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Dr. David Ashley, [email protected] math.smsu.edu/faculty/ashley.html
Dr. Lynda Plymate, [email protected]
Department of Mathematics
Southwest Missouri State University
Springfield, MO 65804
Assessment should enhance students' learning.
(e.g. CAS in Algebra and Calculus)
Complete each of the following tasks.
Using your sheet of definitions, investigate whether the rhombus is a square, parallelogram, rectangle, trapezoid, trapezium, or a kite include measurements that support your statements.
Construct the diagonals of the rhombus. What you can say about the diagonals that you can back up with measurements (Are the diagonals congruent? Do the diagonals bisect each other? Are the diagonals perpendicular? Does each diagonal bisect two angles of the quadrilateral?). What is true concerning the four triangles formed from the construction of the diagonals (are the triangles congruent, similar, equal in area)?
Construct the midpoints of all four sides. Construct a quadrilateral formed by the mid points. What type is this quadrilateral? Find the midpoints of each side of this quadrilateral and connect them to form a quadrilateral. Continue this process until you discover a pattern, or the sides of the quadrilaterals become to small to measure. Back up your conjectures with measurements. How does the area of each quadrilateral relate to the original figure you started with?
What can you determine concerning adjacent angles and corresponding angles for the original Rhombus.
How may lines of reflective symmetry exists. How many degrees of rotational symmetry?
What is the sum of the measures of the interior angles?
Explore: Tell me all you can about Rhombuses!!!!
WORKING WITH EXPONENTSDr. Lynda Plymate
The men from the White House
Grade level: 4th grade
Subjects: Social Studies/ Language Arts/ Math
Materials needed: Internet articles from www.mtrushmore.nethttp://library.thinkquest.org/T0211461/history
The students will understand the importance of Mt. Rushmore.
The students will understand why each of the four Presidents was chosen to be on Mt. Rushmore.
The students will practice using ratios.
The students will practice and improve their writing styles.
Ask the students if anyone knows what Mt. Rushmore is. Wait for their response.
Ask the students if anyone knows who is on Mt. Rushmore. Wait for their response.
Have students speculate why each of those Presidents was chosen. Write their answers on the board.
Explain that we are going to learn about the sculptor, how big they are, how long it took, and why those Presidents were chosen.
Pass out copies of the article from www.mtrushmore.net
Read the article Mt. Rushmore Trivia to the class.
Have discussion on what we just read.
Pass out copies of the article from http://library.thinkquest.org/T0211461/history
Have students who are comfortable and want to read aloud, read the article Mt. Rushmore: Presidents on the Rocks.
Stop at the end of each section and have discussion about what was just read.
to toe, they would be 465 feet.
skills in making something practical. This project allows a lot of creativity and is a great way
to learn and apply geometric knowledge for visual/spatial learners such as myself. Before
working on this project, I had no idea how much geometry was used in quilting. The various
quilt patterns out there are amazing and really show ingenious uses of various shapes. I feel
that this project would be a great way to show children in the classroom a practical way to use
geometry outside of the school setting. Not only is the project fun, but it also can be used as a
creative lesson for children who don't necessarily master objectives easily from a textbook
format. It can be used to teach objectives about reflective symmetry, measuring and finding
midpoints, the different types of triangles, angles, and other important geometry skills.
Overall, this project is a great way to enhance the teaching of geometry.
While this project definitely has many advantages in the classroom, there are also
some drawbacks to teaching it. Some children, most likely boys, may not appreciate the
project or lessons because quilting seems to be such a feminine hobby. Second, this project
and a thematic unit may be too time consuming with all of the other objectives required in
today's classroom. To understand the unit and adequately cover the geometry in this project,
more time is required than would be if simply teaching terms and information out of a
textbook. When state standards require many objectives to be mastered in a short school year,
projects like this can put teachers behind in their teaching schedule. This seems to be a
problem in every subject, though, and I feel this lesson is worth the time and should be
incorporated when teaching geometry at the elementary level.
useful endeavor because it is a "real world" teaching project. It demonstrates how
difficult that teaching effectively can be. With the tremendous pressure placed on
teachers today to fit more and more material in less time, we need more practice doing
interdisciplinary projects such as this one. I have enjoyed the teamwork aspects of this
class, although, frankly, I did not carry my own weight in this project. Sally deserves
most of my points for this project as she did most of the work. I offered help in the
design and some basic suggestions, but she was the star of our show.
The cons to the project were that quilts and learning about them would turn some
children off. I envision very few ten year old boys waking early with Christmas-like
excitement to hurry to get to school to learn about quilts. However, it is a perfect
example of how we must teach everything required, whether we like the material or not.
So, if we have to do it, why not make it fun?! Not all material will appeal to all children
or teachers. Another con with a positive spin is the potential of one student of a group
doing more work than the other. While it is "not fair ...boohoo " ...it is a fact of life that
we must step up to the plate sometimes and carry someone else. In our professional lives
(and our personal lives as well), there are times we will get the short end of a teamwork
arrangement. We have two choices. ..pout or try harder. In our group, Sally tried
harder. It was not that I didn't want to work hard or was bored with the class. I have
three kids (8, 2, 3 months) and a wife to support, and I work fun time.
with a final product that can be useful in a future classroom. I thought the amount of
work was reasonable and it was easy to split between two teammates. I thought the
lesson plans were more effective as far as a future teaching tool, because we came up
with lessons that I would actually use in my classroom. That was the major pro of this
project for me: that I was putting the work into a product that will be useful later on.
That also leads me to the major con of the project, which is that I felt the quilt
making itself was very time consuming and I don't think that quilt will be something we
will use again. Also, I think for this level of learning, we as college students did not
necessarily need to be convinced of the geometric properties of quilts, which seemed to
be the point of making the quilt ourselves. I think that simply designing a quilt block by
using Sketchpad would have been sufficient to prove that we understood how a quilt fits
in with math. However, we as teammates managed the workload so that the quilt making
itself was not overwhelming, and we ended up with a neat design that has a lot of
geometric properties as well as arithmetic properties, so it could be used to demonstrate
how the Fibonacci sequence works at a higher level of education, perhaps.
I thought that this was a unique and interesting project that made me think about
quilts in a new way. I think that it could be modified to be more useful by requiring more
lesson plans, to create a more comprehensive unit, and a less emphasis on the
construction of the quilt itself.
$0.00THE STORY OF TIM and TOM AT 9%
Tim and Tom are interesting characters. Some people think there is an important moral to their story. Tim and Tom were twins. They both went to work at age 20 with identical jobs, identical salaries, and at the end of each year, they received identical bonuses of $2000. However, they were not identical in all respects.
Early in life, Tim was conservative and was concerned about his future. Each year he invested his $2000 bonus in a savings program earning 9% interest compounded annually. Tim decided at age 30 to have some fun in life and he began spending his $2000 bonuses on vacations in the Bahamas. This continued until he retired at 65 years old.
Tom, on the other hand, believed in his youth that life was too short to be concerned about saving for the future. For ten years, he spent his $2000 bonuses on vacations in the Bahamas. At age 30, he began to realize that some day he might not be able to work and then would need funds to provide for his support. So he began investing his $2000 bonuses in a savings program earning 9% compounded annually. This continued until he was 65 years old.
Although separated for a few years, they were joyfully reunited at age 65 at a family reunion and exchanged many stories of the events in their lives. Eventually the conversation got around to retirement plans and savings programs. Each brother was proud of his savings and showed the other a spreadsheet describing his savings activities and accumulations. But they were amazed! Tom had made many more $2000 deposits than Tim. Yet,Tim had accumulated almost $200,000 more than Tom. How could that be? Using a spreadsheet fill in the chart and answer the questions.
Actual Teaching: You will have the opportunity to present your lesson to two 4th graders during the 20 – 25 minutes. You are to actively involve them and have your lesson be student centered not teacher centered. Keep you students involved and on task. I know that you will not have much time but try and find out what they understand and do not understand about your concept. At the end of 20 to 25 minutes you will get a new group of two students and you will repeat your lesson.
Interactive JAVA explorations and lesson plans
f(x) := x a g(x) := a x
f(x) = x 2g(x) = 2 x
Requires time to reflect and reason
Non-routine problem solving
(time to build a working strategy)
Requires work with technology
6. The length of time it takes to paint the gymnasium changed as the number of people painting increased.
i) Create a scatterplot to demonstrate winning time for the 1959 143
given years 1960 141
ii) Find r and r2. Then discuss what each number tells you about 1962 144
the relationship between men's winning time and year. 1963 139
iii) Find the least-squares regression line; and then carefully plot 1966 137
it on your scatterplot. Be sure to include and name at least 2 1967 136
specific points on your line. 1968 142
iv) By how much on the average did the winning time improve 1970 131
per year during this period? 1971 139
v) Use your regression line to predict the winning time in 1990, 1973 136
a decade later. Is this prediction trustworthy? Explain. 1974 134
vi) Complete a residual plot for your data. 1976 140
A house has been invaded by 100 termites. The population of termites triples every two days. If the population reaches 800,000, the building will be in danger of severe structural damage. The house has also become infested with 2,000 cockroaches. This cockroach population doubles every five days. If the population of cockroaches exceeds 32,000, the house will be condemned. If the exterminator can only address one problem at a time, which is more pressing, the termites or the cockroaches? In your process of answering this question, you must also demonstrate (using pencil and paper manipulations rather than the calculator "solve" feature) the following 4 items:
i) the specific function which models the number of termites present
after t days, call it f(t) ;
ii) the specific function which models the number of cockroaches
present after t days, call it g(t);
iii) the number of days it will take for the termite population to reach 800,000;
iv) the number of days it will take for the cockroach pop. to reach 32,000.
A common test extra-sensory perception (ESP) asks subjects to identify which of four shapes (star, circle, wave, or square) appears on a card unseen by the subject. Consider a test of n=10 cards. If a person does not have ESP and is just guessing, he/she should therefore get 25% right in the long run. So, the proportion of correct responses that the guessing subject would make in the long run would be p = 0.25.
Complete 100 simulated tests in which a subject guesses randomly on each of the 10 cards. In your simulation be sure to decide whether each card was guesses correctly; find the percent of cards guesses correctly by each subject; sort the 100 percents in ascending order; find the mean and standard deviation for your distribution of 100 tests; prepare a table showing the number of tests resulting in sample proportions falling in increments of 10% relevant to your data (like 0-10%, 10-20%, 20-30%, 30-40%, … ); and finally prepare a column graph to display those counts.
i. Turn in enough printed pages to convince me you have successfully generated random numbers, identified whether the subject's responses are correct, sorted sample proportions, found the requested statistics, table and graph.
ii. Referring to your simulated results, what percent of your subjects guessed correctly on 3 or more of their questions (which is better than random guessing)?
iii. How many of the 10 cards would a subject have to identify correctly before you would say that less than 5% of all guessing subjects would do that well or better?
This is a problem for you and your lab partner to work on together. You are to use Sketchpad to solve this problem. You are given a line segment AB that is one of the diagonals of a square. Your job is to construct the square from the line segment you have been given and explain your reasoning. What you must do is open sketchpad and construct a line segments AB and then copy it to use as your basis for the construction. Then with that information construct the square, provide an explanation of what you did, and print your results.
To me, this approach does seem to be fair if it is used on a limited basis. I do not feel that this would be the way to go all the time because there is still a great need to measure individual achievement. A good balance between individual and team quizzes would probably work best because it promotes two different styles which everyone can experience. To sum everything up, this quiz approach is very connected to what we are doing in class. It follows right along with the concepts of discovery and teamwork/self-guided learning.