Elayne Weger Bowman
Mustang High School
906 South Heights
Mustang, Oklahoma 73064
e-mail: bowmane@mustang.k12.ok.us
Layne's Lessons
M&Ms and Dogfood:
Sharing Ideas to Enrich Secondary Mathematics Classes
Introduction
Estimating and Graphing with M&M Candies
Finding Ratios and Proportions with Maps
Solving Equations with Cards
Finding Volume with Ping-Pong Balls
Relating Rate and Time to Slope with
Technology
Finding Slopes on Campus - An Algebraic Field Trip
Hula Hoops and Venn Diagrams - Solution Sets
Using Inverse Variation with Dogfood
Measuring a Flag Pole with Trigonometry
Ordering Integers with Bodies
Ordering Rational Numbers with Wrenches
Finding Percent of Change with Newspapers
Internet Project 1: A Functional Housing Market
Internet Project 2: Roller Coaster Statistics
Internet Project 3: Population Clock
Internet Project 4: The Internet Pizza Server
Internet Project 5: The INDY 500
Connecting mathematics to life outside the classroom seems to be one of the major factors affecting the learning and retention of mathematics. So often students want to know when in their lives they will ever use a particular skill or topic of study. I must admit, this was one of my own questions as I went through school. I have dedicated my life to answering that very question. I do not view mathematics as a field of study separate from all others, but rather as a field of study that enables me to succeed at all others. By representing mathematics in this way in the classroom, I am able to not only hold the students' attention, but also, by giving them a way to use their mathematics now, give them a reason to retain it.
Often in the classroom, something seems lacking. Sometimes it is enthusiasm. Sometimes it is interest. Sometimes it is fun. I chose mathematics as my field of study because I found it interesting and fun. Because it was both interesting and fun, I became enthusiastic about my studies. My enthusiasm led to learning. I try to apply those same tactics to my teaching. One reason is because I want to enjoy what I'm doing. If I get bored, it shows. Another reason is because I have found that students learn more if they enjoy what they are doing. On the following pages I have shared some of my lesson plans that I pull out when I'm getting bored. I know if I used plans like this everyday, that they, too, would become monotonous and lose their effect. The students look forward to these special days and when they write their essays for me, these are the activities they always recall.
I do not claim complete originality for these lesson plans. I've collected ideas for over twenty years and adapted them to my own uses. If you recognize one of your own ideas, I hope you will feel complimented. Special thanks to Susan Boone for the Internet Lessons I've adapted from her website. You may visit her website for more ideas at http://www.crpc.rice.edu/CRPC/GT/sboone/. I would appreciate any ideas that you can share with me to share with my students and others. I hope these will help you to bring more excitement into your classroom both for you and your students.
F. Elayne Weger
October 1999
Estimating and Graphing with M&M Candies
Objectives:
The students should be able to estimate an unknown quantity based on experience
and then compare their estimations with actual amounts by preparing graphs.
Materials:
Individual packages of M&M candies for each student
Worksheets to record data
Transparency film and Overhead markers to make graphs
One large sack of M&M candies
Warm-up:
Using the large sack of M&M candies, have students guess the total number
of candies in the bag. Write all guesses on the board. Then have
the students guess about the colors in the bag. Write these guesses down
as well. There should be a wide variance in their guesses. Discuss
what estimation means and its purpose.
Activity:
Divide the class into groups of two or three students each. Give each
student a package of M&M candies and a worksheet, and each group a sheet of
transparency film and overhead markers. Before opening the packages of
M&M candies, students are to estimate and record the total number of
M&M candies in their individual packages and also the color break
down. Students should then open their packages and record the actual data
in the spaces provided on the worksheet. Students then compare and
compile the data collected in their groups and prepare one graph or set of
graphs per group comparing their estimations with their actual findings.
Each group will present their findings and graphs to the class and may eat
their M&M candies.
Wrap-up:
Compare the data from the class. Discuss similarities and
differences. Discuss sampling. Have the students use their data to
make new guesses on the number of M&M candies in the larger bag. This
may be used as a springboard to a unit on ratio and proportion.
Finding Ratios and Proportions with Maps
Objectives:
Students should be able to set up a proportion and solve it to find an actual
distance given a scale model.
Materials:
Transparency of a section of the map
State maps for each student
Rulers and Calculators
Journals and Pencils
Warm-up:
Ask class for examples of scale models. Discuss with the class occupations
that use scale models and why scale models are used. Choose a common
scale model, such as a train, and work an example on the board or overhead
using a proportion to find the length or width of a car. If you have
access to a model train set, it makes a great visual aid.
Activity:
Each student will need a state map, ruler, calculator, journal, and
pencil. Have the students open maps and find the scale for the map.
Discuss what the scale means. Using the transparency as a guide for the
students, choose two towns on the map. Measure the distance between the
towns. Use the scale for the map and the measured distance to set up a
proportion to find the "as the crow flies" distance between the two
towns. Ask a student to find a pair of towns on his own map. Step
the class through the process again. The assignment is for the students
to find the "as the crow flies" distance between ten pairs of towns
and record them in their journals. Names of towns, measured distances, proportions,
and "as the crow flies" distances should all be written in their
journals.
Wrap-up:
Have students volunteer to come to the board and write a pair of their towns
and information. Continue asking for volunteers as time permits.
Use the information given on the map to find the "as the road goes"
distance between two of the towns. Discuss why the distance is not the
same as the "as the crow flies" distance.
Objectives:
Students will be able to find the solution to a multi-step equation.
Students will also be able to write an equation given a solution.
Materials:
Sets of teacher made, laminated cards (half with equations and half with
answers)
Journals and Pencils
Warm-up:
On the board, set a variable equal to a number, i.e. X=5, and ask the class
what it means. Then add a number to both sides of the statement, i.e.
X+3=8, and ask the class what you did. Ask them what they could do to get
back to the original statement. Do it again using multiplication, i.e.,
3X=15. Ask the same questions. Repeat with subtraction and
division. Write an equation using your original statement with two
operations on both sides, i.e. 2X+3=13. Ask the same questions.
Activity:
Pass the equation cards out to one side of the room and the answer cards out to
the other side. If there is an odd number of students, keep one
card for yourself. Have all students stand and go around the room until
they find the match for their card. Choose one side of the room to hold
the pairs. When students find their matches, they are to return to their
seats. When all* students are seated, go down the row and ask for matched
pairs. Write each pair on the board and have the class verify that each
one is a match. Have the students record the pairs in their
journals. Repeat activity with other sets of cards until fifteen minutes
remain in the class period.
*Often two or more students will be unable to find their matches. Decide
whether you would like these students to go around the room looking for
mismatched pairs or for them to find their matches while the pairs are being
verified on the board. Both ways work well.
Wrap-up:
Discuss the activity. Have students write in their journals what they
learned about equations and to make up five equations and give the solutions.
Finding Volume with Ping-Pong Balls
Objectives:
Students should be able to find the volume of a large open space and compute
the number of Ping-Pong balls it would take to fill it.
Materials:
A Box of Ping-Pong Balls
Rulers, Tape Measures, Yard Sticks, & Meter Sticks
Calculators
Graph Paper
Worksheets and Pencils to record data
Warm-up:
Since this lesson should follow a unit on area and volume, spend a few minutes
reviewing vocabulary and methods. (I use Tupperware toy building blocks
to give a visual understanding of the relationship between area and
volume.) Examine the box of Ping-Pong balls with the students and have
them notice how they stack in the box.
Activity:
Divide the students into pairs. Each pair of students will need a
worksheet to record their data, a calculator, and a pencil. Provide
rulers, tape measures, yard sticks, and meter sticks for the students to share.
Have the students describe the shape of the classroom. Discuss the
relationship between the area of the floor and the volume of the room and ways
the volume might be found. Emphasize that there is not only one way to
the solution and in fact there is not just one solution. This is a hard
concept for students, but a very important one. Without giving any more
instructions, tell the students that they are to find the volume of the room in
cubic units and then estimate the number of Ping-Pong balls the room will
hold. As part of the assignment, I also have the students draw a floor
plan of the classroom and give the area of the floor, in addition to the volume
of the room. Monitor the students work, but be careful not to give too
much help. The more they do on their own, the more they will
remember. Mistakes are often better teachers than success.
Wrap-up:
There will be little, if any, time at the end of the period. Wait until
the next day to discuss methods and answers. Some answers will be really
ridiculous and should be addressed. If all of your classes are going to
do this exercise, be sure not to indicate to any of the students that one
answer is better than another as word spreads very fast. As a bonus
homework assignment, or for students who were absent, have the students draw a
scale model and find the volume of their bedroom.
Return to Table of Contents
Relating Rate and Time to Slope with Technology
Objectives:
Students will discover the relationship of rate and time to slope using
TI-CBRs (Calulator Based Rangers) and graphing calculators.
Materials:
*TI-CBRs (one for every 2 or 3 students)
*Ranger Program for TI Graphing Calculators
*TI Graphing Calculators (any TI-73 is a good choice for middle school
students, TI-83 or 86 for high school students)
*TI Graphing Calculator and View Screen for the Overhead (same model as for
students)
Overhead Projector and Screen
Journals and Pencils
*Technology Note: TI will loan the above equipment for two weeks at a time to classroom teachers. You may reserve and order them online at http://www.ti.com
Warm-up:
Introduce or review the relationship between rate, time, and distance.
Use examples appropriate to your grade level and students' interests.
Review or define slopes as increasing, decreasing, and constant.
Activity:
With the graphing calculator and ranger attached to the viewscreen on the
overhead, instruct the students in how to use the equipment.
(Instructions that come with the CBR is quite simple to follow, but should you
need more assistance, TI customer service is more than willing to step you through
any process.) Demonstrate what happens a graph as you walk toward a wall
with the CBR facing the wall. Demonstrate what happens when you walk away
from the wall. Discuss the graph. Ask the students what the slope
represents. Accept all answers. Repeat the above experiment walking
faster. Ask the students what affect that had on the slope of the
graph. Repeat the above experiment walking much slower. Again ask
the students what affect your change in speed had on the graph. Without
any further explanation, allow the students to "play" with the
technology in small groups for a few minutes. Then draw graphs on the
board and have the students to use the CBRs to imitate the graphs on their
calculators. Draw several graphs using a variety of slope patterns such
as increasing, constant, decreasing, or a combination of the three.
Continue until students are able to achieve success with several of the graphs.
Wrap-up:
Discuss ways that graphs can be used in "real life" situations.
Discuss the technology and ways in which technology has changed our lives.
Finding Slopes on Campus - An Algebraic
Field Trip
Objective:
Students will be able to apply to slope formula, where are
two ordered pairs defining the slope of a line, to find the slope of a ramp.
Materials:
Various measuring instruments, measuring tapes, meter sticks, etc.
Calculators
Paper and pencil
Warm-up:
Introducing slope may be done with this assignment, before any formal
"textbook" assignments are made. Begin class with a general
class discussion of the word slope and other words that have the same
meaning. Key words to listen for might be pitch, grade, slant, etc.
Work your way through the discussion to end on the slope of ramps and the
required 1 foot of rise for every 12 feet of run required for ADA regulation on
handicapped access ramps.
Activity:
Continuing the discussion begun in the warm-up, ask the students why they think
ramps have slopes of lesser steepness than stairs. This is a good time to
integrate a bit of science into the lesson involving work, simple machines, and
physics. Divide the students into small groups of four or less.
Send them or take them, depending on the level of the students and their
dependability, to ramps around the school. Have them find the rise and
the run of the ramp. Have the students draw a diagram to show what parts
they measured. Often, students will measure the length of the ramp
itself. This leads to an exploration of triangle relationships and the
Pythagorean Theorem, which also works in nicely with this lesson. When
the students return to class, call on students one group at a time to share
their collected data. Using the verbal description of slope as rise over
run, have students find the slopes of their ramps. Then develop the slope
formula using the same data by assigning the point (0,0) to the lowest part of
the ramp. Have them to find the slopes of their ramp using the formula
and compare answers. Discuss when each method would be appropriate and
how they compare.
Wrap-up:
Discuss occupations that would be concerned with knowing slopes, such as
truckers, construction workers, architects, ski instructors, etc. Use the
information from this lesson to write the equation of a line with the slope of
their ramp. For homework, have them find the slope of another ramp and
tell whether or not it would be approved by the ADA.
This lesson has been used with 8th graders in pre-algebra and honors algebra,
college freshmen in pre-calculus courses, and summer institutes for first year
teachers of mathematics and science with the same overwhelming response -
"Now I see it."
Hula Hoops and Venn Diagrams - Solutions Sets
Objective:
Students will be able to construct Venn Diagrams to show solution sets for
verbal descriptions.
Materials:
Hula Hoops of at least two sizes
Balls of every kind and shape that you can find. I included baseballs,
softballs, soccer balls, basketballs, footballs, golf balls, Ping-Pong balls,
"hacky sacs," rubber balls, jack balls, kick balls and nondescript
balls that I found in the toy box.
Warm-up:
Write the Venn Diagram and set notation terminology on the board. Include
intersection, union, complement, element, set, subset, disjoint, universal set
and all symbols for each one.
Activity:
Saying that the floor is your universal set, dump all the balls out on the
floor. Set one hula hoop on the floor and say that it contains all of the
balls of any description, such as all round balls. Let the student put
all the balls in the hula hoop that belong to the solution set {all round
balls}. Talk about the set and its complement, all of the balls not in
the hoop. Note that a set and its complement make up the universal
set. Use the set terminology throughout the activity. Repeat with other
categories, still just using one hula hoop. Now place two hoops on the
floor and have the students choose two categories that would allow the balls to
all be places within the two hoops. Discuss disjoint sets and the union
of the sets. This is not as easy as it sounds, but will lead directly to
the next activity with intersecting the hoops. Let one hoop be "all
round balls" and the other be "all footballs." If you have
included some round footballs, such as kick balls, hacky sacs or soccer balls,
then there will be balls in the intersection of the two hoops. This
activity is best used by letting the students participate. It is not one
that helps them if you do all the work. Let them get involved. Let
them choose set names and descriptions. Be sure and do the wrap-up
activity.
Wrap-up:
Using the terminology, draw a Venn diagram on the board. Encourage the
students to tell you what each part is, the universal set, etc. Write two
sets on the board, such as A={the first ten even numbers} and B={the first five
multiples of 3}. Ask the students if the sets will have any elements in
the intersection. Have them give you the elements in the intersection,
first and then tell which numbers would go in the sets A and B. Have the
students copy the example and the terminology into their journals. Give
two or three more problems from the board to add to their journals for
discussion the next day.
Using Inverse Variation with Dogfood
Objective:
Students will be able to apply the inverse variation formula to practical
applications.
Materials:
Sawhorse or other fulcrum
Long board, 1"x8"x8'
Several sacks of dogfood, various weights
Carpenter's tape measure
Calculators
Journals, and pencils
Warm-up:
Discuss the students' experiences on playground teeter-totters. Ask them
what they did to balance the teeter-totter when the person on the other end was
heavier. Ask what they did when the other person was lighter. Ask
them why they did what they did.
Activity:
This lesson follows a section on direct and inverse variation. Ask the
students which method they think would be used for a teeter-totter
problem. Have the students help in setting up the sawhorse. Have
the students measure the length of the board and find its middle. Then
have the students try to balance the board on the sawhorse or fulcrum. It
takes several students to do this activity. Have two students stand on
either side of the fulcrum to keep the board on the fulcrum. Have two
students at each end of the board with bags of dogfood. Have students at
the board recording data. Let the students determine which bags of
dogfood they want to try to balance on the board. They will need to read
the weights of the dogfood aloud so the class can give hints on trying to balance
the board. Once the board is balanced, have a student measure the
distances from the centers of the bags to the fulcrum. Have the students
at the board check the validity of the data with the inverse variation
formula. Repeat the activity with other bags of dogfood and other
students.
Wrap-up:
The discussion after this activity is as important as the activity
itself. The formula and the experiment often yield slightly different
results. Have the students discuss possible reasons for the
discrepancies. After the discussion, have the students to write in the
their journals, describing both the activity and what they gained from it.
Return to Table of Contents
Measuring a Flag Pole with Trigonometry
Objectives:
Students will be able to demonstrate their understanding of the trigonometric
ratios by finding the height of a flag pole.
Materials:
Two or more Meter or Yard Sticks
A Chalkboard Protractor
Scientific Calculators
Journals and Pencils
A Sunny Day*
Warm-up:
Spend a few minutes reviewing the six trigonometric ratios:
sin x = side opposite x / hypotenuse
cos x = side adjacent x / hypotenuse
tan x = side opposite x / side adjacent x
csc x = hypotenuse / side opposite x
sec x = hypotenuse / side adjacent x
cot x = side adjacent x / side opposite x
Draw a right triangle on the board or overhead and label the angles A, B, and C. Have students volunteer to label the the sides with a, b, and c as you point to them. Practice the functions by pointing to angles and asking for a specific function of that angle.
Activity:
Open a discussion about finding the heights of tall structures. For some
students it will be necessary to establish reasons for wanting to know the
heights of tall structures. Write all suggestions on the board or
overhead. Many will want to use proportions, because they have done this
before. Extend the conversation into using trigonmetric ratios.
Introduce "Solving Triangles" using the trigonometric ratios.
Do a couple together and discuss how the ratios and triangles might be used to
solve "Real Life" problems. If "angle of elevation"
and "angle of depression" have not yet been introduced, introduce
them. Divide the class into teams and have them bring their calculators,
journals, and pencils with them. Be sure to also carry the measuring
sticks and protractor. Lead the students outside to the flag pole.
*Note: be sure and choose a sunny day or this lesson will not work for
you. Tell the teams that they have a problem to solve. Each team
must find a way to find the height of the flag pole using a measuring stick and
a protractor, but that they may not use proportions. Offer points or
candy or hall passes or whatever other motivation works for your class to the first
team with a defendable answer for the height to the flag pole. Even
though they have seen the problems in the book and worked some using angle of
elevation, it may take some hints to help students figure out what to do with
the protractor. Don't get impatient. Given time, at least one group
will figure out a process and the others will follow. It gets into a
calculation race at the end, but is well worth the effort.
Wrap-up:
Return to the classroom and have each group present their methods and answers.
Angles and measures will be different. Treat the differences as any
scientific experiment and let the students offer hypotheses for why they have
different angles and shadow lengths. Discuss other problems that could be
solved using this method.
Ordering Integers with Bodies
Objectives:
Students will be able to demonstrate an understanding of betweeness and number
line ordering of integers.
Materials:
5x7 index card with integers written on them
Journals and Pencils
Warm-up:
Ask the students to come to the board and write any number they choose.
Keep asking for volunteers until you have a wide variety of numbers (fractions,
decimals, and integers). Use a Venn Diagram to show how groups of numbers
are related to one another.
Activity:
This is an out-of-seat activity that can get very loud, but well worth the
risk. Give each student a card with an integer on it. Call five
students to the front of the room with their cards. Have the
students compare their numbers and then stand facing the class in increasing
numerical order, right to left (this will be left to right for the
class). Ask the class if they agree. Any student who disagrees with
the order should be allowed to change the order. Continue until the class
is convinced that the numbers are in numerical order. Choose two of the
students that are standing and ask if anyone has a number between those two
numbers. Choose of the of the volunteers to come stand between the
students you chose. Ask the class if the volunteer is standing in the
correct place in the number line of students. Continue this process until
all students are standing or the front of the room is too crowded. Then
have all students return to their seats, exchange cards, and start over.
Other ideas for this exercise include using greater than and less than, another
difficult concept with integers. Choose a student at random to come to
the front of the room. Ask for a student to come to the front of the room
with his card. Ask for a student to come whose number is greater or less
and have them stand accordingly beside the first student. Continue until
students seem comfortable with the process.
Wrap-up:
Have the students to take out their journals and order the numbers they wrote
on the board at the beginning of class. Use this as a springboard for
rational number comparisons.
Ordering Rational Numbers with Wrenches
Objectives:
Students will be able to find common denominators and write a set of five
rational numbers in ascending order.
Materials:
Graduated set of open-end, box-end wrenches
Journals and Pencils
Warm-up:
The day before, assign as homework for all students to bring an example of a
rational number from home. Use students' examples to start discussion on
using rational numbers.
Activity:
Open toolbox and talk about being a mechanic's helper. On the overhead,
arrange five of the wrenches in random order. Turn on the overhead to cast
their shadows on the screen. Write the sizes of the wrenches on the board
and ask for a volunteer to write them in the right order. Ask for ideas from
the class about how to order them. Someone will want to arrange the
wrenches. Tell them that will be how they check their answer.
Discuss common denominators. When covering this topic, use practical
denominators, ones they will encounter regularly. Using common
denominators, let the students decide on the order for the wrenches. Have
them copy the example in their journals. Continue the same process with
five different wrenches, allowing volunteers to come check the wrenches after
the class finishes with each set. Each set of fractions should be copied
in the students' journals. Continue until about ten minutes of class
remains.
Wrap-up:
Have students write in their journals about the math skills they used
today. Students should also write about ways these skills can be used
outside the math classroom.
Return to Table of Contents
Finding Percent of Change with Newspapers
Objectives:
Students will be able to use a table to organize data. Students will also
be able to find the rate of change in a sale price and write that rate as a
percent.
Materials:
Newspapers
Calculators
Journals and Pencils
Warm-up:
Open a newspaper to an advertisement announcing a varied percent-off
sale. Write some of the "was" and "now" prices on the
board. Use proportions to find the percent of change. Compare the
percent found to the advertisement and discuss "truth in
advertising".
Procedure:
Divide students into groups of two or three each. Each student will need
his journal, calculator, and pencil and each group will need a newspaper.
Use a table to set up a few examples on the board for the students. The
table should have headings for original price, sale price, amount of change,
and percent of change. Discuss the value of tables for organizing
data. Using the data from the tables, set up proportions to find the rate
of change as a percent. In their journals students are to follow the
above procedure to find the rate of change in price for ten sale items in the
paper. Students within the same groups are encouraged to choose the same
items so results can be compared.
Wrap-up:
Ask for volunteers to come to the board and write one of their problems.
Take as many volunteers as time allows. Discuss what was learned and how
it can be applied while shopping.
Return to Table of Contents
Internet
Project 1: A Functional Housing Market
adapted from Susan Boone, Saint Agnes Academy,
Houston, TX
by Elayne Weger, University of Oklahoma, May 11,
1998
Name______________
Hour______
Computer #_____
Starting Site: http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/Titles/lphouse.html
Topic: Linear Equations (regressions)
Purpose: Students will access the Internet to search for housing prices in Houston, Texas, and compare the prices to the number of square feet found in the living area of a house. A linear equation will be derived from these data on a coordinate plane. Any "best- fit" method for determining the graph of the line can be used. Using information from the graph of the data and the equations of the function, students will answer questions about housing prices.
Materials: Internet connection, graph paper, and ruler.
Prior knowledge: Students should be able to plot points on a coordinate plane and write an equation in slope-intercept form from a linear graph.
Description: Often, actual data do not represent an actual linear function. Students will be asked to access data from the Internet and derive a linear regression from their set of data. These data will be used to answer questions on average cost per square foot, land values, and to predict the cost of various sized homes.
Time: Two class periods (one for data collection and one to determine regression)
Procedure: Students will "search" for information on housing prices on the Internet.
Suggested Houston area URLs
Houston Real Estate Web (http://www.sccsi.com/hrew/houston.html)
Martha Hendrick Home Page (http://www.hendrick.com)
Donna & Karen
(http://www.sccsi.com/hrew/baker.html)
Other Real Estate Links
A Net Search can also be done on real estate. Students should collect data from at least six properties in the Houston (or other specified) area. The data should include the price of the property and the square footage of the house. Calculate the square footage from given room dimensions. Plot the data on a coordinate plane as a relation of price per square footage. After students have plotted their data, instruct them to find a line of "best-fit" so most of the points are close to the ruler. There are several methods to do this, but for this lesson I recommend that a ruler be placed on the graph so that about half of the data points are above the ruler and about half are below. Draw the line, and then write an equation in slope-intercept form.
Be sure to include the URL. Show all of the work you did to calculate the square footage. Do not use any given square footage since you do not know what measurements were included.
Questions: Be sure to include the URL for the location of each of the sites used for your data. (Include the room measurements.) After completing your graph (on graph paper) and writing your equation, answer the following questions.
1. How much does a 5,000 sq. ft. home sell for in the location that was
researched? _________________________________________________
URL _______________________________________________________
2. What does the slope m, of the equation represent? _________________
3. What does the b value in the slope-intercept form of the equation represent? ____________________________________________
4. What does the line represented on the graph indicate about the cost of housing? ____________________________________________________ ____________________________________________________________
5. How would this graph vary if data was collected from other parts of the country? _____________________________________________________ ____________________________________________________________
6. How could this graph help you decide if you wanted to purchase a house?
_____________________________________________________________ ______________________________________________________________
7. If the graphs of new home prices vs. house size from two cites are compared, the cost of lots is about the same in the two cities. How will this fact affect the two graphs? _______________________________________ _____________________________________________________________
8. If the graphs of new home prices vs. house size for two cities is compared, the construction price per square foot for building a house is about the same in the two cities. How will this fact affect the two graphs? ______________ _____________________________________________________________
9. With your partner, ask another question about housing costs that requires
additional information, look up that information, and then answer the question.
Your question: _________________________________________________
_____________________________________________________________
URL _________________________________________________________
Your answer: __________________________________________________
___________________________________________________________________________________________________
___________________________________________________
Return to Table of Contents
Internet Project 2: Roller Coaster
Statistics
adapted from: Susan Boone, Saint Agnes
Academy
by Elayne Weger, University of Oklahoma, May 14,
1998
Name___________________
Hour_____
Computer # _____
Starting Site: http://coasterville.com/
Research the following data and answer the following questions. List the
URL that you used to find your data.
1. Name the steepest roller coaster listed. What is this coaster made of? _______________________________
2. Is the steepest roller coaster the highest? Explain your answer and include statistics to support this data.
________________________________________________________________________________________________________
________________________________________________________________________________________________________
3. Discuss whether the steepest roller coaster (disregarding what they are made of) are the fastest. What could possibly
contribute to a coaster's speed? _______________________________________________________________________________
________________________________________________________________________________________________________
4. Compare the highest coaster with the drop lengths listed. Do any of the statistics match the same specific roller coaster? _____
What type of roller coaster is the highest? ______________________________________________________________________
5. Search for a picture of a roller coaster. Write the name the coaster and record the URL where you found the picture. Using a ruler,
carefully measure the distance from a peak to the lowest section of one of the drops of the coaster. Model the picture on graph paper and
determine the slope of theis particular segment of the roller coaster. Using the Pythagorean theorem and the sketch on your graph paper,
calculate the distance of this particular drop. If statistics are available on this coaster, compare the actual stats with those you calculated.
Explain any differences. _______________________________________________________________________________________
___________________________________________________________________________________________________________
___________________________________________________________________________________________________________
Other Roller Coaster Links
Coasterville: http://coasterville.com/
Ultimate Roller Coaster: http://home.earthlink.net/~egieszl/urc.html
World of Coasters: http://users.sgi.net/~rollocst/a_rc.html
Internet Project 3: Population Clock
adapted from Susan Boone, Saint Agnes Academy,
June 27, 1995
by Elayne Weger, University of Oklahoma, May 11,
1998
Name________________
Hour_____
Computer # _____
Starting Site:
http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/Titles/popclock.html
Topic: Data Collection, Problem Solving, Research Skills, and Interpolation of Data
Purpose: Students will review the Census Bureau's Homepage on the Internet and gather data regarding trends in population. They will study this data and make predictions on future populations and compare their results with the information available on the Internet.
Materials: Internet access, ruler, graph paper (optional)
Description: The Internet site used for this lesson provides a great deal of data dealing with social issues. This lesson lends itself particularly well to social studies. Mathematically, students will be asked to collect data over a given period of time and record this data in a meaningful way. This Internet site provides up to the second population counts. Students should be placed in groups of two or three and instructed to 'gather" the data on the population count. They should record the time and the number. Record this data on the worksheet. This count should be collected at the beginning of their time on the computer, and again at the end of the period. Research techniques will be required to answer relevant questions regarding this particular Internet site.
Procedure: Divide the students into groups of two or three. Over an
assigned period, have students collect data from the Census Bureau Homepage
regarding current population counts of the nation. Students will record this
data and at the end of the lesson, the class will decide on a reasonable
functional representation of the data. Discussions could follow as to how this
interpolation was made. Compare the class results with the available
predictions found on the Internet site. Students should answer the question
portion of this lesson plan. Students can use the Census Bureau Homepage to
research the data needed to determine the answers for the following questions.
Students should include the location (URL) for the location the correct data
for each question was found. This information can be found in the location box
from the Inter browser screen.
Once the assignment is completed by all groups (this could take several
days), compile and study the population data on a classroom chart. Discuss how
these populations were determined. Is the function linear? Could a
different function represent the data better? Using the data, predict the
population for next week, next year, and in ten years. Compare these results
with those found on the Census Bureau Homepage.
Questions: (Be sure to include the URL of the web site that you found the answer to these questions.)
1. Select the Population Clock from the Census Bureau Homepage. Record the
population and time for the nation. Is this the "actual" count?
_______ Explain how this number was determined.
_______________________
__________________________________________________________
(Note that this assignment is designed to be a group project. If you are
working on this individually, collect at least 20 population counts over the
span of the project. Each count should be dated and recorded on a data
sheet. Plot these data points on a graph.)
2. What is Houston's (or any city of your choice) most recent documented population? ________________ What is the URL (location) you were in when you determined this answer? __________________________________
3. What is the name of the director of the Census Bureau? ______________ _______________________
4. What is the fastest growing occupation? ________________________ What
could contribute to the increase in this profession? ________________
_____________________________________________________________
What is the URL (location) you were in when you determined this answer?
_______________________________________________________ The Bureau of Labor and
Statistics is a great place to "search" for occupational Growth
statistics. You will find Occupations with the largest job growth from
1994-2205.
5. What percent of Consumer Expenditures is for food? _______%
for transportation? _______%
URL(location)?_________________________________________________
(hint: There is a search feature within the Census Bureau's web site. The
Bureau of Labor and Statistics also has a search feature. There are even
Consumer Expenditure Surveys found within this site.)
6. Return to the U.S. Census Bureau homepage. What is the population of the nation now? ______________ Record the population and the time. ______ _________________________If you are doing this project individually, you should collect at least ten (10) different population counts. Be sure to record the day and the time you collected them. If you would like to put this data in chart form, the entire class' data can be used to make a graph.
If you are doing this as a group assignment in class, give your answers to
the teacher and record your population data (answer to number 1 and 8) on the
posted chart. If you are doing this as an individual assignment, you should
compare the answers to number 1 and number 6.
Return to Table of Contents
Internet Project 4: THE
INTERNET PIZZA SERVER
adapted from Susan Boone, Saint Agnes Academy,
June 24, 1995
by Elayne Weger, University of Oklahoma, May 11,
1998
Name__________________
Hour______
Computer # _____
Starting Site:
http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/Titles/pizza.html
Topic: Data Collection, Unit Price, Proportions, Research, &
Area of Circles, (many more can be adapted)
Purpose: Students will create their own pizza using choices of toppings. They will be able to "order" their creation from the Internet and see a digitalized version of their pizza. They will use their order to calculate the area of various size pizzas, determine the "better buy," & cost per topping. Students will also have to use research skills to answer questions pertaining to the Internet Pizza Server Home Page.
Materials: Students will need access to the Internet, a metric ruler, and a vivid imagination.
Prior Knowledge: Students must be able to calculate the area of a circle. In order to complete the research portion of the lesson, they should have a very basic understanding of how to "move" through the Internet. (Click once on colored text will send you to that site. To get back to where you were, click on the "back" button.)
Description: This lesson takes the idea of going to a pizza restaurant, ordering a pizza, and determining whether a small, medium, large, or family size pizza is a "better-buy." Students will first need to calculate the area of each of the pizzas. Students will be asked to calculate the price/per/topping and determine whether this price is "fair".
Time: One class period (at least 45 minutes)
Procedure: Students will "search" the pizza servers home page.
Students will be asked several questions regarding their research, and they
will be asked to calculate various costs regarding the pizza selections. The
students begin by going to this URL:
The Internet Pizza Server
http://www.ecst.csuchico.edu/~pizza/
Problems and Questions: (answers for some of the problems depend on individual screen size. All support work should be included with your calculations.)
1. Order a small, medium, large and family size pizza. Use a metric ruler
and measure the diameter in centimeters of a small, medium, large, and family
size pizza. Calculate the area for each size pizza.
Record this data.
Small________________________________________________________
Medium_______________________________________________________
Large_________________________________________________________
Family_______________________________________________________
2. What is the "base" price (without any toppings) of a small,
medium, large, and family size pizza?
Small $______ Medium
$______ Large $______
Family $______
3. Calculate the price per topping.
Small $______ Medium
$______ Large $______
Family $______
4. Does this price change in relationship to the size of the pizza? ________
How does this compare to real life? _________________________________
______________________________________________________________
5. What size pizza, containing two toppings is the better buy? ___________
Explain your answer algebraically and support with a explanatory paragraph.
____________________________________________________________________________________________________
______________________________________________________________________________________
6. What is the most expensive pizza that can be ordered? How did you determine
your answer? $____________
______________________ ___________________________________________________________
7. How much would this same pizza cost if the only thing changed was the
size to small? $ __________
8. What was your favorite topping? ______________________________
9. In the space below, tell what ideas you would use to make this a
better site.
____________________________________________________________________________________________________
______________________
10. What did you find most interesting about this project?
___________________________________________
_______________________________________________________________________________
Return to Table of Contents
Internet Project 5: INDY 500
adapted from: Susan Boone, Saint Agnes Academy,
June 27, 1995
by Elayne Weger, University of Oklahoma, May
11,1998
Name___________________
Hour______
Computer # _____
Starting Site:
http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/Titles/indy500.html
Subjects: 8-12 Mathematics (Pre-Algebra and Algebra 1)
Topic: Mean, Median, Interpreting Data, Finding Rates, Times, and Distances
Purpose: Students will find the mean and median speed for the Indianapolis 500.
Rates per lap will be calculated as well as the length of each lap. Students
will need to research information via the Internet.
Materials: Internet access and calculator.
Prior knowledge: An understanding of mean and median. The formula d = rt.
Description: Students will be directed to various sites on the Internet to collect data pertaining to the Indianapolis 500. They will research information pertaining to the Official Indianapolis results. Given the speed of each of the participants, they will be able to calculate the average speed per lap, and determine the number of miles in each lap. Students will also be asked to find the mean and median speeds for the finishers of the Indianapolis 500.
Time: One 45 minute class period.
Procedure: Students will research The CBS Sportsline-AutoRacingsite. From this page, search the Indy 500 statistics. Another good site to find statistics for the Indy 500 is from the record books of the Indianpolis 500. Students can go to any of the Search Engines found on the Internet to help find the answers to these questions also.
Students will use these results to answer the questions on page 2.
Questions: Be sure to include the URL for the site used to determine the answers to these questions.
Part A.
1.Who was the topped ranked Indy 500 (winner) driver for 1997?
_____________________________________ _______________________________
URL_________________________________________________________
2. What was the fastest lap driven in the 1997 Indy 500? _______________
URL_________________________________________________________
3. At this rate, how long would it take to complete one lap of the Indy 500?
(hint: Do you know the rate? Do you know the distance? I think you should know
both of these! Use the formula t = d/r to calculate the
time.)____________________________________________________________________________________________
URL______________________________________________
4. In paragraph form, discuss how you derived your answer. Be sure to
include any math calculations you used. _________________________
___________________________________________________________________________________________________
___________________________________________________________________________________________________
______________________________
Part B.
1.What is the average "average speed" driven for the top ten ranked
drivers of the 1997 Indy 500? (You will need to find the top ten finishers.)
________
1_________________________2_________________________3__________________________4__________________
5_______________________________6_______________________________7_______________________________
8_______________________________9______________________________10_______________________________
URL_________________________________________________________
2. What is the record finish time for the Indy 500?
___________________
Who set it? _____________________________ When? _______________
URL_________________________________________________________
3. During what years was the Indy 500 not run?
______________________ Why do think there was no race during those years?
_____________________ ______________________________________________________________
_____________________________________________________________
URL_________________________________________________________
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