to him about licensing parts of it openly:

  http://www.cut-the-knot.org/GoogleSearchResults.shtml?domains=www.cut-the-knot.org&q=fractions&sitesearch=www.cut-the-knot.org&sa=Search&client=pub-9118218894256794&forid=1&ie=windows-1252&oe=windows-1252&safe=active&flav=0000&sig=mrXM2kNh6mpIxsUL&cof=GALT%3A%23E9382F%3BGL%3A1%3BDIV%3A%23ffffe8%3BVLC%3A7E3939%3BAH%3Acenter%3BBGC%3Affffe8%3BLBGC%3Affffe8%3BALC%3AE9382F%3BLC%3AE9382F%3BT%3A000000%3BGFNT%3A7E3939%3BGIMP%3A7E3939%3BFORID%3A11&hl=en

• 
  Maria Droujkova   Dec. 12, 2011, 7:59 p.m.

  Here is a fraction video collection from Karismath. We have permission to use it, but we may need to talk about open licenses:

  http://www.youtube.com/user/Karismath/search?query=fractions

• 
  karen   Dec. 7, 2011, 5:50 p.m.

  Lots of nice examples here. Thanks for sharing, everyone.

  I'm wondering what you all think of the fractions interactives at the National Library of Virtual Manipulatives.

  I wish more of this were a) embeddable and b) open licensed.

• 
  suehellman   Dec. 7, 2011, 6:03 p.m.
  In Reply To:   karen   Dec. 7, 2011, 5:50 p.m.

  They're great if you have an internet connection, but the package for downloading and using in a 'poodle' (portable Moodle) is licensed and not free. If you use an i-frame -- you should be able to embed the applets. The instructions in the iframe in my wiki seem to work in some Moodles -- http://goo.gl/lx79U.

  I'm now looking at OER Commons -- searchable by subject, grade, media type, and degree of 'openness' (http://www.oercommons.org/)

• 
  karen   Dec. 7, 2011, 6:05 p.m.
  In Reply To:   suehellman   Dec. 7, 2011, 6:03 p.m.

  Very useful, Sue. Thanks. I think that the iframe version should work for our purposes.

  Curriki is another good place to look for open licensed content like this. The quality is sometimes variable, but there is a lot more k-12 than in OER Commons in my experience.

• 
  MrSteve   Dec. 7, 2011, 7:01 p.m.
  In Reply To:   suehellman   Dec. 7, 2011, 6:03 p.m.

  The Etoys manipulatives I created for Fractions (et al) are open source, run on free software and do not need an internet connection to run.  I have also tested some on smart boards, so kids can get a more tactile feel.

  I would be happy to work with folks to create whatever manipulatives you need.

  Stephen

• 
  suehellman   Dec. 6, 2011, 4:03 p.m.

  I came across this website today with interactives which relate fractions and music: http://www.philtulga.com/resources.html.

• 
  Steve O'Connor   Dec. 5, 2011, 10:49 a.m.

  I haven't made any inter-actives yet, but there are quite a few at the Wolfram demonstrations site (as had been pointed out by Sue). 

  In addition, if you are a K12 or community college teacher, Mathematica is available for $49 through this link. While I barely scratch the surface with the software, it certainly is worth every penny.

• 
  Linda FS   Dec. 5, 2011, 3:50 a.m.

  I am sharing 2 interactivities - one I created in 2007 and the other I adapted from someone else in 2009 (I never could contact him). 

  InterActivity 1: Comparing Fractions

  InterActivity 2: Simplifying Fractions

  I will start the critique myself.

  I1: This is so old and has such an uninviting appearance and non-intuitive interface.

  I2: Definitely don't like the way the numerator and denominator are both horizontal sliders. At minimum an easy fix would be to make the denominators into vertical sliders and use 4 colors (instead of 2).

  Please feel totally free to critique and give suggestions or link to what you think are better interactivities.

  BTW: They are both related to this conversation: http://p2pu.org/en/comments/8571/ with Steve O'Connor about Common Core Standards.  I am thinking that simplifying fractions must be done visually at first (although I do not think that I2 is good enough for this). Probably we need a whole thread just for "simplifying fractions".

• 
  suehellman   Dec. 5, 2011, 9:59 a.m.
  In Reply To:   Linda FS   Dec. 5, 2011, 3:50 a.m.

  1) Linda --  would you share those geogebra files with me so I can download please?

  2) I was struck by a remark you made in another thread that you avoid fractions and try to use decimals where possible. I see that bias in your first applet. I'm not sure that trying to get students to strengthen their understanding of how the comparative sizes of different fractions by comparing them to decimals is going to make the fractions more mearningful. To me decimals tend to be  strings of numbers whereas fractions are more 'thinkable' units.

  An approach I might find more usefbul is to use 0, 1/2, and1 as signposts. I think I want my kids to be able to estimate a new fraction in a more general way -- in terms of its proximity to one of those markers.

  1) How can you describe (verbally) 1/2 in terms of the markers 0, 1/2 and 1 (shown on a number line)?

  • e.g. between 1 and1/2

  2) Can you be more specific?

  • closer to 0?
  • closer to 1/2?
  • a little more than 0?
  • a little less than 1/2?

  How (intuitively) do you know that? How (mecahnically) could you show it?

  2) if the space between 0 and 1 is divided into fourths, where would you put 1/3 now?

  • less than 1/2 but more than 1/4

  How did you make that decision?

  I think this leads later to comparing fractions & percentages than then to bringing in decimals as well.

• 
  Linda FS   Dec. 5, 2011, 12:47 p.m.
  In Reply To:   suehellman   Dec. 5, 2011, 9:59 a.m.

  Haha Sue,

  I told myself - get your work done Linda and you can come back to play here - but no, Sue asks me a fascinating question which I interpret as: "Why do I like decimals bettter than fractions?"  And I think and think. I got it! 

  It is not that I like decimals better than fractions, since I will always say 1.3 means you go "about 1/3 of the way between 1 and 2" so I am actually speaking in fractions.

  But decimals (a) always give me approximate values to judge my result, that is they immediately tell me where I am on the number line, (b) they limit the "amount" of fractions I must think about by restricting the denominator to 10,100,.... and (c) they match up perfectly with percents.

  I will get the ggbs up asap.  Here is a different interactive which actually uses fractions incognito (you need to solve one example): http://www.geogebratube.org/student/m858

   

• 
  MrSteve   Dec. 5, 2011, 1:14 p.m.
  In Reply To:   suehellman   Dec. 5, 2011, 9:59 a.m.

  numbaland.com has some great games for giving kids experiences in estimating fractions. 

  It is a lot like the darts game in Plato from back in the 70's with updated graphics.

• 
  MrSteve   Dec. 5, 2011, 3:42 a.m.

  Okay having created a Task (hope folks don't mind) I decided to share one.

  Here is the blogpost (video below)

  http://www.youtube.com/watch?v=xG9_v8j_HPM

  Commetnts, suggestions, criticisms welcome (espcially the how to improve kind.

  The interactive was created in Etoys (free, runs everywhere - PC, Mac, Linux, XO)

• 
  Linda FS   Dec. 5, 2011, 3:54 a.m.
  In Reply To:   MrSteve   Dec. 5, 2011, 3:42 a.m.

  Oh what great fun and how visual. I will watch it again and comment more - I must go to work. But I really like the idea and interaction (and I have a little OLPC with Etoys too).

• 
  suehellman   Dec. 5, 2011, 9:39 a.m.
  In Reply To:   MrSteve   Dec. 5, 2011, 3:42 a.m.

  Steve -- as a teacher I definitely like the ability to use this tool to explore different ways to get the same result.

  But from the point of view of a confused student, how does overlapping the 2 fractions replicate  the multiplication process? Why does the intersection of the horizontal and vertical regions show the anwser? Can a similar process be used to illustrate 3x5 (3 groups of 5)? How does this get me from what I know to the new understanding?

  There is a similar animation in the Wolfram Demonstration Projects at http://demonstrations.wolfram.com/MultiplyingFractions/ (will need to download the free player to manipulate the applet). [PS I've been playing with it . Although the values show that 0x1 = 0; the shading would seem to illustrate that 0x1=1 Hmmmmm]

• 
  MrSteve   Dec. 5, 2011, 1:10 p.m.
  In Reply To:   suehellman   Dec. 5, 2011, 9:39 a.m.

  Sue, you asked:

  How does this get me from what I know to the new understanding?

  Excellent question.  My guess is it depends on what experiences they have had before and what mental models they have in their heads.  Well, assuming they have been exposed to the Area Model of multiplication (will post a project later) they could make the connection.  I will need to think about this some more, suggestions welcome.  

  I tried the Wolfram Alpha project, I like the use of sliders (vs up/down arrows)  would be good for a touch interface.  Also a good observation about the visually confusing 0x1.

  Also I think its important for kids to know things multiple ways, so I will also build/share another view of multiplying fractions later.

• 
  MrSteve   Dec. 16, 2011, 11:46 a.m.
  In Reply To:   suehellman   Dec. 5, 2011, 9:39 a.m.

  Sue,

  Here is a derivation (and visual proof) for multiplying fractions (courtesy of Alan Kay). To help answer your question "How does overlapping the 2 fractions replicate the multiplication process" and why invert and multiply works (without using Algebra).

   

   

  I am working on re-rendering this explanation in a way that kids can interact and play with it and ideally scaffolds them towards coming up with the proof.

  Suggestions and comments welcome.

   

  Stephen