The 9th Night and 10th Night

On the ninth night, Robert dreamed he was sick with the flu. In the dream the number devil gave him a blanket and began to review all the mathematical concepts learned up to now in the book including the characteristics of infinite numbers, square root, prime numbers, factorials, and then introduced the concept of series.

On the tenth night, Robert found himself in the middle of a blizzard admiring the different kinds of snowflakes. In this dream, he began to learn about continuing fractions, and new explorations of how equations are connected to area and perimeter and how 3-D figures are formed by using nets. 

9th Night
1) Which set of numbers are represented by the first row? second row?
2) How many red-shirted numbers are there compared to white-shirted numbers?
3) Which set of numbers are represented by the third, fourth, fifth, sixth, and seventh rows?
4)  What did the number devil write on the ceiling of Robert's room? What is a series?
5) The first two numbers in the series was 1/2 + 1/3, taking the next four terms in the series and adding them together, predict what the sum will be. What computation strategy was used to predict the answer? 

10th Night
6) How many sides and or points did the snowflakes have? What geometric shape  do they resemble?
7) How does the computer that Robert refers to in his dream similar to the technology used in our mathematics class?
8) Which number do all the numbers "wobble" around? Identify the mathematical term for this number.
9) Take 1.618033989. Subtract 0.5. Double the result. Square the new result. What is the final result? Does the result make sense? Explain your reasoning.
10) Use the figures on page 203 to prove the formula true. Hint: White spaces are closed shapes. What types of figures does this formula work for?
11) Identify the figures that result from folding the nets on pages 204-205.
12) Dots plus spaces minus lines equals two. Translate to mathematical symbols. What types of figures does this formula work for? 

When answering questions in a post, be sure to answer them in complete sentences. In order to avoid echoing someone else's comment, each student will be required to answer one of the questions above. Utilize more of the questions, for more points. In class on Monday, students will share their posts and respond to at least one of someone's response to a question. When answering a question, remember to expand your thinking and think of mathematical examples that will make your response richer. 

Your task this holiday break is to choose one of the following questions from the 9th OR 10th  night and post an intelligent response. The deadline to post for this blog is Sunday, January 3rd by 2pm no later. WRITE OUT YOUR POSTS ON PAPER AND BRING THEM TO CLASS. We will continue our discussion on Monday. Use the bookmark to help guide your comments. Then continue reading through Chapter 11 and 12 which will be due by January 10th. 

Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.

Score	3	4
Ideas & Content	The student expresses some original ideas. The majority of ideas are  related to the subject matter.	The student has many original ideas and expresses them clearly. The great majority of ideas are related to the subject matter. Student makes connections to real-world situations and prior mathematical concepts learned.
Commenting	Student offers constructive comments and/or asks questions that provide assistance in reaching the solution of the problem.	Student offers constructive comments and/or asks questions of at least two classmates that clarify the problem solving process and/or provides assistance in reaching the solution of the problem with examples and counter examples.
Writing Quality	Posts show above average writing style. The content demonstrates that the student reads moderately, and attempts to synthesize information and form new meaning.	Posts are well written, and are characterized by elements of a strong writing style. The content demonstrates that the student is well read, synthesizes learned content and constructs new meaning.
Mathematical     Communication     Clarity of        Explanation	There is a clear            explanation.	There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
Mathematical      Communication   Representation   (when appropriate    or required)	There is appropriate              use of accurate mathematical        representation.	Mathematical representation is              actively used as a means of                  communicating ideas related to the      solution of the problem.
Writing Conventions	There is one spelling or      grammatical error in the                     explanation or comments.	There are no spelling or grammatical      errors in either explanation or                comments.

The Eighth Night

On the eighth night, the Number Devil is positioned in front of the white board in Robert's classroom. The Number Devil teaches Robert how to arrange students in the class in multiple ways. If there are two kids in the class, there are _?__ possible ways. If there are three, there are _?__ possible ways. As more and more students enter the room, Robert and the number devil begin to calculate the number of possible ways, but eventually sends everyone home.

1) How many possibilities are there of seating arrangements for two students? Three students? Four students?

2) How do you read the exclamation point in a mathematics problem?

3) What is the mathematical term for vroom?

4) If each of 5 students shook hands with another student before leaving, how many handshakes would occur?

5) Identify at least two ways to solve the handshake problem without counting each handshake.

6) What type of data display is used to show the number of group consisting of 3 students?

7) If there are 11 students in the broom brigade, how many groups consisting of 3 students exist?

8) How many groups would there be if 8 people volunteered for the broom brigade quartet?

9) Use the number triangle to determine the number of groups there would be if there were 6 people volunteering for the broom brigade duo.

10) If you have 14 volunteers taken 9 at a time, how many groups do you have?

When answering questions in a post, be sure to answer them in complete sentences. In order to avoid echoing someone else's comment, each student will be required to answer one of the questions above. Utilize more of the questions, for more points. In class on Monday, students will share their posts and respond to at least one of the someone's response to a question. When answering a question, remember to expand your thinking and think of mathematical examples that will make your response richer. 

Your task this weekend is to choose one of the following questions and post an intelligent response. The deadline to post for the Seventh night and Eighth night is Monday, December 21st. We will continue our discussion at this time. Use the bookmark to help guide your comments. Then continue reading through Chapter 9 and 10 which will be due by January 2. We will discuss these two chapters on Monday, January 4th.

Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.

Score	3	4
Ideas & Content	The student expresses some original ideas. The majority of ideas are  related to the subject matter.	The student has many original ideas and expresses them clearly. The great majority of ideas are related to the subject matter. Student makes connections to real-world situations and prior mathematical concepts learned.
Commenting	Student offers constructive comments and/or asks questions that provide assistance in reaching the solution of the problem.	Student offers constructive comments and/or asks questions of at least two classmates that clarify the problem solving process and/or provides assistance in reaching the solution of the problem with examples and counter examples.
Writing Quality	Posts show above average writing style. The content demonstrates that the student reads moderately, and attempts to synthesize information and form new meaning.	Posts are well written, and are characterized by elements of a strong writing style. The content demonstrates that the student is well read, synthesizes learned content and constructs new meaning.
Mathematical     Communication     Clarity of        Explanation	There is a clear            explanation.	There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
Mathematical      Communication   Representation   (when appropriate    or required)	There is appropriate              use of accurate mathematical        representation.	Mathematical representation is              actively used as a means of                  communicating ideas related to the      solution of the problem.
Writing Conventions	There is one spelling or      grammatical error in the                     explanation or comments.	There are no spelling or grammatical      errors in either explanation or                comments.

The Seventh Night

On the seventh night, Robert spent his day at school drawing bunnies. After dinner, he placed a ball point pen in his pocket just in case of an emergency, and then fell fast asleep. When the number devil appeared in his dream he took Robert to the white colored house and showed him a new mathematical process strategy using small white squares to make a pyramid. The number devil made a connection to triangles and pointed out that numbers were endless.

1) List three things in nature that understand how numbers work.

2) How many cubes were used to make the base of the pyramid built by Robert and the number devil?

3) Why does Robert tell the number devil, "It'll never be a pyramid."?

4) Which number does the triangles of numbers begin with?

5) How are the values for each cube calculated?

6) If you calculate the sum of each row, which type of numbers do you get?

7) Identify the numbers revealed along the diagonals of the multicolored triangle.

8) What happens when the number devil turns off the odd numbered cubes? Describe the diagram.

9) Compare and contrast the diagram with multiples of 2 and the diagram with the multiples of 5.

10) Using the diagram on page 146, predict what the triangle will look like with multiples of  highlighted. 

When answering questions in a post, be sure to answer them in complete sentences. In order to avoid echoing someone else's comment, each student will be required to answer one of the questions above. Utilize more of the questions, for more points. In class on Monday, students will share their posts and respond to at least one of the someone's response to a question. When answering a question, remember to expand your thinking and think of mathematical examples that will make your response richer. 

Your task this week is to choose one of the following questions and post an intelligent response. I have extended the deadline to next Monday, December 21st. We will continue our discussion at this time. Use the bookmark to help guide your comments. Then continue reading through Chapter 8.

Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.

Score	3	4
Ideas & Content	The student expresses some original ideas. The majority of ideas are  related to the subject matter.	The student has many original ideas and expresses them clearly. The great majority of ideas are related to the subject matter. Student makes connections to real-world situations and prior mathematical concepts learned.
Commenting	Student offers constructive comments and/or asks questions that provide assistance in reaching the solution of the problem.	Student offers constructive comments and/or asks questions of at least two classmates that clarify the problem solving process and/or provides assistance in reaching the solution of the problem with examples and counter examples.
Writing Quality	Posts show above average writing style. The content demonstrates that the student reads moderately, and attempts to synthesize information and form new meaning.	Posts are well written, and are characterized by elements of a strong writing style. The content demonstrates that the student is well read, synthesizes learned content and constructs new meaning.
Mathematical     Communication     Clarity of        Explanation	There is a clear            explanation.	There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
Mathematical      Communication   Representation   (when appropriate    or required)	There is appropriate              use of accurate mathematical        representation.	Mathematical representation is              actively used as a means of                  communicating ideas related to the      solution of the problem.
Writing Conventions	There is one spelling or      grammatical error in the                     explanation or comments.	There are no spelling or grammatical      errors in either explanation or                comments.

The Sixth Night

On the sixth dream with the number devil, Robert learns about the Fibonacci Sequence. To make Robert fully understand about Fibonacci Sequence, the number devil changes one month into five minutes and gives Robert a bunny clock. He shows Robert the sequence of increasing bunny.  When he lists Fibonacci numbers in order, it was 1,1,2,3,5,8,13,21,34,55,89,144,233 and so on. When too many bunnies were created, the number devil turned the clock clockwise and there were two cute bunnies left. At the end of that night, Robert felt lucky that his house's clock isn't a bunny clock.

1)  ‘R_n equals h_n factorial times f of n open bracket a plus theta close bracket. ‘ Translate to mathematical symbols.

2) Which number begins the Bonacci numbers? Identify the mathematical term that refers to the Bonacci numbers. 

3) How are the terms in the Fibonacci sequence generated?

4) The number devil ran through the Bonacci numbers in a singsong. Identify the error.

5)  List 3 ways to generate other Bonacci numbers. Provide an example to justify your response.

6)  Using the special rabbit clock, how long does a month last in the potato field?

7)   How can you calculate the number of rabbits born without counting the rabbits?

8)  What type of data display is used to show the rabbit problem?

9    9)  Solve the tree problem on page 122.

1   10)  List at least two places in nature where Bonacci numbers appear.

When answering questions in a post, be sure to answer them in complete sentences. In order to avoid echoing someone else's comment, each student will be required to answer one of the questions above. Utilize more of the questions, for more points. In class on Monday, students will share their posts and respond to at least one of the someone's response to a question. When answering a question, remember to expand your thinking and think of mathematical examples that will make your response richer. 

Your task this week is to choose one of the following questions and post an intelligent response. Use the bookmark to help guide your comments. Then continue reading through Chapter 7.

Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.

Score	3	4
Ideas & Content	The student expresses some original ideas. The majority of ideas are  related to the subject matter.	The student has many original ideas and expresses them clearly. The great majority of ideas are related to the subject matter. Student makes connections to real-world situations and prior mathematical concepts learned.
Commenting	Student offers constructive comments and/or asks questions that provide assistance in reaching the solution of the problem.	Student offers constructive comments and/or asks questions of at least two classmates that clarify the problem solving process and/or provides assistance in reaching the solution of the problem with examples and counter examples.
Writing Quality	Posts show above average writing style. The content demonstrates that the student reads moderately, and attempts to synthesize information and form new meaning.	Posts are well written, and are characterized by elements of a strong writing style. The content demonstrates that the student is well read, synthesizes learned content and constructs new meaning.
Mathematical     Communication     Clarity of        Explanation	There is a clear            explanation.	There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
Mathematical      Communication   Representation   (when appropriate    or required)	There is appropriate              use of accurate mathematical        representation.	Mathematical representation is              actively used as a means of                  communicating ideas related to the      solution of the problem.
Writing Conventions	There is one spelling or      grammatical error in the                     explanation or comments.	There are no spelling or grammatical      errors in either explanation or                comments.