The Mangoes Problem
One night the King couldn't sleep, so he went down into the Royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes.Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5 of what the King had left.
Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes.
Even later, his brother, the second Prince, ate 1/3 of what was then left.
Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants.
How many mangoes were originally in the bowl?
October 2009 Vocabulary List
Scribes =
Look up each word, note its definition (We’re looking for short, pithy definitions/synonyms) and then use it in a sentence that demonstrates that you understand the meaning of the word. You may use any form of the word you like.
Due:
Theme Goals
o Experience how to take on a new area of learning and practice engaging and immersing yourself in your interest.
o Learn how to manage your time goals and your project goals- you will track your goals over time, reflect, shift and reshape them.
o Create deep and meaningful questions that change over time as you explore your topic.
o Make connections with one another about your topics finding similarities and overlaps.
o Be reflective about how you learn.
Timeline
Now until December 10th- 9 weeks total, 3 hours a week
Step 1- Immersion and Question and Group Forming (3 class periods)
Research possible topics and write questions that interest you. The goal of this step is to move from good questions to better questions that help you create a theme unit that is engaging and though provoking.
Step 2- Learning Contract (1 period)
Write a Learning Contract that give your advisor an idea of what you will be pursuing in your area of interest for six weeks. What are your big questions and what types of learning activities will help you answer those questions?
Step 3- Work and Reflect Weekly (6 weeks)
Engage in your learning activities whether they are research based or experiential based. Dig deeper with your topic and engage. For example, you might go on a field trip, talk to an expert, watch a documentary, build something, read articles and books, etc.
Step 4- Present Snapshot of Learning (Last week of Theme- December 7-11)
You will present a snapshot of your process of engaging in your theme. What types of things did you do to answer your big questions? Show us the artifacts in your box that represent your immersion in your topic.
Here’s what we are looking forward to…
- This is about how well you learn- all about your learning process!
- You will not be expected to take a test/give a presentation at the end- this is not about the product, but instead, the process.
- There needs to be artifacts to show your process of learning over the term.
- We will have weekly one-on one check ins (with your academic advisor)
Deliverables
What do you need to turn in each week? Answer the following in an email to your advisor:
In your subject line of you email write - Your NAME- theme- week ___ (fill in with the week #)
Answer the following questions in your email:
How did multiple drops at each height affect your results? What is the purpose of multiple trials in an experiment?
What did you discover about the influence of height on blood diameter in a blood spatter? Could you now accurately infer the height at which a blood drop originated based on the diameter of a blood spatter? Why or why not?
Exemplary
· Demonstrates good understanding of situation and problem to be solved
(What’s your problem? What information are you given?
How many possible solutions might there be?)
· Thoroughly investigates situation (explores, searches for patterns, uses a viable strategy,
modifies approaches)
(How many ways can you try solving this? What patterns do you see?
How did you change your approach as you solved the problem?)
· Uses applicable mathematical concepts and procedures.
(What math are you using to solve this problem?
Drawing a diagram, making a chart, graphing the problem, etc.?)
· Constructs elegant, efficient, clear, appropriate, valid solution(s)
(What is your final solution?How did you get there? Could there me more than one answer?)
· Demonstrates effective communication in a presentation of exploration of problem and
defense of solution(s)
(Is your strategy presented in a clear manner? How many ways did you explore the problem?
How can you be sure your answer is correct? How can you be sure your answer is the only one?)
· Demonstrates higher order thinking skills (synthesis, analysis, evaluation)
(How much information are you collecting and evaluating? How does new information
help you modify your approach?)
· Go beyond minimal expectations (i.e. extends, generalizes, poses new related questions,
proves, evaluates)
(How could you make this problem harder? What new questions do you have?
How could you look at this problem differently?)
Copy and paste the following on a word document. When you are finished answering the q's print, sign and give to Bert, Ms. A or Darin.
Ø What is your job title?
Ø How will you do your job? What can we look for to know you are “on task?” What tasks will you do on Monday and Friday during our 8th community jobs time- 8:30-9:00 am?
Ø Will any part of your job happen outside of the Monday/Friday time?
Ø Who will you contact if you are absent and your job needs a substitute?
Ø What, specifically, will be the outcome or product of the work you've done each week? How will it be obvious that you've done it?
Ø How will we know what you personally have contributed if you are working with a group?
Ø What support do you need from teachers to do your job?
Ø What support do you need from your peers to do your job?
Ø Do you have a preference for how your peers contact you? (For example, should they contact you in person, email, or write you a note?)
Once you have your contract written, get approval from an 8th grade teacher.
8th Teacher Approval__________________________________________
Your Signature_______________________________________________
Think of a positive integer (e.g. 23).
Count the number of letters in its name (e.g. "twenty-three" has 11 letters).
Repeat this process using the new number (e.g. 11 produces the number 6).
What happens as the process continues?
Can you prove why this happens?
Also, what happens if you replicate the problem using numbers in other languages such as German and Italian?
