Assignments for MATH 3262
Fall 2006
|
Date
Assigned |
Assignment |
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Tues, Aug 22 |
Write your mathography. Due Thursday, Aug 24. Complete the membership form to join GCTM. Print the completed form and bring to
class. (You are in the Central East
region.) Print a copy of the Georgia Performance Standards and
put these in your working portfolio. This printer friendly
version is sufficient. |
|
Thurs, Aug 24 |
Paul Kunkel’s website for
Geometry Constructions can be found at http://whistleralley.com/construction/reference.htm Practice the first 7
constructions for homework. You will need to buy a
compass and straightedge—please let me know if you need help with these
constructions. Work neatly and
carefully. You should be proficient
with these constructions no later than next Tuesday. Put this work in your working portfolio. By next Thursday, August
31, be sure you have completed Tour 1 and Tour 2 for Geometer’s
Sketchpad. Recall the software is in
the labs on campus—go to Programs, Departmental Programs, Teacher
Development, Geometer’s Sketchpad, Geometer’s Sketchpad v. 4.06. |
|
Tues, Aug 29 |
Explore the site “Fibonacci
Numbers and Nature” at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html Plot the points for height
vs navel height—using the data collected in class. Read the process standards
for Grades 6-8. List 3 observations
you can make about the reading. Complete the compass and
straightedge constructions. Complete
the Geometer’s Sketchpad tutorials. For review: What is the Golden Ratio? What is a Golden Rectangle? Do you have any Golden Rectangles in your
house? |
|
Thurs, Aug 31 |
Compass and Straightedge
assignment—to be turned in Tuesday. Question: Are all golden rectangles similar? Provide a mathematical explanation to
support your decision. Vocabulary discussed: similar figures, congruent figures,
rectangle, slope. Go to the InterMath site for the
dictionary. Review finding the slope of
the eyeball fit line for the height vs navel height data. |
|
Tues, Sept 5 |
Review finding the equation
of an eyeball fit line for data that has a linear trend—like the data for
height vs navel height. Work the problems on the
handout entitled Points, Lines, and Planes.
We will discuss these problems Thursday. |
|
Thurs, Sept 7 |
Try constructing a Golden
Rectangle on Geometer’s Sketchpad—use the directions given out in class. You must first begin with a rectangle—and
this must be constructed!! That is, when
you drag on the figure, it should stay a rectangle—so you must construct some
perpendiculars, you cannot just eyeball perpendiculars. |
|
Tues, Sept 12 |
Use GSP to construct a
square, a rectangle that is not a square, a parallelogram, and a
rhombus. Save your sketches as a single
file and use the document options to insert pages for each quadrilateral. |
|
Thurs, Sept 14 |
Investigate the following
problem from the Intermath site. Be
prepared to justify your conclusions. Do the problem: How
Many Rays? Be prepared to justify
your conclusions. |
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Tues, Sept 19 |
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Thurs, Sept 21 |
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Tues, Sept 26 |
We will begin discussing
the minimum conditions for congruent triangles. Return to your file for
Constructing Quadrilaterals with GSP.
Also construct a kite—include a new tab. Investigate the properties of each
quadrilateral. For ex., how are the
lengths of the sides related? How are
the angles related? What do you notice
about the diagonals? Summarize your findings for
each quadrilateral in a Word document.
Save this document and your GSP file.
This will be posted to your webpage. Investigate
the following: Quadrilaterals
Inscribed Inside Quadrilaterals In or
Out? Look up the definition of
altitude of a triangle. Balancing
the Triangular Totter Save your work. GSP would be a
useful tool to explore the following problems. Please write your conjectures for each
exploration and save your work. §
The
segment connecting the midpoints of two sides of a triangle is called a midsegment of the triangle. What conjectures can you make about the
midsegment of a triangle? §
The
line segment connecting the midpoints of the two non-parallel sides of a
trapezoid is called the midsegment of
the trapezoid. What conjectures
can you make about the midsegment of a trapezoid? (To explore with GSP you must first
construct a trapezoid by constructing two lines that are parallel to each
other.) |
|
Thurs, Sept 28 |
Investigate these problems
and be prepared to share your thinking in class. Technology is not required (although could
be used) to investigate these problems.
You should be able to offer mathematical justification for your
conclusions. Read and explore the
activities in the handout Polygons and
Angles (a 6th grade lesson) from the Connected Mathematics
Project. (This was given out in
class.) Be sure you understand the
three ways an angle is considered.
Then write a reaction paper to the article “The Role of Definition.” The activity Polygons and Angles is referenced
in this article. Your reaction paper
should consist of two parts: a brief
summary of the article as well as your reaction to the article. Your summary should be a synthesis of the
main ideas and provide evidence that you understand these main ideas. Your reaction to the article should provide
evidence that you have carefully reflected upon these ideas to consider their
impact or implications on the teaching and learning of mathematics. In your reaction there should be evidence
that you have grappled with the ideas to understand their relevance to you
personally. The Rubric for evaluating
reaction papers will be used for evaluation. You will be evaluated on your summary (3
pts), your reaction (4 pts), and your technical writing (3 pts). Your reaction paper is due Tuesday, October
10. Test Thursday, Oct 5. |
|
Thurs, Oct 13 |
Please create a folder on
your z: drive or on a thumb drive so that all documents related to MATH 3262
can be saved to this folder. Go to the document Justifying Constructions—justify
constructions 1 and 5. We will look at
construction 6 in class. Explore this
problem for homework: Quadrilateral
Conjectures (GSP would be a useful tool). The following problem was
assigned Sept 26. Revisit the problem
and bring your conjectures to class Tuesday for discussion: GSP would be a useful tool to explore
the following problems. Please write
your conjectures for each exploration and save your work. §
The segment connecting the midpoints of
two sides of a triangle is called a midsegment
of the triangle. What conjectures
can you make about the midsegment of a triangle? §
The line segment connecting the
midpoints of the two non-parallel sides of a trapezoid is called the midsegment of the trapezoid. What conjectures can you make about the
midsegment of a trapezoid? (To explore
with GSP you must first construct a trapezoid by constructing two lines that
are parallel to each other.) We will discuss
the problem In or
Out? in class Tuesday (this
problem was assigned earlier). Be sure
you know the definition of an altitude of a triangle. Begin investigating the following
InterMath problems—you are not expected to complete these investigations for
Tuesday. You will select one of these
to write up formally—we will talk about the formal write up in class Tuesday
(see below). For now, begin your
investigation and write down your observations/conjectures/questions—save to
your folder. The following information will be
discussed in class Tuesday—you may want to try downloading the template but
if you have trouble, we will work on it Tuesday. You should put the downloaded template in the
folder created for MATH 3262. You investigated the problem, Sum
of Angles in a Polygon, and we discussed the solution in class. This problem is to be written up using the
InterMath template for a write up found at http://intermath.coe.uga.edu/newInterMath/workshop/portf/writeup.doc. When you click on the link, save the
template—do not open it. Then start
Word and open the template—you will be able to make changes to the template
for your write up. |
|
Tues, Oct 17 |
Investigate the
following InterMath problems. Vertex
Angles in a Regular Polygon You investigated the properties
of various kinds of quadrilaterals and saved your observations to a Word
document (see Tues, Sept 26). Please
send a copy of the Word document and your GSP file to me via an email. Send a copy of this
investigation to me: Quadrilaterals
Inscribed Inside Quadrilaterals |
|
Tues, Oct 31 |
Class: Discuss Justifying
Constructions—construction 6. Discuss: §
The segment connecting the midpoints of
two sides of a triangle is called a midsegment
of the triangle. What conjectures
can you make about the midsegment of a triangle? §
The line segment connecting the midpoints
of the two non-parallel sides of a trapezoid is called the midsegment of the trapezoid. What conjectures can you make about the
midsegment of a trapezoid? (To explore
with GSP you must first construct a trapezoid by constructing two lines that are
parallel to each other.) Investigate this problem:
Draw a triangle ABC on lined notebook paper. Draw a line parallel to one side of
triangle ABC. Conjectures? Proof? Who will share these problems Thursday? Problem 1: Half
as much may be right Problem 2: Vertex
Angles in a Regular Polygon Thinking about
Area—need square tiles Homework: Finding Area by Moving and Combining—do problems 1-4 for
Thursday and remaining problems for Tuesday—we will discuss these in class. Formally write
up a justification of construction #1,
#4, #5, or #6 from the website http://whistleralley.com/construction/reference.htm. Due Tuesday—turn in hard copy. |
|
Thurs, Nov 2 |
Problem 1: Half
as much may be right (discussed in class and justification given) We discussed the
following concepts: Definition of a
circle, radius, diameter, chord of a
circle, inscribed angle of a circle, central angle of a circle, definition of
a sphere Problem 2: Vertex
Angles in a Regular Polygon ( Discussed
meaning of area. What is a square
inch? What is a square foot? Confirmed that two shapes can have the same
area but different perimeters; confirmed two shapes can have the same
perimeter but different areas.
Discussed area of a rectangle and why area of a rectangle can be found
by multiplying length and width. Circumference
of a circle (we will explore this concept in detail next week) Homework: Investigate this
problem: Justification of
construction write up due Tuesday Finding Area by
Moving and Combining—do problems 1-4 on the handout for Tuesday and remaining
problems for Thursday—we will discuss these in class. |
|
Tues, Nov 7 |
Classwork: Discuss Vertex
Angles in a Regular Polygon ( Discuss problems 1-4 on the “Finding Area by Moving and Combining” handout. Circumference
of a circle Homework: Work problem 5 on “Finding Area by Moving and Combining”
handout. Revisit the
ideas about circumference and diameter—what did you learn through the
activity in class? Solve the
problem Rectangle
Squares. Solve the
problem Walking
Around the World Revisit Half
as much may be right—consider the questions on the second page of
this handout to prove the conjecture correct.
Journals will be
collected Thursday. |
|
Thurs, Nov 9 |
Classwork: Check Homework: Find area of
classroom. Check HW: Finding Area by Moving and Combining Investigate: Other area
investigations Homework: Complete problems on “Finding Area by Moving
and Combining” handout. Solve Running
in Circles |
|
Tues, Nov 14 |
Read the essay, The van Hiele Framework. Read this essay for Thursday so we can discuss it in class. Find the area of the trapezoid. |
|
Thurs, Nov 16 |
Read the article, Perimeter
and Area through the van Hiele Model and write a 1-2 page reaction paper. Due Tuesday, November 28. To
evaluate your writing, I will use the Rubric for Reaction Papers. Below
are the investigations that you have been assigned: Properties of a Quadrilateral (Word document) Quadrilaterals Inside Quadrilaterals Sum of Angles in a Polygon Justification of Construction Area of a triangle, a parallelogram, and a trapezoid One of the following: Find the Hidden Treasure Capture the Flag Shark Attack! |
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Tues, Nov 21 |
See the investigation Triangles within a Triangle for a review and an extension of concepts we have studied. Investigate the problem Tangential Circles and provide a write up. You should make a conjecture (perhaps based on a GSP sketch and then try to justify why your conjecture should be true. Work these two problems for practice. Reaction paper due Tuesday, Nov. 28. The article “How
Many Times Does a Radius Square Fit into the Circle?” is for your files. |
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Tues, Nov 28 |
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Thurs, Nov 30 |
Similar Figures--uses the file Similarity.gsp Exploring the Pythagorean Theorem—uses file Pythagoras.gsp |
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Tues, Dec 5 |