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Statement of Authorship
My (our) signature(s) below indicates that:
1) I (we) did not use any resources such as the web or books other than our textbook.
2) I (we) did not get any help from any individual other than my peers in the class and my instructor.
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3) Below, I (we) have identified any other classmates with whom we discussed this problem
whether they gave us help or we gave them help.
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Individual Responsibility When Group Work is Permitted
Opportunities for group work include both situations when several people sign their name to the same
assignment and when one individual receives help from a classmate even when they do not submit
assignments together. Group work is permitted for Habits of Mind problems, projects, group
presentations, etc. This is done in the belief that, done right, it supports learning, minimizes stress when a
mistake is made, and results in a culture of achievement. Many of us recognize that it is often easier to
work on something that is challenging if we get to share the challenge (and the success) with peers. At the
same time, the learning process can be undermined when one person tells another the solution to a
problem (instead of offering a helpful suggestion) or when someone signs their name to an assignment
when they did not contribute their fair share of effort.
When students work together on a HoM problem, each member of the group should sign their name to
this cover page. Your signature certifies that
i) you have participated to a fair degree in the effort to solve the problem, and thus you are
entitled to your share of the credit for the project;
ii) you understand your group’s solution and will present it if requested; and
iii) everyone you permit to sign the report has also earned the right to sign the solution.
Habits of Mind Problem #1
The Odd Number Triangle
Due Aug 30, 2011
Create a number triangle by listing consecutive odd numbers as shown below, with each row having one
more number than the preceding one:
Row 1:
Row 2:
Row 3:
Row 4:
Row 5:
1
3 5
7 9 11
13 15 17 19
21 23 25 27 29
a) What is the first number in Row 20? What is the last number in Row 20?
b) Determine the sum of all the numbers in row 1, the sum of all the numbers in row 2,
the sum of all the numbers in row 3, the sum of all the numbers in row 4, the sum of all the
numbers in row 5. What do you think is the sum of the the entries in row 6? Make a table to
express your answers. What do you think is the sum of all the numbers in Row n?
c) What is the mean of the entries in rows 1? What is the mean of the entries in rows 2? What is the
mean of the entries in rows 3? What is the mean of the entries in rows 4? Make a table to
express your answers. What do you conjecture is the mean of Row 20?
d) Compare the row means with the number of each row and the first number in each row. What
pattern do you see? From this pattern, can you guess a formula for the first number in each row?
e) Can you prove that your guess is correct? What does the word “prove” mean in this context?
Adapted from Foundations for Success Mathematics Expectations for the Middle Grades
Further adapted by SRD on Aug-30-2011