A MAJOR Discovery!

Today we were investigating near trail marker #12 and found a Box Turtle. How amazing!

Polyominoes Challenge

Pentomino Puzzle
In 1953 a mathematician named Solomon Golomb invented the idea of polyominoes: geometric shapes made by connecting a certain number of squares with their sides matching.

Here are a few sample polyominoes:

You are going to design pentominoes. 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. Your challenge is to find all the possible pentomino designs. You can use graph paper or drawings to record your solutions.

Pool Problem

Wondering what we've been up to in math? Here's a look at the problem we've been working on.

Part1

Town Needs a Pool

A brand new research town in Alaska needs a swimming pool. Joanne Truman, a member of the research team, has hired you to design the new pool. She has already chosen one-foot square limestone tiles to be put on the bottom of the pool. These tiles are very expensive and Joanne has decided the town can only afford 36 tiles. Using these tiles, Joanne wants you to find all the possible designs for the rectangular pool. She does not want any tiles left over. It is important that Joanne see all the possible pool designs before selecting one. You must explain how you know you’ve found all the possible rectangular designs. You should use pictures, numbers, and words to explain your thinking. Organize your results so it is easy for Joanne to understand your research and make a decision.

Part 2

*Making Decisions*

Joanne has looked over your results and still can’t decide what size to make the pool. She needs your help. Here are things for you to think about when deciding the design for the pool:

• Joanne wants to put a no-slip tile walkway all the way around the rectangular pool. Each no-slip tile is 1 foot square and costs $4.00.
• Joanne is also concerned about other children in the neighborhood wandering over to the pool. This would be very unsafe. She needs to put a rectangular fence around the pool and walkway. The fence costs $6.00 for two feet.

Given this information, what is the cheapest design for the pool? Joanne wants to make sure you’re giving her the best deal. She is worried you might be trying to cheat the town into getting the more expensive pool. You do not want to lose her business. You must use pictures, numbers, words, or a chart to explain how you found out which pool design was the cheapest (or give the cost of the walkway and fence for each).

Part 1: How many ways are there to design a rectangular pool with 36 tiles. (Clare's work)

Part 2: If you build a walkway and fence, what is the cheapest pool? (Charlie's work)

Tree Websites

Trying to indentify a mysterious leaf at home? Here are some of the websites that we used in school to help with our detective work:

http://www.fw.vt.edu/dendro/forsite/key/intro.htm
http://www.oplin.org/tree/
http://www.fw.vt.edu/dendro/forsite/idfruit.htm
http://www.fw.vt.edu/dendro/forsite/idleaf.htm
http://www.arborday.org/trees/whattree/whattree.cfm?itemid=e6a

If you know of some other good ones, leave us a comment and we'll add it to our list.

We think...

We think we've figured out what type of tree the mystery leaves from my backyard came from. After some research on Friday everyone agreed that the green sphere and compound leaves came from a Black Walnut tree. There is still some disagreement though about the spiky ball. American Chestnut or Allegheny Chinkapin? What do you think?

We started doing some research on Monday about the Black Walnut based on an article we found. We reviewed strategies for reading non-fiction texts, which included: underlining with pencil, highlighting the most important parts, coding the text (connections, connections, I'm confused), and then note-taking/note-making. By only doing one paragraph at a time it seems less overwhelming. All of these skills will be critical once we choose our topics for the nature trail and are expected to conduct research independently.

Below you will see Karen's note-taking page from her Inquiry Notebook:

Nature Sketching

We have been practicing our sketching skills as we get ready to undertake creating the digital guide for the nature trail. In order to learn what real naturlists and scientists do when they sketch we have been looking at exmaples in the book Keeping a Nature Journal by Clare Walker Leslie. In this book we noticed that naturalists don't just sketch but they also write what they notice and record questions they have. Understanding this has helped our own sketching improve. For homework on Monday night students were invited to choose one leaf from around their house to sketch. Here are some examples of those leaf sketches from Anna Grace, Will, and Hannah. Our work is really starting to look like real naturalists.

How many ways did we find?

By: Anna Grace and Tenley
We have been working on a math problem were we have to find all the possibilities to build a town. All the buildings in the town had to be the same hight. We had to fit exactly 60 families in the town. We used cubes to help us solve this problem.  One family could fit in one cube. After we thought we had all the ways we had to organize it and prove it. My partner and I used opposites to help us. Here is an example of an opposite. If my partner and I found out that 5 towers of 12 worked then we would use that and switch it around so it said 12 towers of 5. When we thought we had all the ways we made a chart to organize it. We made two columns. The first column said "number of buildings" and the second columns said "how high." Then under the column that said number of building we wrote the number of buildings. Next we wrote how many cubes high the buildings were under the column that said how high.Then we made a very thin column and numbered the ways we had thought  of, there were  12 we had thought of.Then to prove it we made a chart that looked exactly the same but instead of  having  12 lines it had 60,then we wrote all the ways we had in it. Then we counted the empty spaces. We counted 48. We added 12 to 48 which made 60. We had  found all the ways.