Fraction a Day 17 - Sample Fraction Images

Kids would use cuisenaire rods to answer these questions:

Should add "if your unit is" after "1/2"

Fraction A Day - Day 16 - Rational Number Project

Started reading things from the Rational Number Project.  Two things I like from my initial readings:

"Children learn by having opportunities to explore ideas in these different ways and by making connections or translations between the different representations.

Image from Page 4 of their report

Thinking about how we can encourage and foster those connections seems very worthwhile.

I also liked the style of their assessment questions, where they ask the students to show how they would do a problem on the number line or using decimal boards or grids.


I was surprised when they said:

"that of all the manipulatives available for teaching about fractions, fraction circles are the most effective for building mental images for fractions."

Because by William Clevland (The Elements of Graphing Data) should that Pie Charts were the worst form of information graphic, because people had a hard time comparing area.  Cleveland's research had showed that horizontal lines were best for facilitating comparisons.  Of course it may be that children have more experience with Fractions in their Pizza and Cake form, so for them fraction circles make sense. Me I personally prefer the chocolate bar form ;)

Fraction A Day - Day 15 - Multiplying Fractions

Today I worked on an are model for multiplying Fractions in Etoys.

I created two transparent playfields one with gridding set to 30@300 the other set to 300@30. Then placed and resized rectangles within the playfield.  The created a simple "Multiply" script to move the one playfield to the left (I changed the forward direction to move left, try it, it won't rotate, there is another method, like most things ;) until it overlapped the first playfield.

I have been spending too much time in Etoys trying to do things, rather than simply think about what I want to do, then figure out how to realize it in Etoys.  I hope to spend the next few days looking at other manipulatives and thinking about how to design my own, so that they are simple and fun for teachers and kids.

I also need to think more about fractions and the operations using fractions.  If I find time I will head to Rutgers to check out the Robert B. Davis archives.

Fraction A Day - Day 14 - Numbaland

Check out Numbaland its Battleship Numbaline is a great program that reminds me a lot of the early Plato program Dart (Designed by Sharon Dugdale and David Kibbey 1975) as part of a program at the University of Illinois.  Plato was also used as part of the Madison Project.  It is discussed in chapter 3 of Cynthia Solomon's excellent book "Computer Environments for Children"

Fraction A Day - Day 13 - Randy's Polygon Challenge

Today we are lucky to have a guest Fraction from Randy Caton.  Randy has taught introductory and advanced physics courses and laboratories to classes ranging from 5 to 700 students and has used Peer Instruction and Just-In-Time-Teaching for 30 years. He has directed several science education programs for teachers and students from 1986 to 2008. He is currently retired and lives in northern Minnesota. Randy has used Etoys to develop web-based activities for NASA programs and physics courses.

Randy created a wonderful polygon challenge where kids modify a script and the number of vertices in a polygon to create and discover beautiful things.

Part of what I like about Randy's approach when designing lessons (at least what I can tell from seeing some of them), is that he has the kids discuss the ideas, predict what is going to happen, try it, then record what they observe.



Maria Droujkova of Natural Math joined us for our meeting today and had a wonderful idea to go along with this where the kids are the polygons.  She uses kids as vertices and yarn or rope as the sides.  See images of Maria in action with some parents and kids below:



Our goal is to come up with a set of materials so that teachers, parents and kids can use these activities to explore and learn.  One of the goals for the materials will be that "anyone" can use them, to run these activities and the fact that you are not a mathematician (Maria) or a rocket scientist (Randy worked with them) will not hinder you from using and getting a lot out of the materials and lessons.

Randy's project can be found here Polygon Challenge 1

Fraction A Day - Day 12 - Esteban's Fraction Cutter Design

So I asked the question, how would you create a program to "cut" the polygon in half so you have two polygons and can separate them (similar to Slice It!).

One person asked can we use the slope (she had been studying slope).  I responded its natural to use what you just learned and what you know and its wonderful when it works.  Can anyone think of another way?

Then Esteban suggested:

"You fill the square with little turtles until it all fills up. Then you count how many are on each side to get the percent."   

(this was for the part of the game where it reports the fractional parts as percentages.)

I asked then said that's an interesting idea, how could you tell which side of the line a turtle is on? To which he responded:

"So lets say ou have a tool that measures color and a tool that measures distance. then you merge those tools and make a script that sees two colos and measures the distance between them and from that you can say, what if I do it to measure the whol box and have that tool tell you the area of something.

I then asked: How would you program that?

"Take two basic tools and build a script that uses both of them then build a script that uses two other basic tools, then combine them and keep going so you have like a ladder to the ultimate goal."

 Now, I ask myself, what basic tools could I provide that kids could use to build a "slicer" script.  Dr. Geo and Geogebra come to mind (thanks Karl for the idea).  I like the idea of Dr. Geo (not only because a version is embedded in Etoys, but it allows you to script).

FYI, I already have figured out a way to do this (I think) just have not had the time to program it.

Fraction A Day - Day 11 - Classifying Fractions

This post was inspired by a paper simply titled Fractions  on the  site.

In the paper they had a section titled "Classifying Fractions" and which had an image similar to these I created from my Etoys project:


Changes that I plan to make to this (or volunteers who want to join the team can make, hint, hint, nudge, nudge, wink, wink, you'll get free Etoys training!!!) include:

• embedding visual fractions (which could be easily made with other tools from this project)
• embedding pictures of fractions kids find in the "wild"
• animated feedback options when they properly and improperly classify

One goal of this project is to make it easy, for teachers and kids, to create content.  So if you have a lesson idea you would like to create let us know we'd love to have you (plus your lessons might be used by kids around the world ;)