University of California
Type of paper: Thesis/Dissertation Chapter
* After his mother’s death the young Jack Baker is uprooted from his home in Kansas and is placed in a boarding school in Maine. At the boarding school he feels lost and out of place. While trying to impress the boys and find a place in his school, he can’t help but be drawn to one of the misfits, Early Auden. Early is one of the strangest of boys, who reads the number pi as a story and collects clippings about the sightings of a great black bear in the nearby mountains. When Early decides to set out to find Pi and the black bear in his brother’s boat, the legendary “Fish”, Jack decides to join him. Through the course of their journey the boys begin to realize that Early’s story for Pi is starting to become reality as they come in contact with characters like pirates searching for treasure, a Norwegian still pining for his first love, and a 100 year old women still waiting for her son to come home. The irony of the story is that all 3 boys, Jack, Early and Pi, lost their direction in life and through their journeys they find a way to navigate their way back.
Why this book is a good choice for math?
* The number PI is one of the most common constants in all of mathematics. It is an irrational number, which means that its value cannot be expressed exactly as a fraction (when the numerator and denominator are integers). Nobody knows its exact value, because no matter how many digits you calculate it to, the number never ends. In math it’s obvious that we use PI in calculations for finding the circumference of a circle and finding areas of circles, cylinders, cones, and spheres. What most people don’t know is that PI is also used to calculate numbers that are used in different jobs: for example electrical engineers used pi to solve problems for electrical applications, statisticians use pi to track population dynamics and biochemists see pi when trying to understand the structure/function of DNA. * In the novel, Navigating Early, Clare Vanderpool introduces the mystery of PI in a fun creative way that has the reader egger to find the answer of PI. In the beginning, she has a Math teacher, Mr Blane, introduce his course by explaining the number PI as the Holy Grail of mathematics, in other words it is the mysterious number that has entranced mathematicians for milenia.
“Why do I mention this today? Because this year, we are going to embark on a quest of our own to expand our minds, to challenge what we think we know, and push the boundaries of mathematics. If pi, the most venerable number, can be proven to end, what else are we blindly believing that might be put to the test?”
The way Mr. Blane introduces Pi in the start of his class is a great way to have students use their critical thinking skills as to what Pi really is and get them prepared to what they will encounter in the course. The book, Navigating Early is a great tool for any lesson to get the students excited to learn formulas that incorporate PI. It also teaches the students, to always keep going even when you feel like you want to give up.
Inquiry Circle Design
The book will be divided up into 6 sections.
Section 1-3 students will use the role sheets. Each student will switch roles within each group every week. * Section 1: Pages 1-50
* Section 2:Pages 51-109
* Section 3:Pages 110-150
Section 4-6 Students will use the organizers.
* Section 4:Pages 151-198
* Section 5:Pages 199-253
* Section 6:Pages 254-295
1 section per week, Meet once a week for 20 minutes.
Monday| Tuesday| Wednesday| Thursday| Friday|
| | | | Section 1|
| | | | Section 2|
| | | | Section 3|
| | | | Section 4|
| | | | Section 5|
| | | | Section 6|
What will occur in the meetings:
* Go over role sheets
* Discuss essential questions
* Role sheets
Inquiry Circle Performance Task
For Early, creating a story about the character Pi with the numbers of Pi helped him remember the numbers of Pi. For this assignment you are asked to create your own story to remember the first 15 digits of Pi. 1. You should first brainstorm ideas for your story. The best way to do this is to create a web of ideas. Start with your character, Pi, in the middle of your web and clockwise write ideas for your plot. Make sure you include the numbers of Pi for each idea. You can use either single digits or multiple digits. (NO MORE THAN 2 DIGITS GROUPED TOGETHER!!!)
2. Using your web you should create a rough draft using your ideas. You should double space your rough draft so you will have room for corrections. 3. After writing your draft, find a partner to correct your paper. Make sure when you are correcting your partner’s paper that you look for grammatical errors, digits of pi used correctly, and their ideas make sense. 4. Once corrections are made, type out your final draft with your name and title at the top. You final paper should be single space, sized 12 font, and in times news roman. Your paper should be AT LEAST one page! You can certainly write more pages, but again it has to be at least one page. Don’t forget to include all the digits and that your story makes sense. 5. Once you have created your story, fill out the H chart comparing and contrasting your story to Early’s story. When contrasting, think of the differences of the journeys, what did Pi encounter, and how Pi became a better man from his journey. When comparing the two journeys, think of the plot of the stories: Does Pi in Early’s story face the same problems in your story?
There once was a boy named Pi who had 3 older sisters, Alpha, Beta, and Omega. They all lived under 1 house and split the bills by 4’s. They were always happy living with each other until 1 day at school 5 boys we’re making fun of Pi. They bullied Pi saying because he didn’t have a father and lived with all girls he will never grow up to become a man. One boy piped up and said he killed and skinned 9 deer’s and 2 raccoons in the same night. “I’ll show you!” says Pi and leave that night to go into the woods. Pi has never hunted before but with a knife at hand he was willing to try. 6 birds overhead gave warning calls to the rest of the wildlife throughout the woods. Then behind a nearby tree 5 black bear cubs crawled to Pi. Pi laughed and played with the little cubs until suddenly 3 momma bears ran to attack Pi. Pi thought he was a goner until 5 grey adult wolves came and save Pi’s life. When Pi arrived home, he was bombarded by 9 of his friends and family asking about his journey in the woods. Pi has learned that being a man doesn’t mean going off and killing animals, It means having ethical principles and sticking by them, and protect your family. * The fifteen digits of Pi:3.1415 9265359
Word WizardThe words an author uses are important to the author’s craft. Your job is to be on the lookout for at least one word that has special meaning to the selection for today. Include the word, the page number, the definition, and the reason why you chose the word| Quotations Locate at least one quotation in the text you have read that would be beneficial for your group to discuss. You may look for quotations that are puzzling, interesting, powerful, funny, or those that contain literary devices. Include the quotation, the page, and your reason for choosing the quotation. | IllustratorGood readers make pictures in their minds as they read. This is a chance to share some of your own images and visions with the members of your group and use these images to participate in the conversation. Your picture can take a variety of forms but should represent your thinking. | Essential QuestionsEssential questions are critical to promoting deep and interesting conversations. Write at least one good, quality essential question that you can pose when talking with your group about the passage read.| Literature Circle Role Sheet
Name _____________________________ Circle _____________________________ Meeting Date _______________________ Reading Assignment ________________ Book ___________________________________________________________________ Summarizer: Your job is to prepare a brief summary of today’s reading. Your group discussion will start with your 1-2 minute statement that covers the key points, main highlights, and general idea of today’s reading assignment. Summary:
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Key Points:
1.________________________________________________________________ 2.________________________________________________________________ 3.________________________________________________________________ 4.________________________________________________________________ 5.________________________________________________________________ Connections: Did today’s reading remind you of anything? Explain. ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ————————————————-
____________________________________________________________ Literature Circle Role Sheet
Name _____________________________ Circle _____________________________
Meeting Date _______________________ Reading Assignment ________________ Book ___________________________________________________________________ Questioner/Discussion Director: Your job is to develop a list of questions that your group might want to discuss about this part of the book. Don’t worry about the small details; your task is to help people talk over the big ideas in the reading and share their reactions. Usually the best discussion questions come from your own thoughts, feelings, and concerns as you read. You can list them below during or after your reading. You may also use some of the general questions below to develop topics to your group. Possible discussion questions or topics for today:
1.__________________________________________________________________ 2.__________________________________________________________________ 3.__________________________________________________________________ 4.__________________________________________________________________ 5.__________________________________________________________________ Tips: Consider
A discussion of a work’s characters: are they realistic, symbolic, historically-based? •
What motivates the characters or leads them to make the choices they do? •
An in-depth discussion of the work’s events
A discussion of any confusing passage or event
Literature Circle Roles
Name _____________________________ Circle _____________________________ Meeting Date _______________________ Reading Assignment ________________ Book ___________________________________________________________________ Connector: Your job is to find connections between the book and you, and between the book and the wider world. Consider the list below when you make your connections. •
Your own past experiences
Happenings at school or in the community
Stories in the news
Similar events at other times and places
Other people or problems that you are reminded of
Between this book and other writings on the same topic or by the same author Some connections I made between this reading and my own experiences, the wider world, and other texts or authors:
Literature Circle Roles
Name _____________________________ Circle _____________________________ Meeting Date _______________________ Reading Assignment ________________ Book ___________________________________________________________________ Illustrator: Good readers make pictures in their minds as they read. This is a chance to share some of your own images and visions. Draw some kind of picture related to the reading you have just done. It can be a sketch, cartoon, diagram, flowchart, or stick-figure scene. You can draw a picture of something that happened in your book, or something that the reading reminded you of, or a picture that conveys any idea or feeling you got from the reading. Any kind of drawing or graphic is okay – you can even label things with words if that helps. Make your drawing(s) on any remaining space on this side and on the other side of this sheet. If you use a separate sheet of paper, be sure to staple it to this role sheet. Presentation Plan: Whenever it fits in the conversation, show your drawing to your group. You don’t have to explain it immediately. You can let people speculate what your picture means, so they can connect your drawing to their own ideas about the reading. After everyone has had a say, you can always have the last word: tell them what your picture means, refer to the parts in the text that you