Assignments for MATH 3262

Fall 2005

 

Date Assigned

Assignment

Tues, Aug 23

Write your mathography.  Due Thursday, Aug 25.

Thurs, Aug 25

Complete the two tutorials for GSP by Tuesday.

 

Practice compass and straightedge constructions.  You will need to buy a compass and straightedge—please let me know if you need help with these constructions.  You should be proficient with these constructions no later than next Thursday.

Tues, Aug 30

Investigate the following  Intermath Problem.  Bring two copies of the investigation to class on Thursday.

Specific Slopes

 

Reaction paper for Sept 8:

Read the geometry standards for Grades 6-8 in NCTM’s Principles and Standards for School Mathematics (PSSM).  These standards can be found in Chapter 6 of PSSM.  You can sign up for a free 90-day access to PSSM at http://my.nctm.org/eresources/members/login.asp.

In no more than 2 pages (typed, double-spaces, 12 pt font) write your reaction to these standards.  Your reaction paper will consist of two parts:

§         First in a brief paragraph and using your own words, summarize the big ideas that are evident to you. 

§         Secondly, because the Georgia Performance Standards have been developed with the NCTM standards as a guide, what do these standards mean for you as a future teacher?  What are your concerns as you prepare to teach according to these standards?  What areas do you see yourself needing work?  In what areas do you feel strong?  Is there information given that you do not understand—if so, what?  (Please use these questions merely as a guide as you write your reaction.) 

I will use the rubric for grading reaction papers to evaluate your paper—please see the syllabus for this rubric.

 

Thurs, Sept 1

Review the vocabulary we discussed in class tonight. 

 

Investigate the following Intermath Problem.  Bring two copies of your investigation to class on Tuesday.

Quadrilaterals Inscribed Inside Quadrilaterals (GSP would especially be useful for this investigation.  You can write your conjectures in a text box.  Save your investigation to a disk but also print out two hard copies for class.)

 

The Compass and Straightedge Constructions are due Thursday, Sept 8. 

 

Your journal of open-ended reflections is due Tuesday.

 

I put a link at the top of the syllabus called “Useful Tools” that has the Alpha Shapes template, etc. 

 

Tues, Sept 6

The Compass and Straightedge Constructions are due Thursday, Sept 8.

 

The reaction paper on the NCTM Geometry standards will not be due until Tuesday, Sept 13.  Be sure you see my email about accessing the document if you are having trouble.

Thurs, Sept 8

The reaction paper on the NCTM Geometry standards is due Tuesday, Sept 13.  Write up Quadrilaterals Inscribed Inside Quadrilaterals using the write-up template on the Intermath website.  Use the suggestions I made on the work I returned to you today.  This will be due Thursday, Sept 15.

Tues, Sept 13

Review the terminology discussed in class today.  Work the Cross-sections problems on handout.  Be sure to give the name of the 3-D solid as well as draw a picture of the cross-section.  The Quadrilaterals Inscribed Inside Quadrilaterals write up is due Thursday.

Thurs, Sept 15

Discovering Angle Relationships

Discovering Properties of Parallel Lines

 

Tues, Sept 20

Investigate the following problems from the Intermath site.  Be prepared to discuss your findings in class.

Diagonals in a Polygon

The Third Side

 

Do the problem:  How Many Rays?

 

Thurs, Sept 22

We did not talk about the following investigations so please revisit them if necessary—we will discuss Tuesday.

Diagonals in a Polygon

How Many Rays?

 

Investigate the following problems from the Intermath site.  Be prepared to discuss your findings in class.

Classified Information

Mystery Quadrilaterals

 

Read the handout Polygons and Angles from the Connected Mathematics Project.  (This was given out in class.)  Be sure you understand the three ways an angle is considered.

 

GSP would be a useful tool to explore the following problems.  Please write your conjectures for each exploration.

 

§         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.)

 

Tues, Sept 27

Investigate the following Intermath problem. 

Sum of Angles in a Polygon

 

Write a reaction paper to the article “The Role of Definition.”  Paper is due Tuesday, October 4.  Your paper should be 1-2 pages in length.  Please include a 1-2 paragraph summary of the article and then your reaction to the article.  To evaluate your writing, I will use the Rubric for Reaction Papers (please see syllabus).

 

Test 1 will be Thursday, October 6.

 

Thurs, Sept 29

Investigate the following Intermath problems.  You should write up one of these problems.

Find the Hidden Treasure

Capture the Flag

All Swimmed Out

Shark Attack!

Intersecting Circles

 

Investigate these two problems for homework.

 

 

Tues, Oct 4

Determine which of the pentominoes (if cut out) will fold into a box without a top.  Do not cut the pentominoes out—just visualize which would fold into a box.

 

Test—Thursday, Oct 6

Thurs, Oct 6

Continue Intermath investigations.  Revisit the first problem on homework.

 

Tues, Oct 11

You are given a Post Test Opportunity to earn 1/3 of the points lost on the first test.  Please follow the directions given—observe that not only are corrections required but also an explanation of why you missed the problem.  The post test opportunity is due Tuesday, Oct 18.

 

Complete the pentominoes investigation given out in class.

 

Work on the Exploring Quadrilaterals investigation—this should be posted to your Class Docs folder by Tuesday, Oct. 18.

 

Thurs, Oct 13

Review the definition of exterior angle of a polygon.  Investigate the problem Sum of Exterior Angles.

 

Mark asked about an exterior angle in a concave polygon—specifically at the vertex of the polygon where the interior angle is a reflex angle.  What do you think? 

 

Work on problems a and b in Part 2 of the Tessellations handout from class—the questions are:

a.  Can any triangle be used to make a tessellation?  To investigate this problem, you will need to make multiple copies of a triangle (in other words, the triangles must be congruent).  Then see if this triangle can be used to make a tessellation.  Then investigate for a different triangle—make multiple copies of this triangle and see if it can be used to make a tessellation. 

 

b.  Can any quadrilateral be used to make a tessellation?  Again, make multiple copies of a quadrilateral and see if it can be used to make a tessellation.  Explore for various sizes and kinds of quadrilaterals. 

(These two questions are given on an Intermath investigation called Tessellation Restrictions.)

 

Bring your copies of triangles and quadrilaterals to class Tuesday. 

 

Please note that I misspelled “tessellation” on the board—it should have two s’s and two l’s!!

 

I am giving you the link to the article I mentioned in class Tuesday.  From Tesselations to Polyhedra:  Big Polyhedra.”  This article is for your file—you are not writing a reaction paper to this article.

 

Journals are due Tuesday.

 

Tues, Oct 18

Investigate the problem Symmetry Lines II for class Tuesday.  You do not have to do a formal write-up.

 

Write-ups for the following four investigations should be in your Class Docs folder.

Quadrilaterals Inscribed Inside Quadrilaterals

Sum of Angles in a Polygon

Exploring Quadrilaterals

One of the following Intermath investigations.

Find the Hidden Treasure

Capture the Flag

All Swimmed Out

Shark Attack!

Intersecting Circles

 

Thurs, Oct 20

NO CLASS

Tues, Oct 25

Due Tuesday:  Write a paragraph/paper describing the perfect solids (also called Platonic solids or regular polyhedra).  In your paper, you should give the defining characteristics of a perfect solid.  You should also explain why the 5 perfect solids we found are the only ones possible—be sure your explanation offers sound mathematical justification.

 

Please work on getting your webpage functional.  If you have trouble, Drew will come back Thursday—so you need to let me know Tuesday if you are having trouble.

 

A good website to reinforce the information on polyhedra is Exploring Geometric Solids and Their Properties: Unit Overview.  The website refers to “vertices” as “corners.”   

Tues, Nov 1

Write up this one: SAM

 

Write up one of these:

Biggie Size It!

Penning for Pony

Two Squares

 

Thurs, Nov 3

Complete the areas of geoboard shapes—handout from class.

Do “Moving Areas by Moving and Combining” questions 1-4. 

 

Work on these problems for discussion:

Rectangle Squares

Tripling Perimeter

Triangle Inside a Rectangle

Prime Scalene

Walking Around the World

Wrapping Around the World

The Bicycle Problem

 

Be prepared to discuss the first three problems Tuesday.

 

Write up one of these:

Perpendicular Bisectors

Passing thru the Center

Tues, Nov 8

Complete problems 5-7 on handout (this is really the third page of the handout entitled “Moving Areas by Moving and Combining”).

 

We did not discuss Triangle Inside a Rectangle so please be prepared to discuss this Thursday.

 

You should be prepared to discuss the following problems:

Prime Scalene

Walking Around the World

 

Thurs, Nov 10

You should be prepared to discuss the following problems:

Wrapping Around the World

The Bicycle Problem

 

Read the essay, The van Hiele Framework.  Then read the article, Perimeter and Area through the van Hiele Model.   Write a 1-2 page paper in which you include:

1) a description of your understanding of the van Hiele framework or model;

2) your reaction to the ideas presented in the article, Perimeter and Area through the van Hiele Model. 

The Paper is due Tuesday, November 22.  To evaluate your writing, I will use the Rubric for Reaction Papers (please see syllabus).

 

Tues, Nov 15

Find several ways to determine the area of the trapezoid given to you in class, using no formulas other than those for the area of a rectangle, triangle, and/or parallelogram.

 

Create a triangle that has the same shape as the one assigned to you in class.

 

Revisit The Bicycle Problem

 

Tues, Nov 22

Directions for the Final Reflective Portfolio

 

The following 3 Intermath Investigations should be written up:

Changing Cubes

Circle Inscribed in a Semicircle

Your choice of an Intermath investigation that has not been assigned.  Choose from the list of geometry investigations (either a recommended or additional investigation is OK).

 

The homepage for Intermath is at this address http://www.intermath-uga.gatech.edu/

Tues, Nov 29

Find the area of the circle—do not use a formula.

 

This is a useful website for graph paper—add it to your favorites list!

http://incompetech.com/beta/plainGraphPaper/

Thurs, Dec 8

Concept sheet for final exam

 

Here is the website for the Ferris Wheel at Navy Pier.   http://www.navypier.com/SubLink.cfm?Main_ID=15&Sub_ID=3