M.C. Escher The Mathematical Artist
Developed by,  Douglas von Hollen

Curriculum: mathematics, geometry, problem solving, technology, art, history

Grade Levels: 4-8

Educational Setting: Students will work in pairs or independently depending on computer availability.

Objectives: Students will use the web to research information on M.C. Escher and his art, and report their findings.

Goal: Students will begin to gain an understanding of the relation between fine art and mathematics.

Materials: Students will need access to the Internet and focus questions to respond to.

Prior knowledge and understanding: Students do not necessarily need any prior knowledge to begin this lesson.  They should be questioned for prior knowledge, however.
· Does anybody know of Escher?
· Do we remember what tessellations are?
· What relationship is there between art and math?

Procedure: The teacher should either direct students to the following websites, or have them book marked prior to students’ arrival http://library.thinkquest.org/16661/escher.html or http://www.geocities.com/williamwchow/escher/escher.htm
Once at one of these sites, students will begin to read through the text on Escher and answer the focus questions.
M.C. Escher Focus Questions:
Who was Escher?
Where was he born?
Where did he live?
What was different about his art?
Did he always want to be an artist?
What inspired him to begin his artistic career?
How do you describe his art in general?
Pick a specific Escher artwork, and describe it as completely as you can.  (print the design if necessary)

Assessment: Students will be evaluated on:
· their ability to navigate the world wide web effectively.
· the accuracy of their informational report
· their ability to describe the chosen artwork to the class; if they can describe the technique used to design the specific tessellation, it will be considered beyond expectation at this point.
 
Extensions:  Extensions to this lesson are:
· tessellations in history
· tessellations in religion
· tessellations in art
· how to construct tessellations
· analyzing tessellations

Ideally, this lesson would be followed by a more in-depth investigation of the origin of, the art of, the construction/design of, and the applications of tessellating patterns.
 

Interactive Tangrams Lesson

Developed by, Douglas von Hollen

Curriculum: mathematics, geometry, problem solving, technology, social studies

Grade Levels: 4-8

Educational Setting: Students may either work independently or in teams.

Objectives: Students will use an electronic tangram to solve geometric puzzles, and show their knowledge of basic shapes.

Materials: Students will need access to the internet.

Prior knowledge and understanding: Students should be familiar with tangram puzzles previous to going to this site.  They should also have knowledge of basic geometric shapes such as the triangle, square, and parallelogram.

Procedure: The teacher should either direct students to the following website, or have the site bookmarked prior to student arrival. http://enchantedmind.com/tangram/tangram.htm  Once at the site, instruct students to click on the “tangram” box halfway down the screen.  Once into the tangram applet, use the “AppletInfo” button for directions on how to use the puzzles.  It is very simple.  Once students are familiar with the controls, they can work at their own pace solving puzzles either in teams or independently.

Assessment: Students will be evaluated on their ability to solve tangram puzzles according to individual ability to be judged by the classroom instructor.  i.e. students with greater aptitude should be expected to solve a greater number of puzzles.  Evaluation should also take into account the individual efforts of the students.  Perseverance should be rewarded.   As a review of basic polygons, students should be able to identify the different shapes used in the tangram puzzle.

Extensions: This lesson can be tied into skills using proportion and fractions, social studies, and art. If you travel to:
http://www.geocities.com/TimesSquare/Arcade/1335/  you will find the history of the tangram and all kinds of other links for solving and creating tangram puzzles.  More free downloads of tangram puzzles can be found at: http://www.tangram.i-p.com/  If you want more ideas on how to use tangram’s in your classroom, there’s more to be found at AskEric
http://ericir.syr.edu/Virtual/Lessons/Mathematics/Geometry/GEO0005.html
 

Lesson Plans for Grade 6 Fractions:
Identifying Parts of a Fraction
By Joan Racicot

Grade Level:  Sixth Grade

Subject:  Identifying parts of a fraction.

Objectives:  To have the students learn to use the keyboard to type mathematical terms while they identify the different parts of a fraction.

Purpose: To review the use of the keyboard and fraction parts.

Student Arrangement:  Students will work in the computer lab with the instructor.

Time Allotment:  One forty-minute class.

Procedure:

1. The students will meet in the computer lab.

2. The teacher will state the purpose: To review the use of the keyboard and fraction parts.

3. The teacher will show examples of numerators, denominators, and the division sign for fractions with the class computer.

4. Each student will use his or her own designated disk using Word.

5. The disks will have 3 questions asking parts of a fraction.

6. The student will use the keyboard to answer the questions into complete sentences.

7. The student will use spell check.

8. The teacher will ask students to the class computer to fill in the answers.

9. The student will complete 5 more questions on his or her own.

10.The student will print out the answers for the teacher.

11. The student will print out the 5 remaining questions to complete as homework.

Assessment:  Students will reach the objective first correctly completing the in class assignment and correctly completing the homework.

Lesson Plans for Grade 6 Fractions:
Converting Fractions into Decimals
By Joan Racicot
 

Grade Level: Sixth Grade

Subject:  Converting Fractions into Decimals

Objectives: To have the students learn how to find and use the calculator on the computer to convert fractions into decimals.

Purpose: To expose the student to the calculator on the computer and learn how convert fractions into decimals using the calculator.

Student Arrangement:  Work in the computer lab with the Math teacher.

Time Allotment: One forty-minute class.

Procedure:
The students will report to the computer lab.

The teacher will demonstrate how to locate and use the calculator to convert fractions into decimals with the class computer for everyone to see.

The students will then find the calculator.

The teacher will state a fraction and the students will use the calculator to convert it to a decimal.

The teacher will pass out a sheet including twenty fractions.

The students will convert the fractions into decimals by using the calculator on the computer.

The teacher will review the first two problems with the students.
 

Assessment: The students will reach the objective when they complete the worksheet correctly.
 
 

Lesson Plan Aaradhana Prajapati
Elementary Class- Grade 1
Topic Math 1/10/01
 

Objective: Students will be able to work on the Jump Start 1st Grade program by Knowledge Adventure.  The students will be able to work on a few simple subtraction problems by using the computer.

Procedure: Students will be assigned a partner to work on the math problems.  Together they will take turns at figuring out the answers for the problems.  They will be able to work at a higher or lower pace depending on their level of knowledge for the word problems.

Materials: Students will only need their computers to work on for this lesson.

Closure/Evaluation:  At the end of the activity on the Jump Start Program students will be quizzed at their ability on the math problems. They will do this at their own pace and individually.  The computer program then will add up the scores and give a final result for the students performance.
 

Recording Temperature on Spreadsheet Lesson developed by Teresa Maturino-y-Buschman
What was the Average Temperature?
Grades 3-5

Objectives:

     To learn to organize and record information
     To practice the use of spreadsheets
     To review the vocabulary words spreadsheets, columns, rows, and cells
     To practice calculating averages

Assumptions:
The students have been introduced to the use of spreadsheets and the mathematical
concept of average.

Materials:
computers with Excel software
blank copies of spreadsheet printouts (1 copied for overhead use)
overhead projector
student recorded weather information
calculators
rulers
pencils

Procedure:
Give each student a blank copy of a spreadsheet.  Ask them if they remember what it is
called.  Lead the discussion based on student responses or questions.  The point here
is to remind students that the paper is called a spreadsheet, that spreadsheets are made
of columns and rows, that each square is called a cell, that a column letter and a row
number identify each cell, and that a computer program creates spreadsheets.  It may
be helpful to use an overhead projector to review the parts of a spreadsheet and for the
first part of this assignment.

Part I
Tell the students they will learn to use a computer spreadsheet to organize and record
their weather information and that they will also use the computer to calculate the
average temperature per week.  Before continuing, organize students in groups of 2 to
3  (the basis for grouping is based on students' abilities and available resources.).

Begin by telling the students to label the cells in column A, beginning at row 2, Week 1,
Week 2, Week 3, Week 4, and Week 5 with their pencils on the blank copy, as it is being
demonstrated on the overhead.  Depending on the students’ knowledge of the
spreadsheet, either ask what the cells in Row 1 will be labeled or demonstrate for the
students to label them in the following way:  cell B1 Monday, cell C1 Tuesday, cell D1
Wednesday, cell E1 Thursday, and cell F1 Friday.

Once students have labeled their spreadsheets, either ask them what temperature will
be recorded in cell B2 for week 1, or demonstrate on the overhead how to record the
weather for week 1, doing it day by day on the overhead.  This will serve only as an
example.  Students will record their actual data on the computer in Part II.

Part II
Once each group of students is stationed at their computer and the spreadsheet is on
the screen (ready to go!), explain that they will begin by labeling the cells as they have
done on their paper.   Tell students that they will label two more cells: cell G1 should
be labeled Estimate and cell H1 should be labeled Average.  After they have typed in the
correct labels, they may type in each cell the appropriate temperature for each day
based on their weather handwritten weather charts, graphs or records.  Cells in the
Estimate and the Average columns should be left blank.

After students have filled in their data (assuming there were no major problems), each
group will estimate the average temperature for each week.  Have students type in
their estimate under the Estimate column.  Next, ask students to calculate with pencil
and paper the average temperature for week 1 (It may be necessary to review
“averages” for some groups.).  Ask students to write one sentence explaining how they
calculated the average, reminding them to identify the cells they used by column letter
and row number.  Once students have explained that they added cells B2 through F2
and divided the total by 5 (teacher support for this will vary), demonstrate on the
computer or on the overhead how the computer can calculate this for them by writing
the formula in the cell.

Example:  In the first cell of the Average column, which would be G2, type
=(B2+C2+D2+E2+F2)/ 5.   This means the daily temperatures for Monday, Tuesday,
Wednesday, Thursday, and Friday are added and divided by 5.  When the
return/enter key is pressed, the computer will calculate the average and print it in the
cell.  Ask students to calculate the average temperature for each of the remaining
weeks by using the same technique.  Leave the copied formula on the overhead or
written on the chalkboard, so students may refer to it.

Allow students ample time to calculate each average.  Some students may grasp the
concept quickly, but others may need more time to understand what they are doing.
For those students who finish quickly, have them use the spreadsheet to calculate the
average age, average number of family members, average shoe size, etc. for their
group.  Students may also challenge each other to see if the average may be calculated
quicker on the computer or on the calculator.

Wrap-up the lesson by saving and printing out all student work.  At this time, it does
not matter whether all the work was completed but whether students began to
understand the use of a spreadsheet to organize their weather information and to
calculate averages.  Ask students to share whether they felt that using the spreadsheet
was useful or confusing, what were the difficult and easy parts to using the
spreadsheet, and what would they like to calculate next on the spreadsheet (these are
only sample questions).

Assessment:
The accurate completion of the spreadsheet printout may be a standard form of
evaluation, but it may not be the most appropriate one.  A point-based assessment
rubric may be created to evaluate each group’s printout and collaborative work.  The
teacher may use a group or individual based checklist to identify areas mastered or
areas that need improvement.  The printout may be included in a unit portfolio as one
part of an overall evaluation.

A lesson plan for an Algebra II class by Vera Richardson

Objective: Students will learn to solve and graph inequalities.
Role of teacher:

     Teacher will direct students to use Maple V and Excell and Microsoft Word.
     Teacher will monitor and assist students on the use of these programs

Resources/Materials:  A computer lab that has PCs' with Maple V ,Excell and Microsoft Word included.
Teacher will hand out the problem for homework prior to discussing the topic.

Classroom Management: Teacher will assign groups of 3 or 4 to a computer for them to use
for the day.

Initiation: Teacher will ask students if they have read the chapter on inequalities in their
textbook before coming to class. Have students describe what they read for homework
before starting the project.

Procedure:

     Teacher will explain objectives.
     Teacher will have the groups discuss the problem out amongst themselves for 5 min.
     Teacher will have the groups use Maple V to solve the Problem they did for homework.
     Teacher will have the groups use Excell to graph the problem they solved using Maple V and
     homework.
     Teacher will have the groups use Microsoft Word to write about what they have accomplished that
     day and what they learned from this topic. Also if they liked this approach of teaching.

Closure: Teacher will go over the problem with the students to give them the correct answer. Then the
students can compare to their own work.

Evaluation: Teacher will evaluate groups performance by having them print out the work.
Further information about the groups understanding will be obtained through
conversation at the end of class period.
 

Lesson Plan #1 (Using MAPLE V)
Subject Matter for the Lesson: Calculus
Grade(s) Level for the Lesson: Grade 11 (advanced); Grade 12
Developed by: Angela Gouthro
Time Limit: 2 fifty-minute class sessions, and outside class preparation

Objectives:
-The student will be able to use and understand the concept of a derivative
to calculate average velocity over a time interval;
-The student will be able to explore average and instantaneous rates of
change for general functions;
-The student will be able to graph functions using MAPLE V;
-The student will be able to create a table of average velocities using
MAPLE V;
-The student will be able to comprehend and utilize the following functions
in MAPLE V: ‘evalf', ‘plot', ‘limit', ‘expand.'

Anticipatory Set:
-The teacher will initiate the class by discussing the terms average
velocity and instantaneous velocity;

Teaching:
Input/Modeling/Guided Practice:
-The teacher will guide the class in a tutorial of MAPLE V, which will
include entering values, plotting graphs, and basic math functions (‘evalf',
‘plot', ‘limit', ‘expand.'  He/she will also demonstrate basic Calculus
problems which use MAPLE V that involve average velocity and instantaneous
velocity;

-The teacher will ask the students to plot a graph using MAPLE V, and the
teacher will check each student's graph before continuing with the lesson;

-The teacher will pose the following question which relates average velocity
to a "real- world" problem:
‘Taking into consideration air resistance, a suitcase dropped from an
airplane falls
        968(e^(-0.18t) - 1) + 176t feet in t seconds."
Throughout this lesson, students will be exploring this statement, and will
be calculating average velocities and instantaneous velocity.

-The questions the students need to solve using the above statement include:
a)Find the average velocity of the suitcase over the time
intervals t=1.99 to t=2 and t=2 to t=2.01.  Use this to estimate the
instantaneous velocity of the suitcase at time t=2;

b)Plot the graph of the average velocity from t=2 to t=2+h as a function of
h and use it to estimate the instantaneous velocity at time t=2;

c)Find the instantaneous velocity of the suitcase at time t=2 by calculating
the appropriate limit.  Compare this to the two estimates in the above two
questions.

-The teacher will guide the students in solving the above questions:

The first question involves the function ‘evalf" in MAPLE V; the solution
can be found by entering evalf((s(2) - s(1.99))/0.01) and evalf((s(2.01) -
s(2))/0.01), and then taking the average of these two answers.

The second question involves the graphing, using the function plot((s(2+h) -
s(2))/h, h= -1..1) , and zooming into the graph at h = 0 when it is plotted.

The third question involves determining the limit using the following
functions:
        expand ((s(2+h) - s(2))/h)    AND limit(", h=0).

The teacher can also demonstrate to the students that the solutions can be
determined by making a table of average velocities.

Checking For Understanding/Independent Practice:
-The teacher will give the students three problems to be worked on
independently using MAPLE V.  These problems include the following:

a)You drive for one minute at a constant velocity of 60 miles per hour.  You
then instantly slow down and drive for one more minute at a constant
velocity of 40 miles per hour. Assuming you lost no time in slowing down,
what is your average velocity for the two minutes?

b)You drive for one mile at a constant velocity of 60 miles per hour.  You
then instantly slow down and drive for one more mile at a constant velocity
of 40 miles per hour. Assuming you lost no time in slowing down, what is
your average velocity for the two miles? (NOTE: 50 miles per hour is not the
right answer).

c)You drive for one minute at a constant velocity of 30 miles per hour.  You
then want to instantly speed up and drive for another minute so that your
average velocity for the two minutes is 60 miles per hour.  Assuming that
you lost no time in speeding up, what velocity must you drive for the second
minute?

Closure:
-The teacher will go over the answers for the assignment with the students,
emphasizing that it is important for the students to understand why they are
using the functions of MAPLE V, and how they help to solve each problem.
 

Lesson Plan #2 (Using Microsoft Word, Excel and Graphing Calculators)
Subject Matter for the lesson: Geometry and/or Introductory Algebra
Grade Level(s) for the lesson: Middle School
Developed by: Angela Gouthro
Time Limit: 3 forty-minute classes, as well as outside class preparation

Objectives:
-The student will be able to apply the concepts of area and perimeter to a
‘real-life' situation;
-The student will be able to construct responses to problems by using
physical models,calculators, and computers;
-The student will be able to use spreadsheet tables and graphs (using
Microsoft Excel) to help solve a mathematical problem;
-The student will be able to use the ‘trace' function with a graphing
calculator in order to help solve a mathematical problem;
-The student will be able to organize data collected and present a report on
his/her findings using Microsoft Word.
 

Anticipatory Set:
-NOTE: It is assumed that the students have a thorough understanding of the
terms area and perimeter.

-The teacher will introduce the topic by describing the following situation:
Mary is designing quilt sections made of square pieces.  When the quilt
section is finished, she will finish the edges by sewing a wide ribbon
around the outside.  Suppose Mary uses six squares.  There are numerous
arrangements for these six squares (including placing the squares side by
side, putting three squares on top and three on the
bottom, etc.)  What are the possible arrangements for this quilt?

-The teacher then asks the following questions:
a)Would the same amount of ribbon be required to go around each quilt?  If
not, which quilt would take more?

b)If each quilt is one square foot, then how much ribbon would be needed to
go around each quilt (ignoring the overlap of ribbon needed on the corners)?

c)What other perimeters are possible using the same six squares? (Each
square must be attached to at least one other square on a full side).
 

Teaching:
Input:
-The class should now brainstorm ideas as to how to go about solving this
problem.

-The teacher should guide this discussion by asking questions such as the
following:
-What is the maximum perimeter? The minimum perimeter?  What would happen if
the number of squares changed?  Can a pattern be detected?

-The teacher should use a chart to organize the class data and observations;
this is important, as the class can then visually search for patterns and
generalize results.

-NOTE: Through exploring rectangular shapes, certain patterns emerge.  It
should be realized that a rectangular quilt will give the maximum perimeter
for each area, but not always the minimum.  The number of squares determines
which shape will give the minimum perimeter.  If an even number of squares
is used, then a rectangle will give the minimum perimeter.  If an odd number
of squares is used, then a nonrectangular figure will give the least
perimeter.

Modeling/Guided Practice:
LOOKING FOR PATTERNS:
-By exploring their data, the class should recognize that the maximum
perimeter increased by two each time another square was added.  Furthermore,
the maximum perimeter is the number of squares times two plus two.

-The pattern for the minimum perimeter is not as obvious.  However, with
guidance from the teacher, it should be noted that whenever the number of
tiles was a square number, it gave the minimum perimeter (for example, given
9 tiles, a 3X3 square gave a minimum perimeter of 12 units).  However, the
pattern for other numbers of tiles is not
evident; thus, the teacher may want to stop at this point and attempt to
discover with the class some of the patterns for minimum perimeter.

-The teacher should then introduce to the class the fact that a graphic
representation of both the maximum and minimum perimeters might help them
generalize their results to any number of squares.  Thus, assuming that
computers are available to the students, the
teacher should arrange the class into groups of three.

-The teacher will introduce the program Microsoft Excel to the students,
explaining to them that it is a spreadsheet, and can be used to represent
data.  A brief explanation of the columns, rows, and general functions of
Excel should be provided.  The teacher will explain to the students that
they need to create two columns to determine maximum perimeter:

-The first column should be labeled "Number of Tiles/Area", and the data
should be entered so formulas can be used in the program.  Thus, if the
block A4 was the first area, then the next entry underneath would be A4+1,
the next, A5+1, and this would continue.
-The second column should be labeled "Maximum Perimeter", and the data
should be entered in the following format: if the first entry was in the B4
block, then the student should enter 2*A4+2 for that block, 2*A5+2 for the
next block, and this would continue.
Therefore, the students are introduced, through guided practice, the basic
functions involved in Microsoft Excel.

-The students, lead by the teacher, should then graph "maximum perimeter vs.
area" using the graph functions in Excel (this should be a linear function).

-In the same type of manner, minimum perimeter should be explored.  The
students should be able to place their data into a table, and graph their
results.  The graph will not be a straight line, and the students are
encouraged to continue to look for patterns.

-After the work on the spreadsheets, the students should be able to derive a
general mathematical formula for maximum perimeter: y=2x +2.  The teacher
can then explain to the students that this formula can be translated to a
graphing calculator (such as a Texas Instruments 85 graphing calculator).
The teacher may have the screen of the calculator projected for the
students, or, ideally, each group should have a graphing calculator of their
own.  The teacher should then explain the "TRACE" function of the graphing
calculator.  By using the TRACE function, the students can discover that by
tracing the graph, several points that were not on the spreadsheet can be
found (such as(2.3, 6.6).  Discussion should follow about the meaning of
such points and whether or not they would occur with tiles.

Checking for Understanding/Independent Practice
-The students are then asked to present their findings in a report, which
should be typed using a word processor, such as Microsoft Word.  This report
should include a statement of the investigation, the procedure,
observations/results (using the spreadsheets tables and graphs), extensions
of the problem (using the TRACE function), generalizations, and conclusions.

Closure:
-The class, after this investigation, should discuss the way in which they
solved the problem.  It is interesting to talk about the fact that problem
solving often leads to more problem solving.  Investigations which use
physical, concrete models and technology can encourage in-depth explorations
of mathematics.
 
 

Lesson Plan #3 (Using SPSS software)
Subject Matter for the lesson: Statistics/Marketing Research
Grade Level(s) for the lesson: High School
Developed by: Angela Gouthro
Time Limit: 4 or 5 fifty-minute classes, as well as outside class
preparation

Objectives:
-The student will be able to design a marketing research survey;
-The student will be able to work cooperatively in a group;
-The student will be able to conduct their survey, and collect and organize
data;
-The student will be able to enter data using SPSS software;
-The student will be able to perform and understand calculations using
functions such as mean, median, mode, normal distribution, using SPSS
software;
-The student will be able to draw conclusions base on the calculations
performed, and present these conclusions clearly and accurately.

Anticipatory Set:
-The teacher will introduce the lesson by presenting to the students samples
of simple, effective marketing research surveys.  The class will then
discuss the aspects of each survey which allows it to be effective.

Teaching:
Input/Modeling:
-The teacher will divide the class into groups of three, and present their
assignment to them: to perform a basic, ‘real-life' marketing research
survey and to analyze the data using SPSS software;

-Each group will brainstorm ideas for their survey topic, with advice from
the teacher; sample topics may include choices of music for the school's
population; preferences and opinions of the school cafeteria, etc.  The
survey should involve more than four variables (for example, age range, sex,
favorite category of music, and least favorite category of music).

-Each group will design their own marketing research survey, modeling the
examples of effective surveys; the group's completed survey must be approved
by the teacher before the group continues;

-The group can now proceed to implement the survey, being careful to obtain
a representative population for the results;

-When the data has been collected, the teacher will guide the students in a
basic tutorial of SPSS, demonstrating how to input data, and perform basic
statistical functions;

-Each group will now input their data in SPSS, and perform calculations such
as mean, median, mode, and normal distribution.

Check For Understanding:
-The teacher will monitor the students' progress and ensure that their data
is entered correctly.  The teacher will also assist the students in drawing
conclusions based on their data;

Closure:
-Each group will present their findings in a report, which includes data
tables and the calculations which were performed.  The report should state
the situation, procedure,survey, results, and conclusions.

Patricia Ferryman
Lesson Plan #1

Middle school math

Objectives:  Students will review math topics from the year by creating a Hyperstudio presentation on a topic of their choice to be used with next year’s class. Students will work in small groups.

Anticipatory Set:  For the next few classes we will be working in groups to tie together the new concepts we’ve learned this year.  You will be choosing a topic from the list I have on the overhead.  Every group must choose a different topic.  You  will then research the topic and prepare  a Hyperstudio presentation which reviews the topic.  The presentations will help us review for the final exam.  You will be graded according to the rubric...

Teaching:  Students will break into groups.  In some classes teacher will assign groups.  Students will be given the remainder of the class period to review rubric, ask questions, organize tasks etc.
Next class:  students will go to computer lab and begin working on their presentations.  Teacher will model a presentation created by herself or a former students.  Teacher will check for understanding by conferencing with each group re: progress, etc.

Monitoring:  Teacher will monitor progress throughout the project.

closure:   Students will present their hyperstudio presentations to the class.  Class will discuss and comment.

Independent Practice:  Students may use each other’s stacks to prepare for final exam and review topics they were unsure of.

Patricia Ferryman
Lesson Plan 2
Middle school pre algebra

Objectives: Students will use Excel to calculate simple and compound interest.  Students will understand the value of compound interest.

Anticipatory Set:   Compound interest has been called the eighth wonder of the world.  Let’s use our computers and a few formulas to see why it’s so powerful.

Teaching:  Introduce formulas.  Review vocabulary: interest, principle, rate, etc.
 Have students “invest” $100 at 10% interest.  Help students fill in spreadsheet by modeling.  Have students write formulas to create a spreadsheet which will calculate both simple and compound interest for each year 1-15.

Monitoring:  As students work, move around room answering questions and guiding students.

closure:  Have students discuss their spreadsheets.  Are they all the same?  Should they be?  What formulas did students write?  Can we achieve the same results with different formulas?

Independent Practice:  For Homework have students answer questions such as: How many years will it take to double your money using simple/compound interest
 

Patricia Ferryman
Lesson Plan 3
Middle school math
 

Objectives:  Students will become familiar with the concept of interest on credit cards by using the excel spreadsheet.

Anticipatory Set:  Suppose you buy a stereo for $800.  You put $50 down on the stereo and make payments of $25 each month.  How long do you think it will take you to pay off the stereo?  (wait for answers)  Do stores usually let you pay a little each month with no penalty?  What if they charged 5% interest on the unpaid balance each month.  How could we figure out how much more we’d be paying with the interest figured in?
 

Teaching:  Teacher will model a spreadsheet on Excel which will calculate the no interest balance and the balance each month with 5% interest.  The spreadsheet will also show the amount of interest paid each month.  Students will then develop their own spreadsheets including developing formulas.

Monitoring:   Teacher will monitor each student and check for understanding and accuracy throughout lesson.

closure:  Teacher will have students compare their results.  Check to see which formulas worked and why others did not.   Have students discuss how long it took to pay off the stereo with /without interest.  How much interest did they pay?

Independent Practice:  Have students repeat scenario using different interest rates

Patricia Ferryman
Lesson Plan 4
8th grade math

Objectives:  Students will create a math story using  Microsoft  Word

Anticipatory Set:  Put several different line graphs on the overhead and discuss what the “story” behind each one might be.  Make the stories very creative with student participation.  For example, a graph of dairy product consumption over time may have a villain who is killing all the dairy cows so nobody can get their recommended calcium etc.

Teaching:  Present students with a graph which shows change over time.  The graph should be interesting and catch their attention for example the amount of sand on a beach, the amount of dog food a dog eats throughout a month etc.  The graph should have unexpected changes in slope which cannot be easily explained.  Ask students to create a story to explain the graph.  Each story should be different and must accurately reflect the changes in the graph.

Monitoring:  Conference with each student during the brainstorming time to make sure their stories are appropriate and accurately reflect the graph.

closure:  Have select students read their stories to the class.  Ask the class if stories reflect the graphs.

Independent Practice:  Give students several graphs for homework with questions that require interpretation.

AFRICAN ANIMALS AND MATH lesson plan
developed by MARY K HAMMERSTEIN

SUBJECT: MATH

TOPIC: GRAPHING

MATERIALS:
CRICKET GRAPH SOFTWARE
GRAPH PAPER
CRAYONS

OBJECTIVE:
TEACH GRAPHING AND SORTING

PROCEDURE:
1. INTRODUCE THE STORY BRINGING THE RAIN TO KAPUTI PLAIN
2. READ THE STORY
3. DISCUSS THE FOUR ANIMALS IN THE STORY AND INTRODUCE THE GRAPH AND SOFTWARE
4. MODEL THE GRAPHING PROCEDURES WITH BOTH THE SOFTWARE AND GRAPH PAPER TO
THE STUDENTS
5. HAVE STUDENTS BEGIN GRAPHING OWN ANIMALS WHILE CHENCKING FOR UNDERSTANDING
6. AFTER ALL STUDENTS HAVE FINISHED, DISCUSS RESULTS

Lesson Plan for a Stock Market unit within a sixth grade Math class developed by Peter J. Crump

Topic:  Students will be introduced to spreadsheets and have their basic math skills
reinforced by buying and selling stocks throughout the entire school year.

Resources:

   1.The students will use the classroom computer.
   2.The students will use the spreadsheets that are contained within Appleworks,
     version 5.0.
   3.They will be given worksheets with current stock prices every two weeks.
 

Assignment:

   1.One class period will be devoted to showing the students the creation of a
     spreadsheet.  The basic assignment will be outlined and a sample spreadsheet
     will be created, showing them how to create the boxes, title them, and enter the
     formulas.
   2.The students will be divided into teams of two and they will be allowed to name
     their team.
   3.Each team will be given a list of one hundred popular companies that are listed
     on the New York Stock Exchange.  Each team will choose from the same one
     hundred companies.
   4.Each team will be given a sum of fifty thousand dollars to buy stock in as many
     companies as they choose.  They will be given the closing stock price of those
     companies from the previous days business.  After choosing their companies,
     they will enter their data on their spreadsheet.
   5.Every two weeks they will be given some class time to evaluate their companies
     by looking at the current stock price of those companies and decide if they want
     to sell, buy or do nothing.
   6.By the end of the unit the students should have a clear understanding of the
     basics of buying and selling stocks, the ability to understand how money invested
     can make or lose money, and  how spreadsheets can make math calculations
     simple and time saving.

Evaluation:

   1.The students will not be graded on how well they preform in the stock market.
   2.They will be graded on how well they create and update their spreadsheets.

Lesson plan # 1 by Glenn Blaisdell
Lesson: Computer and Math Program Familiarization
Grade:  3rd or 4th

Materials:      Computer, Kids Math, Big Math Attack,
Planet Math

Objective:      The students will be able to find, open and
use the following math programs:
                        Kids Math
                        Big Math Attack
                        Planet Math

Procedure:      1) The teacher will have the students sit
down the computer and then review how to use a mouse
and the keyboard. 2) When the students are comfortable
using the mouse and keyboard the teacher will
demonstrate how to open one of the math programs. 3)
The teacher will observe each of the students opening
the math program. 4) After each student has
successfully opened the math program the teacher will
demonstrate how to enter or find you name in the users
menu. 5) The teacher will demonstrate step-by-step how
to use the game for subtraction, addition,
multiplication, and division. 6) Steps 3 - 5 will be
done for each of the three math programs.

Assessment:     The students will be evaluated on their
ability to open each of the math programs and complete
one lesson in each program.

Lesson plan # 2 by Glenn Blaisdell
Lesson: Addition and Subtraction
Grade:  3

Materials:      Computer, Kids Math, Big Math Attack,
Planet Math

Objective:      The students will be able to add and
subtract single digit numbers with proficiency.

Procedure:      1) The students will open Planet Math and
begin at level 1 addition or subtraction. 2) After
completing the first two levels of Planet Math the
students will open Big Math Attack and play up to
three games.  This will increase their proficiency in
addition or subtraction. 3) When the student has
completed one to three levels of Big Math Attack and
fills comfortable with their ability to bad or
subtract single digit numbers they will open Kids Math
and do lesson one.

Assessment:     The students will be evaluated on the
proficiency tests after completing Kids Math lesson
one.

Lesson plan # 3 by Glenn Blaisdell
Lesson: Multiplication
Grade:  Late 3rd or 4th

Materials:      Computer, Big Math Attack, Planet Math,
pencil, paper

Objective:      The students will be able to complete
multiplication from 1 to 12.

Procedure:      1) Each students will develop one
multiplication question and write it on a piece paper.
2) The teacher will gather all the questions and
generate one page containing all questions. 3) Each
group we use the questions developed by the class and
other questions to quiz each other on multiplication
from one to twelve. 4) Each student will take pay his
or her turn using the computer.  The students will
open Planet Math and do multiplication lesson one and
two. 5) After completing lessons one and two in Planet
Math the student will open Big Math Attack and play
games on level one and two. 6) When the student fills
that his or her proficiency is developed sufficiently
they will open Planet Math and do multiplication test
No. 1.

Assessment:     The students will be evaluated on their
proficiency and ability to correctly answer
multiplication questions between one and 12 on the
multiplication level one test and Planet Math.

Lesson plan # 4 by Glenn Blaisdell
Lesson: Metric System Conversion
Grade:  4th or 5th

Materials:      Computer, Big Math Attack, pencil, paper, a
ruler with both metric and standard             measurements

Objective:      The students will be more familiar with
metric system conversion.

Procedure:      1) The teacher will ask the students to
measure objects in both metric and standard units. 2)
Each group will take measurements on items they can
find around classroom and they will write their
measurements down on paper. 3) Each group will be
asked to develop ten questions concerning metric
measurements. 4) The groups will exchange their
questions and then answer the questions from each of
the other groups. 5) While the students are answering
the questions for the other groups each student will
take his or her turn using the computer. 6) The
students using the computer will open the program big
math attack.  They will step through the metric lesson
on measurement.  After completing the lesson on metric
measurement they will play one round of metric
measurement attack.

Assessment:     The students will be evaluated on their
ability to answer the questions generated by the
groups and their ability to quickly identify metric
measurements

Lesson:  Computer/Math (graphing)…M&M graphing developed by Kirsten Samokar

Grade:  Three

Materials:  Mac Computer, "ClarisWorks" Software, information sheet
containing data collected from previous math lesson.

Objective:      Students will transform collected date into a graph
reinforcing graph skills.  Students will become familiar with the software
program "ClarisWorks."

Procedure:  Teacher will review steps used to open "ClarisWorks", to insert
information and to complete graph, whole group, using computer with large
monitor for easy viewing.  Teacher will review the concept of graphs.
Students will work independently transferring previously collected data to
the ClarisWorks program creating a graph of color and amount M&Ms.  Students
will title and label graph.  Teacher will assist students as the need arises.

Assessment:  Final printed out product of graph.

Lesson:  Computer/Math…Geometry developed by Kirsten Samokar

Grade:  Three

Materials:  Mac Computers, "ClarisWorks, Sample File" software

Objective:      Students will gain knowledge of spatial relationships.
Students will become familiar with manipulatives on the computer.  Students
will identify various geometric shapes.  Students will become familiar with a
new aspect of "ClarisWorks" and its use.

Procedure:  Teacher will review vocabulary (tangrams, flip, rotate,
horizontal, vertical, square, triangle, rectangle, parallelogram).  Teacher
will review steps needed to use "ClarisWorks, Sample File".  Students will
work independently with teacher assistance when needed.

Assessment:  Correct completion of each of five puzzles.
 

Lesson:  Computer/Math/Language Arts developed by Kirsten Samokar

Grade:  Four

Materials:  Mac Computers, "ClarisWorks (templates)", previously created
timelines

Objective:      Students will become familiar with another aspect of
ClarisWorks and its use.  Reinforcement of calendars, dates, and timelines.

Procedure:  Teacher will review steps needed in "ClarisWorks" create
calendars.  Students will transfer information from a timeline to a
"ClarisWorks" calendar template in correct order for one given month.

Assessment:  Final printed out calendar product.
 

Lesson Plan for 8th Grade Math Class
Developed by Shannon Gantick, for EDU 360

Purpose:  This lesson plan will exercise children in basic addition and
subtraction by teaching them how to balance a checkbook.

Materials:  The students will be given a folder containing a checkbook
with ten checks, paychecks, bills and monetary gifts.  They will also be
given deposit and withdrawal slips.
Everyone’s folder will be different.

Methods:  We will start the class by teaching the children how to fill
out a check and what everything on the check means.  Once they have
grasped that they will then learn how to fill out their deposit slips.
After this is done, we will then begin to enter the deposit slips and
pay the bills that each student has.  This will be done on their own, as
the teacher circulates the classroom helping each student along.  Once
everyone is finished with his or her checkbooks, we will come together
as a group and discuss the lesson.

Four Lessons developed by Sabrina Papadopoli

Lesson Plan: Understanding Graphs
Grade Level: 9th or 10th grade

Materials: Microsoft Excel

Objective: To get the students to understand what happens to a line when an integer is added, subtracted, multiplied, or divided.

Procedure:  The students will split up into groups of three or four.  The will begin with a list of lines (each group will have a different list).  All of the groups will begin by graphing the equation of a line (y=x).  Then the students will work down the list.  One group will be adding integers, another subtracting.  The third and fourth groups will either by multiplying or dividing the graph by an integer.  Upon graphing the lines, the students will try to find a pattern as to what happens when the equation is changed.  They will then come up with a general statement applying to all lines.

Assessment: The teacher will print up each group’s work and have them present their findings the following day.  Everyone will be given a copy of all of the graphs to be quizzed on at the end of the week.

Lesson Plan: Understanding Probability
Grade Level: 9th or 10th grade

Materials: Microsoft Excel

Objective: To get the students to understand probability through experimentation.

Procedure: Students will be spilt into small groups and given an outline of the experiment.  They will construct a chart, using Microsoft Excel, that allows them to keep track of all possible sums when two die are rolled.  Upon rolling the dice, the students are to find the probability of rolling each sum.  The computer can compute the probability, if the proper equation is entered into the spreadsheet.
The students must then create a second chart, comparing the actual probability of rolling each sum with the experimental probability (found by each group).  The students will then find the margin of error (again, the computer can find these computations).
Finally, the students are to present their findings to the class in graph form.

Assessment: Everyone will be given a copy of all the presentations.  A quiz will be given at the end of the week, based on the experiment.
 

Lesson Plan: Learning Derivatives
Grade Level 12th grade

Materials: Maple V

Objective: To get the students to understand how and when to use Maple and also to understand the concept of derivatives.

Procedure: The students will be given twenty-five derivatives to do for homework (over a period of two days).  They will be split into groups of six to compare their answers to the problems.  They will work together until all six students have the same answers to all twenty-five problems.  Then, the students would split up further, into pairs.  They would then use Maple to check their derivatives.

Assessment: The pairs will hand in a packet.  The packet will include their original derivatives, done by hand (each student will hand in their own work), and a printed version of their Maple program.
 

Lesson Plan: Utilizing the Internet
Grade Level: 9th or 10th grade

Materials: Any Internet Service

Objective: To help the students to learn how to use the Internet.  In using the Internet, the students will learn research skills and how to write a research paper.

Procedure: The students will do an individual project on a well-known mathematician.  They will learn to use search engines, such as Yahoo, Lycos, and GoTo.  The students will do research until they find a mathematician who interests them.  They will then do the necessary research to write a five-page paper, bibliography included.  No sources, other than Internet sources will be accepted.  Upon the completion of the paper, the students will give presentations to the class to share what they have learned.

Assessment: The papers will be turned in for grading.  The presentations will be graded on a separate level.

Lesson Plan developed by Sarah Bond
Grade Level: 8th grade

Materials: World Wide Web and Microsoft Excel

Objective: To have students utilize the internet to track a companies
daily stock reports and use Microsoft Excel to chart those reports.

Procedure:  Students will choose one company to follow on the stock
market.  Every class for two weeks, students will individually use the computers to
access the world wide web.  They retrieve information on the daily rise or fall of their
chosen company's stock.  They will then chart this information using microsoft excel.  At
the end of the two weeks, the  students will write a summary on the progress of their
companies stock from their information.

A Look at Mathematics
A Lesson Plan by Tim Boudreau

Lesson 1: Exploring polygons
Grade 7-9

Objective: To get students to visually recognize various polygons through LOGO applications.

Materials: Computer with LOGO software pre-installed.

Procedure: Recognizing various polygons can be a fun activity.  For this activity, students will gather around the computer in a horseshoe shape.  The teacher will then give a brief introduction to the activity.  The teacher will then ask students to name various polygons, such as a square, rectangle, triangle, and pentagon.  The teacher will then have one student come up and draw a polygon that was listed using the LOGO software.  Another will be selected to “draw” the polygon using LOGO until there are no more polygons left.

Assessment: The teacher will print of a copy of the class’s LOGO drawings and photocopy them and pass them out the next day as a quiz.  The students will be evaluated on whether or not they could distinguish between the various geometrical figures.
 

Lesson 2: Who made up this stuff anyway?
Grades 8-10

Objectives: To have students prepare research presentations on famous mathematicians using cooperative learning and the Internet.

Materials: The students will need the following materials: access to the Internet, reference material, and materials to make a presentation.

Procedures: The students will be broken down into groups of three or four.  Each group will be assigned a famous mathematician to research.  They will have a month to put an entire presentation together, with weekly deadlines to meet.  The first week, the groups will have an outline due, showing what they planned on finding on their assigned mathematician.  The next week, the groups will have to show the teacher how much research they have done.  It is recommended that the research be done on the Internet and using encyclopedias.  The week after, a copy of research material is due along with a diagram of their presentation board.  The final week, the presentations are due.  During one or two class times, the groups will each present their findings on their mathematician.

Evaluation:  Each group will be graded at each of the deadlines to ensure that progress is being made.  The first three parts of the presentation will be averaged together for a quiz grade.  The final presentation will be graded separately as a test grade.  These two grades will be averaged into their overall grade accordingly.  The grading will consist of an evaluation sheet for each step of the presentation progress.

The Know Zone! lesson developed by Jessica Nahas
Grade Level 6-8

Objectives:
The students will be able to review math skills using the Know Zone software
program by Scott Foresman

Materials:
The Know Zone software provided by Scott Foresman Mathematics

Procedure:
This online learning center allows children to link what they have learned in the
classroom with the internet. It not only reinforces skills in math but also enables
students to become more accostomed to using the internet. As the children browse
through the software, they will be offered warmups to review math skills, practice
standardized tests, and receive immediate feedback as to how they are doing.

Equivalent Fractions lesson developed by Jessica Nahas
Math Lesson
Grade Level:  6-8

Objectives:
The students will be able to use and manipulate the program, Equivalent Fractions,
developed by Tenth Planet/Sunburst Communications

Materials:
Equivalent Fractions software

Procedure:
After completing initial lessons and review on equivalent fractions, the students will
have opportunities to explore the program, "Equivalent Fractions." This program is a
sequential addition to the investigation of fractions. This program will enable the
students to use animaiton and video to demonstrate equivalency. As extension, the
students can test their knowledge by using the program to solve real-life problems.
They do this by building their own fraction equivalents to solve a variety of
multimedia problems. Guided practice and auditory feedback occur as they engage
with the program.

Assessment:
This software is designed to be used during and even after the initial teaching of the
concept on equivalent fractions. For many purposes, this software will be used as a
positive reward.

Lesson plan #1 by Julie Walter
Class: Algebra I
Grade: 9

In this class students are learning to plot graphs.
What we need: Computers with the Maple software program.

At the beginning of class, I will hand a sheet of paper with a list of
equations that I will have students graph during class. Equations that I
may use would be:  y= x, y= x^2, y= x^3, and others that are similar.
Before they start, I must first show them how to use Maple. Once they
know the different commands that are used on Maple, they can begin. As
students are plotting these equations I want them to think about what
solutions they are finding. Some people have an easier time seeing the
problems and solutions rather than solving them in their heads. By using
Maple, I am trying to enhance the students ability to solve problems in
ways that are not all on pen and paper. Using the computers are more
helpful than the graphing calculators because, for one thing it is a
bigger picture that they are seeing. Secondly, if they graph lines
simultaneously, they can tell which line is which. This lesson is
basically used to introduce students to the Maple program.

Lesson plan #2 by Julie Walter

Class: Pre-calculus
Grade: 11,12

In this class, the students are learning how to solve trigonometric
problems. What they are learning to do on Maple is to graph equations
like: y= cos x, y= tan x, and solving them. They will be able to see in
which quadrants the angles of the trig functions are positive and
negative. Many students may have already been introduced to Maple, but
some have not. Therefore, I must first teach them how to use the
program. Once I have gone through an introduction about the software and
how to use it, the students are then expected to begin plotting the
equations I have given them.

Probability Lesson Developed by April Shoemaker
Grade 8 +

Objectives:  Students will be able to differentiate between Experimental and
Theoretical probability.  They will use Sierra's Hoyle Casino program for
example of experimental probability; specifically Roulette

Materials:  Sierra's Hoyle Casino program, and a machine to run it.

Procedure: Working in groups of two or three, following an introductory lesson
on probability, students will use Hoyle Casino, specifically Roulette, to test
and record the results.  This information will be used to identify the
difference between Theoretical and Experimental probabilities.  Using the
recorded information, students may create individual or a class chart of the
results.  Some questions to guide the application of the results will be:
1.  In the game of Roulette, what is the probability of landing on black? On
red?  On an even number?  An odd number?
2.  Are the experiments' results consistent with the theoretical results?
3.  Explain the difference between the two probabilities, and explain which
one you think is more reliable.

Evaluation:   Students will be evaluated on the neatness and organization of
their charts, and on completion of the questions posed above.

Knowing Multiples by: Carlos Ivan Flores

Grade: 5th

Objective: For kids to review their table of multiplication

Activity: A game at the end of class

Procedure: Each time the game is played a different number is picked.
After the number is picked one students starts the game by saying the #1
and it continues in sequence, but once a multiple of the number choosen
comes up the student has to skip to the next number. If he says it he is
out of the game. The game continues until only one student is left or
the classs has ended.

Math in Sports by: Carlos Ivan Flores

Grade: 4th

Objective: Learn averages and probabilities.

Material: Boxscores from newspaper, paper & pencil.

Learning Activity and Procedure: Students will look find batting
aveages, fg %, or what ever they are interested in of their favorite
player. This way students are able to enjoy learning probabilities.
 

LESSON PLAN #1
BY:  TERRI WAZER
GRADE: 3RD
OBJECTIVE:  TO PRACTICE AND REINFORCE THE CHILDRENS KNOWLEDGE AND
SKILLS IN MATHMATICS.
THE CHILDREN WILL WORK TOGETHER IN GROUPS OF TWO USING THE SOFTWARE
"CARMEN SANDIEGO MATH DETECTIVE."  THEY WILL USE THERE SKILLS
THROUGHOUT THE PROGRAM BY SOLVING PROBLEMS IN ADDITION, SUBTRACTION,
MULTIPLICATION, AND DIVISION.

LESSON PLAN # 2
BY:  TERRI WAZER
GRADE:  2ND
OBJECTIVE:  TO REVIEW WHAT THE CHILDREN HAVE LEARNED USING MATH
SKILLS.
USING THE CD-ROM CALLED "STICKYBEAR'S MATH SPLASH" THE CHILDREN WILL
WORK INDIVIDUALLY AT THE COMPUTER ON TWO OF THE FOUR ACTIVITIES
DESIGNED TO HELP WITH MATH.  IF THEY WOULD LIKE ONCE ALL OF THE CLASS
HAS HAD A TURN TO TRY TWO OF THE FOUR THEY MAY GO BACK AND WORK ON
THE OTHERS.

A Math Lesson Developed by Scott Magnano

Subject:  Math

Overview:
Students need an opportunity to collect and exchange data with other
classrooms.This
activity provides opportunities for making comparisons, making
predictions,and
communicating electronically through computer networks. Students will
also become familiar with Microsfoft Word and Excel.

Objectives: Students will gain practice in the following activities:

   1.patterning
   2.predicting
   3.graphing (with Excel)
   4.networking via computer

Resources/Materials Needed:

computers, computer network hook-up, "electronic classroom partners",
Excel, Word.

Activities and Procedures:

   1.Collecting, calculating, patterning, and predicting
       A.Collection of data (time of sunrise and sunset) can be obtained
by student
          observation or from local weather station. Make a table to
record the data:
Groups are responsible for recording each day and sending the data at
the end
          of the week.
        B.Calculating the daylight hours - provide students with clocks
and model
          strategies for calculating elapsed time (adding minutes and
hours is different
          because you must use 12 instead of 10).
       C.Look for patterns and make predictions
             1.After a couple of weeks of data collection, have a whole
group
               discussion about patterns.
       D.Small group prediction assignments (based on data patterns).
             1.1st day: "Predict the time of tomorrow's sunrise. Show
your work and
               explain your answer."
             2.2nd day: "Predict the time of tomorrow's sunset. Show
your work and
               explain your answer."
             3.3rd day: "Predict tomorrow's daylight hours. Show your
work and
               explain your answer."
             4.Extension: "Predict the sunrise in your area (or another
geographic area)
               one week from today." Students may have to wait a week to
confirm
               their predictions if you are networking weekly.
   2.Sharing data with students in other geographic regions (via
computer network)
       A.Contact other teachers to decide what, when, and how to send
data. Agree on
          the format and the time frame (starting and ending date). It
is important to
          obtain a firm commitment from each teacher because the success
of the project
          will be minimized if some of the participants stop sending
data.
        B.Students use word processor (WORD) to write a weekly report.
They may include some
          personal information (about themselves and their town because
socializing
          greatly appeals to students of this age group!)
       C.Groups learn to get on-line and send text.
       D.Groups post copies of the messages sent and received under the
weekly data
          table:

3.Graphing and Comparing data
       A.Use Excel to make a vertical bar graph from midnight to
midnight (24
          hour period).
        B.Groups also graph data from other places.
       C.Tables and graphs from different areas are compared.
             1.Discussion on the reason for changes may lead into
                  a.lesson on time zones or earth rotation.

Tying It All Together:

Display graphs, predictions, and conclusion at a Science Fair or School
Parent Night.
 

Math Lesson Plan developed by  Ruth W. Rose

"Multiples and Factors"

Grade Level:  Fourth Grade

Content Subject Area:  Mathematics

Time: 35-40 minutes

Objectives:

1.  Students will identify multiples of  2, 3, 4 and 5 through the use of
software, "Math Deluxe Munchers," (MECC), before their four "math munchers"
are used up in each category.

2.  Students will identify factors of 3, 4, 5, 6, 8, 9 and 10 with the
software, "Math Deluxe Munchers," (MECC), before their four "math munchers"
are used up in each category.

3.  Students will record their scores with pencil and paper in the form of a
table.

4.  Students will discuss in groups of four what they learned from using the
software (specifically how they arrived at correct answers and avoided
"pitfalls").

Materials:
Computers: IBM-compatible Windows 3.1 or higher, 486 running at 50MHz or
greater or      Macintosh 68030 required (LC III or greater).
"Math Deluxe Munchers" software.
Paper and Pencils.

Grouping:
Students will work individually on computers if there are sufficient numbers
of computers available to class. If not, students will work in pairs on the
computer, taking turns.

In discussing outcomes, students will work in groups of four.
 
 

Introduction:
Students and teacher will discuss the concept of "multiple" of a number.
Using input from class, teacher will make a web on the board with the
multiples of "3" up to 30 (i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30).

If factors haven't already been discussed, teacher will introduce the concept
of "factor."  He/she will then proceed to factor out the number "24" on the
blackboard will all possible factors, i.e., 1, 2, 3, 4, 6, 8, 12, 24.

The teacher will also explain to the students how to insert the CD Rom into
the computer and how to set up the program for use.

Content:
Students will then have the opportunity to explore the "Math Munchers"
software.  They will start work on "Grade Level 3" in the categories of
"Multiples" and "Factors."   They can progress on to the grade levels 4 and 5
if there are successful with level 3 and if there is sufficient time.

Methods and Procedure:
After completing each section (i.e. each category of multiples or factors
within each grade level), the student will record his/her score in the form of
a table with pencil and paper.  The student will then move on to the next
category until all categories are completed in the multiple section and then
in the factor section.

The student will learn that he/she has four "math munchers" for each section
and will attempt to complete all examples, using the fewest number of
"munchers."  Each time an incorrect answer is given, a muncher disappears; and
if the muncher comes in the path of a "troggle," the muncher is "eaten."  This
provides an additional challenge for the student.  As well as recording
his/her score in each section, the student will also record how many
"munchers" were required to complete each category.

Upon completing all categories, students will discuss in groups of four their
results.  They will compare notes on correct answers, how best to avoid the
"troggles" and how to complete each category with the highest score possible.

Closure/Evaluation:
After the groups of four students each have had ample opportunity to discuss
their results (about five minutes), the class will come back together as whole
to compare highlights from the group discussions.

The teacher will be the discussion leader and will tie in their results with
the earlier work performed on the board.

As a challenge, the teacher will ask the students, working in the groups of
four, to factor the number: 2,520.  Each group will choose a group leader, who
will share their results on a section of the blackboard.  The class will
discuss the results and vote on the correct answer.

The teacher will collect the tables of the students' work for evaluation.

Note:  This is an appropriate lesson for fourth-grade students because it
gives them time to explore the computer while working on developmentally-
appropriate math concepts.

The only part of the software that I found objectionable (as a teacher and as
a parent) was the simulated "commercials" interspersed between some of the
lessons.

**Title**
Designing a Home  developed by Allison Belanger

**Grade Level**
late 7th or 8th

**Background Knowledge**
 Last week the students were shown how to search out a certain web site from a list of web sites.  The students were taught yesterday how to convert between measurements in drawing a house to scale.  As a class discussion, we went over the necessities that every house must have.  The students then made a list of what types of rooms they wanted in their design.

**Objectives**
1.)  Students will be able to successfully find one or more of the ten web sites the teacher gave them.
2.)  Students will be able to save and print the house plans of at least two homes.
3.)  Students will be able to use the material they printed in designing their own type of home.

**Role of the teacher**
1.)  The teacher will act as the expert and facilitate any knowledge the students do not know about how to save and print.
2.)  The teacher will walk about the room and help any student who has a problem.

**Classroom Arrangement**
Students will be in the computer lab and working on the computers on an individual basis.

**Materials & Resources**
computers, paper, pencils, graph paper, rulers, erasers, disks

**Initiation**
 The teacher must make sure that all the computers are ready to go by the time the students come to class.  The teacher will write on the board (depending on if there is one available) how to print out a page from the web site, and how to save any material that the students may need in the future.

**Procedure**
 As the students come into the room the teacher will inform them not to touch the computers until they are told.  The teacher will have the students sit down at the computer they normally sit at and guide their attention to the blackboard.  He/she will explain how to save and print.  At this point, the teacher will hand out a list of ten architectural web sites.  He/she explains that they must choose one or more web sites they like for examples on how to architecturally draw their dream house.  They must save and print at least two house plans that will help them design their home.
 While the students begin working on the WWW, the teacher will walk about the room.  The teacher will ask each student how they are doing and make sure they understand the assignment.  With about fifteen minutes left of the class period, the teacher will make sure that each student has at least two house plans printed and saved.
 If any students finish early, they may begin their actual house plans.  The teacher will give them a ruler, pencil and graph paper.  The teacher will have them begin drawing a rough draft of their dream home.  Students should be encouraged that the more samples of house plans they get, the better their house will look in the end.  The teacher will tell the students who are now working on their dream home, to remember to include all the necessity rooms (such as the bathroom, kitchen, bedroom, etc...).

**Conclusion**
 About five minutes before the bell is going to ring, the teacher will tell the students to stop working on the computers and to bring them back to their original screen.  He/she will tell the students who are graphing their home to put away their graph paper
and hand in the pencils and rulers.  Once all the computers are ready and all the items are returned, the students can talk and wait for the bell.

**Evaluation**
1.)  Were the students able to locate at least one web site?
2.)  Did the students have problems saving or printing the house plans they chose?
3.)  Was the lesson too easy for the students or too difficult?  Did a lot find a few house plans and then begin designing?  Did a lot not have enough time to find at least two plans.
 

Below is a List of Actual Names of Architectural Web Sites
(The teacher may use this list or create their own.)

1.)  Alternative Home Plans, House Plans for Unique Houses - Architect Designed Custom Homes Homeplans Houseplans and Residential Design Blueprints
2.)  Barn Plans - Blueprints, Gambrel Roof, Barns, Homes, Garage Workshops, Dormer Window
3.)  Brunier & Associates Inc - home plan design
4.)  house plans, home plans and blueprints from National Award winning DesignHouse available by calling 1-888-909-PLAN
5.)  House Plans by: A Larry Farnsworth, Residential Designer
6.)  MOUSE-IN-THE-HOUSE (TM) RESIDENTIAL DESIGN SOFTWARE
7.)  Bungalow Bungalows Victorian Arts & Crafts Craftsman Period Homes for the New Urbanist
8.)  W.D. Farmer’s Home Plans
9.)  Virtual Home Design
10.)  Classic Cottages, house plans to view online
 

Two Classroom Tested Lesson Plans for Excell

#1:  Reinforcing the Rules for Operations with Signed Numbers

Students must have been exposed to the rules for operations with signed
numbers.
        When adding signed numbers, like signs yeild the same sign.  Unlike signs
have an additional step.  The absolute values of the numbers are
subtracted, the sign of the number with the greatest absolute value
determines the sign of the answer.
        When subtracting signed numbers, the problem must be changed to adding the
opposite of the number being subtracted. Then follow the rules for
addition.
        When multiplying or dividing like signs, the answer is positive.
        When multiplying or dividing unlike signs, the answer is negative.

It is interesting to see how fast the computer is able to do a number of
operations with signed numbers in a fraction of a second.

Anticipatory set:  There are many careers that demand the analysis of data.
 Being able to use the computer to do operations with numbers is a
prerequisite for success in these careers.  On the computer, the symbol for
multiplication is *, and the symbol for division is /.

Procedure:  Have student bring up Excell.  Have student input a value in
cell A1 and a different value in cell A2.  Then in cell  B1 write the
formula =(A1 + A2),  in cell B2 write =(A1 - A2), in cell B3 write =(A1*A2)
and in cell B4 write =(A1/A2).  Have students change the values of what is
in cells A1 and A2.  Have them input same sign integers and unlike sign
integers into those cells and then monitor how the answers in the B column
change.

Extension:  Have student write spreadsheet formulas for the areas of a
rectangle, triangle and circle.
 

#2:  Using Excell to Graph the Data Collected in a Slope Lab.

Materials:  Small model cars, lengths of a piece of gutter or other sided
material to be used as a ramp.

Students must be familiar with the concept of "slope" being "rise/run".
Review that NO  slope is a vertical line, and that ZERO slope is a
horizontal line.  Have students predict that at what slope will the model
car go the maximum distance after leaving the  ramp.

Anticipatory set: Skiers use the slope of the land to differentiate between
the more difficult slopes.  Road side signs warn us when trucks must switch
into low gear because the slope of hills on the highways could be
dangerous.

Procedure:  Have students create different slopes with the ramp, and
record the rise and the run. When the ramp slope has been recorded, have
the student place a model car at the top of the ramp and release it, also
recording the distance the car travels after leaving the ramp.

Have students order their slopes from least to greatest together with the
distance the model car traveled.  On Excell have students record the slopes
in one column and the distance  traveled in the next.  Excell is capable of
graphing data.  High light the cells to be graphed and go into the chart
wizard part of the program.  Go through the steps for creating a chart.
Have the students bring in a text box and write their conclusion about what
they found.

Assessment:  Students should have discovered that the maximum distance the
model car traveled would be at a slope of 1/2.

        Shopping Using Excel
Author:  Blaik Doucette

Purpose:
To familiarize students with Excel Software by collecting and comparing data

Recommended Age:
Fifth grade up

Time Needed:
Allow students the time over Christmas vacation.  This way each student will have enough time.

Objectives:
Given the use of the school computer lab (and excel) the students will enter in the data they collected.  The students are expected to by the end of this lesson to better understand the excel program enough that they could use it on their own next time.

Procedure:
? Over Christmas break have each student find three items and record their prices.
? Find the prices of these same items at different stores.  Record the prices and the name of the store
? Bring data to school after break
? (Students should be able to price three items.  It may only be three candy bars, or it could be three sweaters.  Students who could not make it to the store should not be penalized)
? Back in school have the students organize their information into table form
? The top of the table should have the name of the Item
? The left of the table should have the store name and price
? Give students access to the computer lab and the excel program
? After a brief explanation of the excel program have them enter their data.
? As an instructor show the students how to command the computer to give averages

Discussion:
Which store sold the item the cheapest?
Which was the most expensive?
How did excel make table reading easier?
How did the math formulas help you to learn more information?

Assessment:  Asses students on their overall performance and participation in the project.  If students could not make it to the store provide them with fake information, but do not penalize them.
 
 

Math Lesson from Debi Berube Greeneville Intermediate School, Grade 6

 Materials
POW worksheet printed off Internet, PC, Internet access

 Instructional Arrangement
Cooperative Groups or individual

 Initiation
Have students recall last week¹s POW, word problem where they were asked to use a 3 and 5 cup container to measure 1 cup. They successfully solved the problem. This week, we will gain participate in the Online POW but we will submit our solutions via email.

 Learning Activity
Students will work individually or in groups of no more than three members to solve the POW and then submit their solution via email to ruth@forum.swarthmore.edu. During initial lesson, fifteen minutes will be allowed to get started. Subsequent time will be allotted daily for students to complete problem.

 Solutions must include student¹s name(s), grade, teacher¹s name, e-mail address, school and location, along with the answer.

 Close and Assess
Wish students good luck and then act as facilitator for submission of solutions only. She will monitor student progress by observing and questioning.
 
 

Lesson Plan #1 Barbara Archer
Title: Introduction of Numbers
Grade Level: Pre Kdg.- Kdg.

Poceedure:
Students will be encouraged to "explore" the computer keyboard to
become more comfortable with the computer and familarize themselves
with the layout of the keys.

The teacher will next intoduce the number program of "Mup Stage"
where the student is allowed to choose a number from the keyboard and
a variety of characters appear on the screen and dance and sing.

Evaluation:
The instructor will evaluate the student's dept of understanding of
the numbers 1 to 10 and their understanding of the computer operations
by observing their work.
 
 

Barbara Archer
Lesson Plan #2
Logo Graphics and Classroom Layout
Grade level: 4-8

 Proceedure:
It is assumed the students have an indepth understanding of the use of
Logo and are aware of the programing aspects of the software.
The class will be presented with a current layout of the classroom
area and will be asked to develop a "new and improved" design for the
room using their computer and Logo and developing their own scale for
room size (ie: 1"=1'). They will be reminded: of fire codes,
consideration for moving/walking space, not to block windows or
doorways, to make sure to have room for all students and teacher, have
all necessary areas easily accessable, etc.

 Evaluation:
The teacher will assess the student's designs based on:
1. ease of understanding of design
2. meeting the above criteria
3. creativty and originality

 As an added bonus the students will be asked to present their ideas to
their peers and the class will decide democratically on a new layout
for their classroom.
 
 

SPREADSHEET LESSON PLAN developed by Laura
GRADE: 3

 SKILL: Moving in a spreadsheet

 PREPARATION: Teacher will prepare a spreadsheet template.

 PROCEDURE:

1. Open spreadsheet template.

 2. Have students survey classmates regarding assigned topic, e.g., favorite ice cream,

 hair color, and total responses.

 3. Enter frequencies in assigned cells.

 4. Choose appropriate chart style and create chart. Save.

 EXTENSIONS:

 1. Observe how changes in the data result in changes in the chart.
 
 

Math Lesson Plans

Topic: Geometry

 Entry Level Characteristics
The students have had some exposure to the LOGO program, including: working with the turtle and creating other symbols to use as their cursor. They have practiced moving the turtle in different directions, with guidance from the classroom teacher. Also, they understand some of the commands that are present in the LOGO program, but will need more practice.

 Objectives
Students will continue exploring the LOGO program and will also create at least two different geometric shapes.

 Materials
-Macintosh Computer
-Printer
-Mouse
-LOGO Software

 Procedures
The students will work independently in creating two geometric shapes. The teacher will aid the students who are having difficulty understanding the various commands. The teacher will circulate around the room, to evaluate the students' procedures in the assignment. Finally, the students will pair-up and discuss their inventions.

Closure
The teacher will lead the class in a discussion that relates to what figures were created and how they were created. The teacher will encourage the students to become process-thinkers, throughout this classroom discussion.

 Assessment
The teacher will observe the procedures performed by the students, while creating a geometric shape. Also, he will review the final product, for understanding of the command that are used in LOGO. Finally, through questioning the students, in the classroom discussion, the teacher can evaluate their verbal understanding of the components of the LOGO program.

 Math Lesson Developed by Katie Pentore

 Grades: Kindergarten

Topic: Mathematics, number recognition using Muppet Stage on Macintosh computers

 Entry Level Characteristics: Students have experience in counting basic numbers

 Objectives: Students will effectively be able to recognize numbers that appear on Muppet Stage. They will also play games with a partner

 Role of Teacher: Teacher will serve as a facilitator, guiding the pairs if needed.

Resources/materials: Students will work with Mup Stage on Macintosh Computers

 Classroom Management: Students will work with a partner on the computer

 Initiation: Teacher will ask children to count to twenty while holding up the numbers. Teacher will then explain that the students will play number games on the computer with a partner. Sharing will be discussed.

 Procedures: Children will work with their partner on the computer in which they will cooperatively recognize letters and play number games

 Closure: Teacher and partners will have a discussion on what was learned. Numbers will be reviewed

 Assessment: Students will write in their journals about what they liked about Stage. Partners will also be assessed on how they worked together (cooperation, sharing, etc.)
 
 

Grades 4-7 - Computer program-Number Munchers

 objective
The objective of this lesson is to see if one can identify all
the correct numbers that are associated with a certain number's
multiples, factors, prime numbers, equalities, and inequalities.

 class arrangement
small groups, or partners

 resources
macintosh plus number munchers cd rom

 initiation
Begin this lesson by reviewing what it means for a number to
be a multiple, factor, prime number, equalities, and inequalilties.

 procedure
Explain to your students that they will have to choose which
technique they want to use when they open the program on the computer.
Tell then that they will be using the up, down, and side arrows, to
move their frog on the screen that will be "eating" up the correct
answers to a question displayed at the top of the screen. Also tell
your students that the space bar will be used to "eat" the numbers
that they believe are correct.

 closure
Teacher will review what was don on the computer and ask
for comments and questions.

 reflection
Teacher will evaluate how well the students were working
with this computer program and if they feel it was an effective
manipulative and a fun tool for the students to use.

 (This program is appropriate for students in grades 4-7)
 
 

Math Lesson Plans developed by Katie Pentore Grades 3-6

 Entry Level Characteristics: Students have had previous experiences in graphing throughout the year

 Objectives: Students will learn to graph data and observe the shape of normal curves

 Resources/materials: Maple Software will be used in which the students will record data from a sheet

 Classroom Management: Students will work independently at their own computer. Peer interaction will also occur

 Initiation: Teacher will have a discussion with students about the shape of a normal bell curve. This will be an open discussion.

 Procedures: Teacher will discuss with the students what is expected of them; objectives. Teacher will assist students on the operations of Maple Software. Students will then proceed to enter data information using graphing print-outs to observe the shapes of the curve. A discussion will follow.

 Closure: Teacher will serve as a facilitator in which the students will lead a conversation about what was learned

 Assessment: Teacher will have students write in their math journals about what they learned. Teacher will also collect the work that was performed in class to see who is making progress and who needs more assistance.
 
 

Grades 3-6, Mathematics, Geometry developed by Kathleen J. Green

 Entry Level Characteristics:

 Students have been introduced to turtle geometry on the computer and have spent
time estimating commands. They have become fairly accomplished at moving the
turtle freely around the screen and understand relevant commands.

 Objectives:

 Students will explore geometric figures using LOGO to develop procedures for
patterns and designs.

 Procedures:

 Students will work in pairs to develop a procedure for making a square and
circle on the computer, using LOGO. Then two pairs of students will compair
and discuss their work together.

 Closure:

 Students will discuss their findings with the class.

 Evaluation:

 Each student will create their own geometric shape on the screen and show it to
the teacher.
 
 

K-3 Shapes/Geometry Kid Cuts - RLA

LESSON PLAN FOR MATHEMATICS 
developed by Mary Ellen Dannehy

Preparation: Students need to be familiar with the spreadsheet concepts of ROW, COLUMN, and CELL. They also need to have a basic understanding of the spreadsheet as a tool for solving mathematical problems. Teachers should develop formulas for solving the problem if working with younger students. Older students will benefit from developing their own formulas as part of the activity. VERY IMPORTANT! Teacher will also need to prepare a handout with a clear statement of the problem.

 Activity: Present a clear statement of the problem: Each week Matthew receives an allowance of $5.He wants to save part of his allowance to buy a skateboard, which will cost $60. But he also wants to spend part of his allowance on candy and part on video games, which cost 25 cents a game. If Matthew plays six video games each week and spends $1 for candy, how many weeks will he have to save in order to buy his skateboard? How many weeks if he stops buying candy and plays four video games each week? Assist students in inputting numerical data and formulas. Then instruct the spreadsheet to solve the problem.

 Evaluation: Verify the results. Do the students understand that the computer made no problem-solving decisions on its own but rather followed their instructions?
 

Follow-up: Allow students to create their own allowance budgets by supplying information that applies to them. Lead the class in a discussion of potential uses for the spreadsheet. How might their families use it as a tool for managing the household budget?

 Special note: An interesting variation of this lessson is to divide the class into two groups. One group will use the spreadsheet to solve the problems while the other group uses paper and pencil. This helps students appreciate the tremendous speed at which computers can perform mathematical calculations.

Topic: Slope of a Line / Linear Equations designed by Laura Dawley

Aims/Purposes: The purpose of this lesson is to have the students discover graphically a pattern between parallel lines and identical slopes, as well as relationships between perpendicular lines and negative reciprocal slopes.

The students will distinguish the slope of the line using two sets of points formula identifying the slope using y1-y2/x1-x2.

 the student will distinguish between slopes of parallel and perpendicular lines

 Procedure: Have each student follow verbal instruction to open computer and go to on software program chapter 5 graphing linear equations..

 Have students plot 2 lines with different slopes and name differences they see.

 Have students plot one line with m slope and another with -1/m slope and describe the relationship they see.

 Have students create their own equations for parallel and perpendicular lines and then graph them.

 Closure: Have student print the lines they created and share them with each other.

Statistics developed by Virginia Jacoby

ENTRY LEVEL CHARACTERISTICS
Students have experience in graphing.

 ROLE OF TEACHER
Teacher will direct students to work on activity, and monitor progress. If students need help, teacher will assist.

 RESOURCES/MATERIALS
Students will work with Maple Software, and will record data from sheet.

 CLASSROOM MANAGEMENT
Students will sit at computer consoles individually as the number of computers will allow.

 INITIATION
Teacher will ask students if they know what a normal, bell-shaped curve looks like.

 PROCEDURES
Teacher will explain objectives to students.
Teacher will direct students on operation of Maple Software.
Students will enter data information, and use graphing print-out to observe shape of curve.

 CLOSURE
Teacher will discuss important points of information gathered, such as why data forms this type of curve.

 EVALUATION
To evaluate students, teacher will collect work performed in class, and this will help teacher discover in what areas that students need more practice.

Probability Lesson developed by Virginia Jacoby

ENTRY LEVEL CHARACTERISTICS
Students have basic idea of probability, but no further background.

 ROLE OF TEACHER
Teacher will direct students to use Maple Software. Teacher will monitor students' progress, and assist when necessary.

 RESOURCES/MATERIALS
Students will work with Maple Software, and get data information from data sheet.

 CLASSROOM MANAGEMENT
Teacher will have students sit at computer terminals as the number of computers will allow.

 INITIATION
Teacher will ask students if they can describe the process to find probability.

 PROCEDURES
Teacher will explain objectives. Teacher will have students use Maple Software to insert data information. Students will access probability information from computer.

 CLOSURE
Teacher will go over main topics of lesson, such as how to use computer to accesss probability information.

 EVALUATION
Teacher will evaluate students by collecting work done in class. Further information about students' understanding will be obtained through converstion in class.

LESSON: MATH - PI AND CIRCUMFERENCE developed by Darcy Bardwell

 OBJECTIVES: STUDENTS WILL DISCOVER THE RELATIONSHIP BETWEEN CIRCUMFERENCE AND DIAMETER BY CONSTRUCTING CIRCLES AND FINDING THERE DIAMETER USING LOGO. THEY WILL BE ABLE TO USE THIS DISCOVERY TO COMPLETE THEIR HOMEWORK WHICH REQUIRES THAT THEY USE THE FORMULA C =PI X DIAMETER IN SOME FORM. THE SUCCESS RATE SHOULD BE 80%.

 ASSUMPTIONS: STUDENTS HAVE USED LOGO TO CONSTRUCT RANDOM CIRCLES USING A POLYGON FORMULA SUCCESSFULLY. THE STUDENTS HAVE MASTERED THE CONCEPT OF DIAMETER AND RADIUS.

 MATERIALS: 1 COMPUTER PER STUDENT PAIR TO RUN LOGO.

 INITIATION: "TODAY WE ARE GOING TO USE YOUR KNOWLEDGE OF DIAMETERS AND RADII TO SEE IF WE CAN DISCOVER IF THERE IS A RELATIONSHIP BETWEEN THEM AND THE PERIMETER OF A CIRCLE. WE ARE GOING TO WORK IN PAIRS ON LOGO TO EXPLORE THIS POSSIBILITY.

 PROCEDURE: FIRST WE NEED TO REVIEW THE DEFINITIONS OF DIAMETER AND RADII. LET THE STUDENTS COME UP WITH A GROUP DEFINITION.
2. TALK ABOUT THE PERIMETER OF A CIRCLE AND TELL THE STUDENTS THAT CIRCLES ARE SPECIAL BECAUSE THERE IS SPECIAL NAME FOR A CIRCLES PERIMETER - CIRCUMFERENCE.
3. ASK THE STUDENTS HOW THEY CAN MAKE A CIRCLE ON LOGO. (SOME WILL UNDERSTAND TO USE THEIR POLY PROGRAM IMMEDIATELY, SPEND MORE TIME WITH THOSE WHO DON'T)
4. PUT SOME EXAMPLES OF CIRCLES USING THIS POLY PROGRAM ON THE BOARD AND ASK THEM TO FIGURE OUT WHAT THE CIRCUMFRENCE IS.(EXAMPLE: SIDE=1 # OF SIDES=360 CIR =360)
5. LET THEM GROUP IN PARTNERS, THEY ARE TO MAKE 4 CIRCLES AND DRAW THE DIAMETER OF EACH. THEY NEED TO MAKE A TABLE AND RECORD THE LENGTH OF EACH CIRCUMFERENCE AND EACH DIAMETER(SOME GROUPS WON'T GET ALL FOUR BUT THE WHOLE GROUP WILL SHARE.
6. AFTER 20 MINUTES AT THE COMPUTERS THE CLASS COMES TOGETHER AS A WHOLE GROUP. THE TEACHER RECORDS EIGHT DIFFERENT CIRCLES ON THE BOARD. THE STUDENTS TRY TO FIND A PATTERN.(AFTER 5 MIN OR SO THE TEACHER ASKS THEM ALL TO DIVIDE THE CIRCUMFERENCE OF EACH BY ITS DIAMETER)
7. THE CLASS RECORDS THIS INFORMATION ON THEIR TABLES. IT ALL SHOULD BE AROUND 3.14.
8. THE TEACHER EXPLAINS THAT THIS IS A SPECIAL NUMBER CALLED PI AND THAT FOR EVERY CIRCLE THE EQUATION C/D = 3.14 IS TRUE.
9. ALLOW QUESTIONS ABOUT THIS AND WHY THE STUDENT'S NUMBERS MIGHT OF VARIED.
10. ASSIGN THE HOMEWORK PAGE.

 CLOSURE: GO OVER WHAT DIAMETER AND RADIUS ARE. HAVE A STUDENT EXPLAIN WHAT CIRCUMFERENCE IS. ALLOW FOR ADDITIONAL QUESTIONS ABOUT THIS. THEN REITERATE THAT PI IS A SPECIAL NUMBER. HAVE AT LEAST 2 STUDENTS EXPLAIN THE RELATIONSHIP BETWEEN CIRCUMFERENCE AND DIAMETER. ALLOW FOR QUESTIONS. REPEAT HOMEWORK ASSIGNMENT AND LET THEM GO.