Tick, tick, tick! The deadline for article submissions has come and gone and I am pleased to say all students made the midnight December 11th cut-off (well, close enough :>)
Issue II of The Mosaic Monthly has been up-loaded to the printer, and barring any last minute glitches (as can happen in the newspaper biz) we should be distributing and enjoying our paper on Monday.
On Monday we will also plan our final issue (sadly!). Instead of volunteers, I will be assigning sections to students in the hopes that everyone will take advantage of the opportunity to contribute to the paper. For some students, this may be significantly out of their established comfort zones, so I apologize in advance for any "kvetching" you may hear. Please continue to support them as much as possible at home, and let me know if I can be of any assistance!
This week we shared our fairy tales that were written from the perspective of a minor character in a well-known story. The students' preferences for creative writing are very clear and we enjoyed the momentary departure from "serious" journalism.
They were so delightful, we agreed that before the semester is over, we should have them bound up in booklet form and distributed to all for posterity's sake. I will be asking for the finished pieces sometime after the holiday. Please have your student type his or her fairy tale and make sure it is ready for publication. Prepping for publication is very time consuming and any editing you can assist your student with is much appreciated!
We also discussed on Monday the similarities and differences between perspective, prejudice, and bias and how bias can be detected in media. I distributed a personal bias audit and asked the students to keep their answers private from the other students so they could feel free to answer honestly. Without revealing any personal biases, we discussed how we might have arrived at these pre-conceived notions and challenged ourselves to consider the sources that may have contributed to our view points.
There is no additional homework this week, however, if your student has still not written an in-depth, please encourage them to do so before the break. I am always looking for stand-out articles for an up-coming issue!
Bravo to all of the students who worked on their tessellation art and brought something in for the class to see! It was wonderful to observe the variety of visual ideas students have developed in these early efforts.
Students should continue to work at home on creating their own unique tessellation patterns from regular polygons, using the translation method we learned in class last week. Try using rotation and reflection in your designs, and don't be afraid to experiment with color, or perhaps combinations of polygons. The possibilities are truly as unlimited as your own imagination!
The Intrigue of Pascal's Triangle
This week in class we took an introductory look at the seemingly simple yet powerful triangular arrangement of numbers known as Pascal's Triangle. While Blaise Pascal, a 17th century mathematician, is credited for developing many of the properties and applications of the triangle, this amazing combination of numbers was actually known independently by both the Persians and the Chinese as early as the 11th century.
We covered a lot of material in class this week and most of it was new to the students. I provided them with a handout of information summarizing what was discussed in class (also found HERE). I strongly encourage all students to carefully review this material again as part of their homework.
We discussed how to create the triangle (each number is the sum of the two numbers above it) and spent time looking at some of the interesting hidden patterns within it:
If, for instance, you pick any two of five items, the number of possible combinations is 10, found by looking in the second place of the fifth row (not counting the 1's). We worked out a similar problem in class, first using inductive reasoning, and listing all possible unique combinations. Then, we looked at how easily we can apply Pascal's Triangle to solve the same problem.
This can be worked out mathematically using a simple formula, referred to as "n choose k" where n = the number of total items and k = number of items chosen. So, for the example above, n = 5 (5th row) and k = 2 (2nd place in the row), which yields the answer 10 from the triangle.
As part of this week's homework, students will solve several of these types of problems. Additionally, I would like them to express their answers using the entire mathematical formula, including the factorial math:
This can be very useful because now you can work out any value in Pascal's Triangle directly, without constructing the whole triangle!
Fun with Pentominoes
Finally, we wound down our class this week with some relaxing (or was it frustrating?!) hands-on geometry time using pentominoes. Students were challenged to make rectangles out of pentominoes (five equal squares that share at least one side, with no windows) and solve various puzzles from a worksheet. These were much more challenging than they initially seemed!
If you would like to continue working on these types of puzzles at home, you can try "virtual" pentominoes HERE.
Yesterday we learned about dimensions and perceptions via a little story telling!
We built a "flat city" with houses and streets that connected with one another and heard a version of the classic Edwin A. Abbott novel Flatland. This led us into fairly deep territory where we thought about what a
2-dimensional object might look like to a 1-dimensional object, and in turn, what a 4-dimensional object might look like to a 3-dimensional object (us!). I provided the students with a handout which explains how a 4-D "hypercube" or *"tesseract" is created, and challenged them to think about how a 5-D object might be constructed. I promised them a look at a 5-D "cube" or "penteract" and here it is:
Better yet, here is a 5-cube penteract projected into 3D:
We moved from our dimension story into a story about perception and played with shadows. This story is well illustrated by the claymation video below. This is not the version we enjoyed, but it is a wonderful adaptation of Plato's Cave. Watch it with your student and let it open up a discussion! Are we limited by our own experiences?
For "play at home" I assigned a visual puzzle called Block Twins. You can find the color version HERE. Warning: the answer is listed below the puzzle sheet, so you might want to print it out for your student or sit with them while they look at it so they don't inadvertently scroll to the bottom. Answers will be shared Monday!
*term was spelled incorrectly on handout -- sorry!
We use curriculum from Art of Inquiry, LLC
Yesterday, we shared our in-depth articles. We heard three articles, of varying lengths, that used the required elements of an in-depth; research and attribution (quotes or paraphrasing). It's not too late to submit an in-depth. In fact, I want to stress that the assignment was not optional. Everyone should be giving as much effort as possible on all assignments. This is the right venue to try and even fail! There are no grades and we are all here to support one another...and learn! Students can change their topic if they like.
Next week, we will have our layout session for Issue II! I am very excited about this issue as we will be increasing our publication by four pages and including broader and very relevant topics such as beach erosion, working conditions in factories, and the presence of corn and corn by-products in our food supply.
Our in-depth article that secured the students' votes to be included in Issue II was an article on the role of cakes in cultural celebrations. Bravo!
The publication date for Issue II is December 17. On Monday, December 10, your student will receive their article back from the News Editor. We are going to be experiencing the true meaning of deadline with this issue. Your student must email to me by MIDNIGHT December 11, his or her edited article, or it will not be included in this issue. Since we would have secured a spot for the student's article in the layout session, this means that failure to meet the deadline will result in major content problems for the paper (and the Editor-in-Chief, i.e., Yours Truly), therefore, missing the deadline is not optional.
To lighten the mood a little yesterday, we used the Grimm Brothers' version of "The Three Little Pigs" to illustrate the concept of "the missing voice" in a story, commonly known as perspective. To investigate "the other side of the story" we read through (in readers theater style) "The True Story of the Three Little Pigs" by Jon Scieszka, where we learn the "Big Bad Wolf" was mistakenly labeled through a simple misunderstanding. :>)
For homework, students were given the mission of re-writing a fairy tale from the perspective of a minor character that appears in the story. I gave them several options, and we went around the room and each student committed to a tale and a character. They are allowed to choose a different story and character if it stays true to the purpose of the exercise, but everyone should present a fairy tale on Monday. The choices were; Rapunzel, Cinderella, Hansel and Gretel, Rumpelstiltskin, and The Wizard of Oz.
Next week in addition to the layout session, we will be exploring bias in media and how it differs from perspective. See you then!
Our discussion of Ben and Me began this week with a short geography lesson and mapping exercise, as students worked on identifying the states in the northeastern US on an unlabeled map, and finding Benjamin Franklin's birthplace (Boston) and the setting for the story (Philadelphia), where Franklin spent much of his life. This was a challenging exercise for most of the students! I have provided the blank map (HERE) and would encourage students to repeat this exercise at home to become more familiar with our regional geography.
Students then discussed two of Ben's famous maxims from the first chapters of the book ("Waste not, want not" and "The laborer is worthy of his hire"), and gave their personal interpretations of the meanings of these sayings, with examples of how they apply in everyday life. We will continue to discuss the meaning and application of Ben's maxims as we encounter them throughout the book.
We then began our dictionary of vocabulary words together and I provided the class with three words from Chapters 1-4. Students should find two new vocabulary words (of their own choosing) from the assigned chapters each week and add them to their dictionary page. I have asked them to list: the word, the sentence from the book where the word is used (for context clues), their initial guess at the word meaning, and then the dictionary definition. The process of stopping to examine the context for word meaning, and then confirming with a dictionary is a great habit to reinforce for vocabulary development.
We concluded our class with a hands-on invention activity, having just read Chapter 2, where Ben and Amos together design and build the first Franklin Stove. Students were divided into two teams, given identical sets of everyday supplies (straw, dixie cup, paperclips, rubber bands, mini marshmallows, etc) and then allowed 15 minutes to invent anything they could think of! Teams were not allowed to see what the opposing team was building. Each team was then asked to carefully examine the opposing team's invention, and relay their assessment "telephone-style", with only one team member actually viewing the invention, then explaining to the next team member what they observed, and so on. The last team member provided the class with the final explanation (and drawing) of how the invention was constructed. Both teams ended with good overall explanations of the opposing teams invention, but also missed important aspects and details. A very good exercise for illustrating the importance of effective listening and communicating!
Assigned reading for next week: Chapters 5-10.
Students practiced a basic translation method to develop their own tessellation shapes from regular polygons (square, triangle, or hexagon). They should continue to work on designing their tessellations at home over the course of the next few weeks. We will share our final designs in class in the coming weeks, and it is my hope that we can turn one or more of these tessellations into a design for Mosaic Freeschool t-shirts! Very fitting, don't you agree? (<:
It's a (problem) festival!
This week in Creative Thinking, we took some time to sit back and play some games!
We kicked off the morning with a little dice magic. Please ask your student to show you the "dice trick." I'd love to find out if they remember the solution and can pull off the presentation. Please share any stories!
We then tried to guess how many handshakes there would be if everyone in the room shook hands with one another. We got some pretty interesting predictions and even though none were correct, we were able to walk through the problem and work through to a solution.
We spent the last 45-minutes of class playing five different strategy games courtesy of ThinkFun. We played Ducks In A Row, Nim, Star 29, Pig & the Fence, and Dodge 'Em. All games, plus a few more, are available at the link, if you are interested.
For work at home, I handed out a Sudoku Puzzle Challenge, which is more difficult than the one provided earlier in the semester. There are two puzzles, both are optional. I would like students to come to class next week with an answer to The New Star Puzzle. If you need the handout, it is located here (scroll down to second half of page), along with dozens of wonderful printable puzzles should your student be left begging for more.
See you next week!
We use curriculum from Art of Inquiry, LLC
The Tree Gap News Team!
We wrapped up our discussion of Tuck Everlasting this week with a "live" news broadcast of breaking stories from the investigative reporting team of the Tree Gap News.
Students read aloud the news articles they had written and based on exciting incidents from the book. They did a great job including facts from the story, along with their own creative twists.
We talked about the value of developing good public speaking skills, and worked on reading the articles with strong voice projection and clear articulation (and of course, a fair bit of drama!)
And Our Next Book Selection Is...
Students will now begin reading Ben and Me by Robert Lawson. This is a delightful tale of Benjamin Franklin's life and work, told through the eyes of his clever mouse companion, Amos. As a work of historical fiction, it will allow us to explore the ideas, inventions, and discoveries of one of America's most famous and inspiring men; all from the perspective of a most witty and amusing mouse!
Students should read the Forward and Chapters 1-4 for next weeks class discussion. Homework sheets were sent home.
This week we also began "What's the Big Idea, Ben Franklin?" as a read-aloud in class. This is a short, engaging biography meant to provide the students with an introduction and further background information on Franklin's life. We will continue reading this book together in class, as we discuss Ben and Me and work on related in-class projects.
Happy Reading! See you all on Monday.
Since we are nearing an important deadline for our December issue of "The Mosaic Monthly," I wanted to get a class summary and re-cap to our students as soon as possible. Please let me know if there are any questions.
Today we discussed why research is essential, where information can be found, and how do we ask the right questions to get the information we need.
Each student completed a handout titled "Research Notes." I asked the students to choose one of their three sub-topics they had prepared for their in-depth, and to list the basic facts (the 5 W's and H). This should assist your student in composing the lead paragraph of his/her article.
Next, we tried to list five questions that need to be answered about the sub-topic and if possible, another five questions that could be asked about the story. These are separate from interview questions and should help the student compose the body of the article. We then broke into our three groups from last week, shared all questions, and with my help, settled on the three most compelling. These three most compelling questions do not need to be stated within the article, rather the questions are a vehicle to help the writer address the topic they are researching.
This week, writers should interview their sources and write their in-depth article using the "Research Notes" as a guide. We also discussed how to use attribution in a news story. They should now be familiar with how to use quotes, paraphrasing or a combination of both.
Their in-depth articles will need to incorporate the elements of interviewing, research and attribution. A tall order, but I'm confident they will deliver. All in-depth pieces should be brought to class next week. We'll read them and vote as a class on which one will appear in the next issue. I will also be selecting a second piece that will not be revealed until publication!
As a side discussion, we delved into a little history lesson on the Progressive Era in the United States (c. 1890 - 1920). This era was known for its "muckraking" journalists and was responsible for bringing to light the plight of the immigrant population in New York City. Known as the "father of photography" Jacob Riis used his photographic and journalistic talents to shed light on the quality of life in the slums. We viewed three Jacob Riis photographs (similar to the one at left) and each student wrote a news article that might have appeared in a Progressive Era paper using the photograph as the only source of information. Students were initially very intimidated by this exercise, but when we shared our individual stories, I was impressed by the level of creativity but adherence to realism and proper news story creation. I think we may be getting somewhere! :>)
In addition to the in-depth article, students should bring in a typed or very neatly written first draft of their article for the December issue, if your student is responsible for writing one. The first priority is the article for the paper, the second priority is the in-depth, however, I would like to see both done and handed in by Monday, December 3rd.
On 10/22, we tackled several Distribution Dilemmas. These are problems that require the student to think beyond the boundaries suggested by the problem, to reach a not-so-obvious solution. Specifically, we looked at a couple of inheritance puzzles which required the use of unit fraction proportions to determine how to divvy up sheep left by a shepherd to his children. It was a good review of basic fraction calculations for most students, and pushed them to think of a creative way to resolve the dilemma of having proportions that do not add up.
We then played an Iterated Sharing game, involving....Candy! Everyone sat in a circle and candy was distributed randomly to each person, though all were given an even number of pieces. A reserve supply was placed in the middle of the circle. At each iteration, students gave half their candy to the person on their left, and recieved a supply of candy from the person on their right. We then recounted our individual totals. If you had an odd number, you take a piece from the reserve supply to boost your pile back up to even, and everyone iterates again. I asked students to contemplate what would happen if we continue to perform this maneuver again and again. Will everyone's supply grow without bound? Will the distribution stabilize at some point? Will any pattern emerge? Is it possible to even predict the result? Interestingly, most students initially thought their piles would grow unbounded (or perhaps that was wishful thinking!). However, once we stepped through a few iterations, it started to look like the piles were beginning to even out, and students changed their predictions. At the beginning of the game, we noted the students with the largest and the smallest number of pieces before any iterated sharing began. At the conclusion of the game, everyone had the same number of pieces and we discussed how we can determine an upper and lower bound on the amount of candy simply by noting the largest and least initial amount received. The fact that we continued to halve, pass, and then even out our piles forces the distribution to stabilize. No matter what the initial distribution of candy or how many people are in the circle, the distribution will eventually equalize.
This exercise was a great introduction to the basic concepts of computer simulation and modeling. And, as luck would have it, a hurricane called Sandy was brewing out in the Atlantic, and soon would provide a real-life example of just how important simulation and prediction can be!
On 11/12 we met after two weeks of cancelled classes due to the hurricane aftermath. I took the opportunity to explain the basics of hurricane prediction and the use of 3-D global and regional climate simulation models. The basic iterated sharing game with candy had laid some groundwork for understanding how scientists develop and run simulations to model highly complex physical processes, such as weather.
We also began work on our on-going class project affectionately known as, The Popcorn Problem. I have split the class into two teams and challenged each to determine how much popcorn it would take to completely fill our classroom. For the past few weeks students have been measuring the classroom dimensions, estimating the size of popcorn, and developing a plan for determining their solution.
More to come on this strange and tasty endeavor!
For our class on 11/19, we shifted gears to focus on concepts of geometry and Symmetry. We looked at imagery of all the myriad places we find symmetry in our world - art, architecture, nature (animals, plants), music, dance, etc. and learned about the three main types of symmetry - reflection (mirror), rotational, and translation. Students then worked problems to find all the lines of symmetry in regular and irregular polygons, played around with decoding messages in mirrored text and worked on creating their own mirrored codes. The most challenging work was sent home with them - finding congruent halves in shapes that contain a combination of reflection, rotation, and translation symmetry. Students must be able to visually see how to flip, turn, and/or slide one figure so that it fits exactly onto the other congruent half in order to solve these problems.
We will continue our look at geometric properties in our next few classes as we discuss tessellations and fractals.