Theme for the Day: Fractals

Remember my earlier post on fractals?   Well, I'm truly hopeless at this point, so I need to share my obsession.

So what are fractals anyway?

Wiki says:  a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.

Well (for the non math people like me) that basically that means layers of repeated shapes that can be calculated by a formula.  But you don't need a formula to enjoy them.  Check these out:

• Fractals in nature and even in the garden 
• Fractal art gallery on Cool Math
• Also check out the wiki link for some lovely examples

Ready to make your own?  Try these cool (free!) online generators:

• "Snowflake" style - design your fractal with five straight lines
• Cool Math has five
• Easy Fractal Generator lets you draw a Julia or Mandelbrot set (or a custom one if you are mathematically inclined) and lets you export your finished work to a file for printing.  Nice.
• This generator is similar to the snowflake one above but lets you overlap fractals and export the finished work
• Sierpinski Triangle

Hands on and fun links for the younger kids:

• this pbskids.org    project 
• The fractal foundation project
• Sierpinski Triangle color page
• Sierpinski carpet (cubes) color page
• Sierpinski gear (circles) color page
• A youtube.com search for "fractals" will give hundreds of results
• Fractal your dinner with the unusual  Romanesco cauliflower (see the details here - scroll down)
• Fractal cookies!  (Okay - a brave parent will have to help with this)
• Fractals in clay  (again better to stick with fewer iterations- repeats- with the little ones)

For the older kids and the lesson planners:

• pbs.org has a wonderful fractal lesson from Nova episodes including:
• A generator
• An article on Benoit Mandlebrot
• A fractal lesson that includes an interactive and a   discussion of fractals 
• A working video link to an interesting story about fractal analysis of tapestries
• You might notice the link to the Nova episode Hunting the Hidden Dimensions which is no longer available on PBS.org.  It is available for free on Hulu however. 

• Hoagies has some recc'd some interesting sites also.

Downloads

• A caltech worksheet for the Sierpenski Triangle. Notice! This is a word doc that will want to immediately download.
• A PDF worksheet on fractal math from fractalmath.com, advanced HighSchool+
• A PDF worksheet from Randoff College for grades 5-8
• Open Source software to download. Note: I have not trialed, so use at your own risk.
• A trial copy of (not-free) fractal software. Note:  I have not trialed, so use at your own risk.

Treehouse Part 5

And finally the completed tree house.

The Treehouse

As you can see we had a last minute addition.

The sunshade

Once all the constructing and gluing was done, Junior thought something wasn't quite right.  What about all the sun up in a tree?  What we really needed was a roof; or better yet, a canopy.  So we went digging through the fabric scraps and found a length of muslin.   But the trouble was how to fasten it.  In a burst of inspiration, Junior grabbed a handful of pipe cleaners/chenille stems and made a complicated support structure for the roof.  Then using a combination of more pipe cleaners, glue and rubber bands, we secured the canopy on.

Success.  One treehouse and one happy doll.

Close up of lower platform 

and climbing rope.

Now for lesson planning, here's what we counted.

• Art:  architecture, design, color, 
• Math: measuring,  addition, subtraction, ratios, scales
• Writing:  journaling, project planning notes, final project write up, success of plan, modifications made
• Science: structural engineering,  

 Still trying to squeeze the whole tree in one photo

Globe Genie

If you you've never heard of Globe Genie, you are missing out.  It's a neat little app using Google Street View first developed at a university and later spun into it's own site.   I don't even recall where I first ran across it, but I loved it immediately.  It can be a lesson in social studies, cultural and/or physical geography or just a really fun pastime.

Road tour of the French countryside

Road tour of the M27 near Southhampton, UK

When you arrive at the landing location, simply click all the continent boxes for the most varied journeys and click "Teleport."   Be sure to encourage "traveling"  in each destination; click down the roads, zoom in on the buildings and scenery.


You can find some ideas for building a lesson plan for this activity here.


I went for the cultural geography angle and made a worksheet with the following:




Travel to four locations. For each answer the following questions:

• Address:
• State/Country

• Describe the following: 
• Type of buildings:
• Plants:
• Animals:
• Rural/Suburban/Urban:
• Vehicles:

• What details stand out for you?
• How does this location differ from where you live?
• How is it similar?
• How far away from you?

After all four trips are taken and the questions answered, evaluate the journey.

• How do these locations differ from each other?
• How are they similar?
• Which location is the most similar to where you live?
• Which location is the most different?
• Which location is the farthest away?
• Which location is nearest?
• Which location would you like to visit most and why?

Happy travels!  How will you use Globe Genie?

Oldy But Goody

For an easy lesson on engineering and geometry the old marshmallow and toothpick towers are always fun.   We did one for cubs and used this lesson plan (PDF)with visual aids (PDF) to help us.  (This was soooo much fun to bring home intact.  We had another one, but it didn't do as well and ended up eaten. Hmmm. )