Work on the Nature Trail

Here's an album of us collecting items on the Nature Trail for our Journey Sticks.

http://picasaweb.google.com/thirdgradestonypoint/Trail#

Make sure you get to see the slug and little green frog!

Journey Sticks

      In many ancient cultures (e.g. Australian aborigines) recording an event takes place in several different ways such as songs and stories, dance, drawings or tokens. In many countries people have developed the idea of creating a journey stick to help them tell the story of their journey to others. It involves tying objects and colors to a stick that represent different experiences, feelings or parts of the journey.

When Australian Aboriginals went on their journeys they collected things and tied them to a stick in chronological order. After a long time they finally returned to their people. Referring to the objects attached to their stick, they were able to remember their journey and recount the stories. This formed a verbal map which described the journey to someone who wasn’t there. It was a very personal way of recording their journey and unlike a map, there was no right or wrong way.

Throughout the week we have been out on our Nature Trail collecting "small" items from Posts 1-6. At each sight we also recorded things that we could hear, smell, feel, and see. Documenting these things was important so that today in the Art Studio we could create our own Journey Sticks. It was a little tricky wrapping string and tying on our objects, but we worked together to figure it out. We even chose the yarn color to represent something we smelled, saw, touched, or heard on that part of the trail. The Journey Sticks look like a very organic form of collage or mural. Of course the trail has 12 posts so we are only half way done. We'll finish up next week and do some writing to accompany them. What do you think so far?

New Apartment Design

Last Friday we started work on the following problem:

We were amazed how many different patterns we found. Take a look at the list we came up with together:

Patterns we noticed

• Each time a row pushes up from the bottom with one extra block on the end, it’s like looking at a staircase from the side 
• In the chart it goes: 0+1=1, 1+2=3, 3+3=6, 6+4=10 (To get the total number of blocks, each time you add the number of the apartment to the previous total to get the new total. For example, in apartment #3 there were 6 blocks, to get apartment #4 you add 6+4=10.)
• The apartment number tells you the number of blocks on the bottom row and the left column
• The columns keep decreasing by one each time from left to right
• When the apartment number gets bigger, the actual building gets bigger too
• First it adds 1, then it adds 2, then it adds 3, then it adds 4, and so on.

Some of us are working on the challenge of finding how many blocks would be used in the 100th apartment. We know that drawing a picture of this apartment would take FOREVER, so we are we using what we know about the pattern to find the answer.

Area and Perimeter (and symmetry)

We used our pentomino pieces to explore area and perimeter and review symmetry. The 12 pentomino pieces are given names based on the letters they resemble. Finding the perimeter of the pentomino shapes was pretty easy, but when we tried to find the perimeter of a leaf later we realized how tricky perimeter can be. Some of us were surprised to discover that even though the area of the pentomino shapes was always five, the perimeter was different depending on the shape. The P shape had a perimeter of 10, which was the smallest. The other shapes (F, I, L, N, W, X, Y, Z, T, U, and V) all had a perimeter of 12.

The shape with the most lines of symmetry was the letter X.

A Mathematical Puzzle

Mathematicians use pentominoes pieces to create rectangles. The first tiling problem using the 12 pentominoes was designed by mathematician Henry Dudeney and published in 1907.

The most challenging rectangles to create are ones that use all 12 pieces. Suprisingly, there are many ways to do this... but we haven't found any yet. It is possible to make a 6x10, 5x12, 3x 20, and 4x15 rectangle. Will, Henry, Caleb, and Aiden are working hard to find all different size rectangles. If families are interested in trying this at home, the kids are welcome to take home a package of pentomino pieces for exploration. We'd love to hear about what you find out!

Pentomoninoes

A pentomino is made out of five congruent squares. Each square must share at least one complete side of another one of the five squares. The sides may not overlap. Our challenge was find all the possible pentomino designs.

You can see from Liam's work that we found 12 different possible designs for pentominoes. Some of are us are continuing this work and looking for all the ways to design hexominoes. Hexominoes are made from six congruent squares. How many ways do you think there are?

Interested in knowing more about the history of polyominoes?
http://en.wikipedia.org/wiki/Polyomino

Nature Trail with Bruce

Today a guide from Ivy Creek came to school to teach us a few things about our own Nature Trail. Some of the new things we saw were:

• Toad
• Daddy Long Legs
• Ant hill
• White Oak Tree
• Acorns
• Sugar Maple Tree
• Dogwood Tree
• Sycamore Tree
• Vines
• Moss
• Mushrooms
• Decomposing logs
• Fungi
• Two year old White Oak Trees
• Red Hickory Tree
• Cicada Shell
• Birds
• Squirrels
• Woodpecker holes
• American Cedar

Some of the new things we learned:

• White Oak trees have shingle-like bark
• White Oaks have different shaped leaves, both with lobes
• You can write on Sycamore bark - it's like paper
• Oak trees grow wider and objects can grow into the bark (fences, bricks, etc.)
• Sycamore trees have three different leaves
• Hickory has compound leaves - 5, 7, or 9 leaflets make up one leaf
• If Daddy Long Leg loses a leg it wiggles around on its own
• If Daddy Long Legs (DLL) loses both of its antennae it dies because it can't hear, see, or smell
• DLL antennae are longer than legs
• Leaves need sun to grow, that's why many small trees in the woods never make it because they don't get enough sunlight
• Roots of White Oak go down as far as the tree goes up, and as wide as the braches are
• Dogwood Trees need lots of sun to grow berries (the Dogwoods in front of the school have many more berries than the Dogwoods in the forest... now we know!)

Questions we're still wondering about:

• Why do some of the trees have fungi growing on them?
• Why does the Holly Evergreen have shiny leaves?
• Why does the Holly Evergreen leaves lose their spikes when they fall off the tree?
• Why do trees need sunlight?
• How can the toad fit through holes that are so small?
• Why does the Maple have sugar in its leaves?