1
April 1 to April 7,
2002 is National Sleep Awareness Week. There is a good Science lesson
(number 01) on the Florida website (External Links)that is all about sleep
deprivation and its effects on the brain. There is a handout that lists
the problems associated with sleep deprivation (poor concentration, faulty
memory, low creativity, mood swings and depression, etc.)A website can
also be used for more information about the importance of sleep. This
can be found at: www.sleepfoundation.org.
After the students
digest the material on the importance of adequate sleep, they are asked
to survey 20 people on how many hours of sleep they get each night (on
average). The students are to use this information to make a bar graph
illustrating the ratios of those who get less than 6 hours, 6 hours, 7
hours, 8 hours, and 9 or more hours. Students will then change the ratios
to a decimal number, and then change the decimal number to a percent.
Bar graphs can then be compared within the class. Further comparisons
with ratios and percents can be made to compare the responses of men and
women or adults and children.
Eileen Downard
2
Non-Math Lesson Plan:
I expanded on a geography lesson that helped students understand directional
arrows on a map an to understand time zones.
I added mathematical elements to this lesson that included estimating
the cost of a vacation.
:Learning to read a map scale and convert the scale into miles.
:Calculating ths distance between cities by adding the road segments.
:Calculating how much gas will be needed based on the average miles per
gallon.
:Calculating the total time to destination based on traveling the speed
limit.
:Using the above calculations to estimate distance, time, and fuel cost
for a round trip to a beach vacation.
:Calculating the cost for a beach house per day allowing for additional
people arriving midweek.
:Estimating food and restaurant costs.
:From all of the above, preparing a budget for the trip.
:Finally, allowing for time differential between time zones in terms of
travel departures and arrivals.
John Isaac
3
Objective: Students will gain a better understanding of the following political labels: radical, liberal, moderate, conservative, and reactionary.
Materials: paper, graph paper, newspapers, colored pencils, pencils.
Procedure:
1. The class will participate in a class discussion about political labels.
2. After the discussion and notes, students will look through various
newspapers looking for the political labels to be used. Results will be
shared with the class.
3. Students will work in pairs to gather data and graph the results of
questioning all students and staff in the building about which political
label best describes their views.
Evaluation: Review
of newspaper articles and graph of political label results.
By Cindy Young
4
Brian DeFluri
Currently I am doing lessons on oceanography as well as lessons on volume.
I believe that there is a wealth of assignments that can be generated
by these topics. One such assignment that I am going to assign my class
is to figure out how many gallons of water is needed to fill up certain
thing such as the room, the YMCA swimming pool, etc. This will also tie
in nicely when I start to discuss pressure and depth of the water. I would
also like to assign how much water will fill up a 1' by 1' by 2,500 column
of water and pose the question, "Will that column of water fill up
the room?"
5
Nancy Ash
This is a good lesson
for teaching students paycheck terms, but it can also be developed into
a math lesson.
On chalkboard the instructor will write a sample bi-monthly paycheck.
One row will have the terms used in a paycheck, and the row directly under
the terms will have the terms or amounts the instructor makes up.
First row:
EMPLOYEE'S NAME / PAY RATE / PERIOD END/ CHECK NO.
Next:
EARNINGS / HOURS/ AMOUNT/ YTD/ DEDUCTIONS(FICA
MEDICARE PA. STATE W/H)/ AMOUNT/ YTD/
Next:
GROSS EARNINGS:
Next:
NET EARNINGS:
Ask students how many deductions were taken out of the paycheck. Have
students determine what percent is taken out for FICA, Medicare, and state
taxes. Have students add up to see if the amount of hours worked agrees
with the earnings. There is a lot an instructor can do with this sample
paycheck. For example, students can make a pie chart and do all sorts
of percent calculations. They can also figure out how much the employee
will make in one year or 6 months. Often the students will keep the ideas
flowing!
6
Katherine Stamler
Have students read
the labels on the Skittles, Life Savers, and M & M packages. Look
up information on the Internet about the products, contents, and manufacturing
of the products.
How does the website name and the product name compare?
Discuss the flavors and colors in the packages. Write an essay about the colors and flavors of each product and why the manufacturer chose those.
What can you find out about the contents of the Skittles product? Is it the same or different for every color? What is the nutritive value of Skittles? Tell me about what you found in an essay.
Are there similar products on the market? Organize the class in groups and make a list of the similar products. Devise a survey to distribute to people for quality and taste testing.
Individually, make
a list of questions that you would ask and answer the following questions.
What kind of information would you need?
What kind of questions would you ask?
To whom would you pose the question?
Is there anyone you would eliminate?
Conduct the survey with approval from your teacher.
You are the Skittles
manufacturer and are going to SELL your product.
Write an ad for your product and design a poster with a caption.
Activity 2:
Each student gets a bag of skittles.
Open the bag of Skittles
and organize the skittles by color.
What percentage of the Skittles in your bag is yellow?
Organize the skittles and make a bar graph demonstrating what you found.
Now convert the numbers to % and make a pie graph to demonstrate what
you found in your bag.
Based on your research.
What can you predict about the colors in a bag of skittles.
Investigate the graphs
of other students.
Are your predictions accurate?
Why or why not?
Combine the numbers
on a chart of the entire class and make a bar and pie graph.
What are the percentages now?
Can you predict the % of each color better now?
Why or why not?
Make a prediction
on what color the first piece out of the bag will be.
Make a prediction on what color the fifth piece out of the bag will be.
7
Activity Title: Sleep Today-No Maybe Tomorrow
Goal/Objective: To read and analyze informational text and to plan and create a classroom bulletin board or visual display.
Lesson Outline: The original outline tells students about the fast paced world we live in and how people are getting less and less sleep. This lesson is aimed at getting students to read and interpret science information.
Activity: The original lesson instructs students to read the article "Working Ourselves to Death" and then discuss it. It also suggests dividing the class into groups of four to develop a bulletin board.
Adaptation: The students will be asked to keep a log of their sleep for one week. When they come to class, they will chart the hours slept. They will then add them up to see if they are in line with suggested sleep amounts. They can also figure out what percentage of their day is spent: sleeping, working, relaxing, etc.
Real-Life Connection:
Students will be made more aware of the time they spend on various activities.
They can relate the way they feel to the amount of sleep they get. They
can plan their schedules to make their day more balanced.
Charlene Berti
8
Math Lesson Plan
Objective: Students will be able to explain the benefits of energy conservation.
Lesson: As an extension of my social studies lesson on energy prices and the need for the US to become less dependent on foreign energy sources, I would have the students calculate the amount of money they personally could save on energy costs in a month. I would be emphasizing how different percentage cutbacks in usage would translate into extra money for their household budget.
Barb Stoner
9
Stephanie Kline
Math Lesson Plan
Percentages in everyday life
Objective: To familiarize students with how to figure out percentages off of everyday merchandise
Materials: The newspaper, handouts, paper, & pencil
Lesson: I will first go over what percent means. After that I will show how to figure out how much a percentage is off of an item on sale. Then I will hand out clippings of a newspaper listing sale price and regular price. I will have the students figure out what percentage off the items are. I will give handouts that have the normal price and a percentage listed. They are to find out what the sale price is. We will then discuss how this skill will help out in the everyday happenings of life.
10
How
Many Ways Can A Team
Win A 7-Game Series?
By: Kent Anderson
Introduction: Students will discover how many ways a team can win a 7-game series (NBA Finals, World Series, Stanley Cup) by accessing the Internet and then systematically constructing a sample space which lists all the possible ways.
Prior Knowledge: Basic introduction to sample spaces.
Grade Level: 8-12
Task: Students will systematically construct a sample space listing all the ways a team can win a 7-game series. For example, in the 1996 NBA Finals, the Bulls beat the Sonics by winning the first three games, losing the next two, and then winning game six (Win-Win-Win-Loss-Loss-Win or WWWLLW) How many other ways are there?
Resources:
http://198.77.124.13/sports/basketba/skn/sknplsc.htm
1996 NBA Playoffs
http://www.infoplease.lycos.com/ipsa/A0003843.htmlNBA Finals 1997
http://www.nba.com/finals97/1998 Playoffs - NBA Finals Recaps
http://www.sportserver.com/SportServer/basketball/nba/98playoffs/1997 World Series
http://www.sportserver.com/newsroom/sports/bbo/1995/mlb/mlb/stat/97postseason.html1998 World Series
http://www.cnnsi.com/baseball/mlb/1998/postseason/1999 World Series
http://www.cnnsi.com/baseball/mlb/1999/postseason/world_series/SportServer - Major League Baseball - World Series Archives
http://www.sportserver.com/
Process:
- Students will access
the Internet address above and list the examples of winning a 7-game
series. For example, in 1996, the following occurred:
a) WWWLLW (Win-Win-Win-Loss-Loss-Win)
b) WWWW
c) WWLWLLW
d) WWLWW
e) WWWLW
f) WWWW
g) WLWWLWThen have the students determine if these are all the possible ways.
- Have the students
consider a 5-game series. Model systematically constructing a sample
space by creating or having the students help you create the following
for all to see:
Win 3-0 Win 3-1 Win 3-2 WWW LWWW LLWWW WLWW LWLWW WWLW LWWLW WLLWW WLWLW WWLLW
These are the only 10 ways to win a 5-game series. Note the position of the losses. Note that a series never ends with an L. (A series can't be won by losing the final game)
- Have each individual student systematically construct a sample space on paper listing all the possible ways a team can win a 7-game series. A teacher might want to mention there are 35 possible ways. Or maybe a teacher would rather leave it more open-ended.
Learning Advice: Some students may need to study the nature of a 3-game series before working with a 5-game series or a 7-game series.
Evaluation: If this activity is done near the end of a unit which contained many examples of constructing sample spaces, individuals could be graded on an objective basis (example: 90% correct=A, 80% correct=B, etc.). If this activity is done at the start of a unit, a teacher might want to have groups of students work together and try to list as many ways as possible.
Extensions: Pascal's Triangle Combinations and Permutations
Conclusion: Students who successfully construct a sample space listing all the possible ways will have solved a real-life problem as well as improving their skills in probability and mathematical reasoning.
SCORE Mathematics | | SCORE Mathematics Lessons Index | | SCORE Mathematics Search
California Mathematical Academic Standards:
Grade 8-12:
Algebra II #18
18.0 Students use fundamental counting principles to compute combinations
and permutations.
NCTM 9-12: Mathematics as Problem Solving; Mathematics as
Reasoning; Mathematical Connections; Probability.
August
1996
Revised August 27, 1999
Copyright © Kings County Office of Education
SCORE Webmaster
11
Measures
of Central Tendency
Group 1 Mathematics Lesson
Objectives:
- Identify and calculate
the mean, median, mode, and range of a given set of data.
- Learn to utilize
the calculator for calculating the mean or checking answers.
- Display and interpret
bar graphs.
- Practice using grid answer sheets.
Materials:
- Prepared sets of
data or a computer with statistical software such as Minitab containing
sets of data. (Be sure to include some data sets that contain a few
extreme values and data sets should be of a reasonable size, 10-20.)
- Chalkboard or overhead
projector.
- Calculators - Casio
fx-260 series.
- Set of 2002 type GED answer grids for students.
Procedure:
Instruction on the definition of the mean, median, mode, range, and the measure of central tendency will be given along with several examples. Include an example of a bar graph using the mode. Students will start with a set of data such as the weight, age, or height (in inches) of each individual in the class. Each student will calculate the mean, median, and mode of the data gathered in the class, followed by a class discussion of their answers. The students should calculate the mean by hand the first few times and use the calculator to check their answers. Students will work in groups of two to calculate the measures of central tendency for sets of data. They will use the bar graph to determine the mode. Other answers will be entered on the grid sheets.
Evaluation:
Students will turn in their work at the end of class for evaluation.
12
This lessons was found on PBS's website.http://www.pbs.org/teachersource/mathline/concepts/historyandmathematics/activity1.shtm
Activity I: Proving the Pythagorean Theorem (Grade Levels: 6-9)
Objectives:
The Pythagorean theorem can be proven using several different basic figures.
This activity introduces student to two such figures with a brief explanation
of how to go about the proof. The activity will demonstrate alternate
solutions to the problems as well as provide a glimpse into the way early
mathematicians reasoned about mathematics.
At the end of this activity the students should be able to:
- understand that
there are many ways to approach a problem
- not to be completely
reliant on a given drawing
- recognize that not all geometric proofs are two column deductive proofs so familiar in traditional textbooks
Student
Activity (PDF File)
Answers
(PDF File)
Activity 1
| This activity is a high school level activity that can be adapted for middle school and upper elementary students by simply having the students determine as many as possible Pythagorean triples. |
Proving the Pythagorean
Theorem
Pythagoras of Samos,
c.560–480 BC, was a Greek philosopher and religious leader who was
responsible for important developments in the history of mathematics,
astronomy, and the theory of music. He migrated to Croton where he founded
a
philosophical and religious school that attracted many followers. Because
no reliable contemporary records survive, and because the school practiced
both secrecy and communalism, the contributions of Pythagoras himself
and those of his followers cannot be distinguished. The most important
discovery of this school was the fact that the diagonal of a square is
not a rational multiple of its side (that is, the diagonal of a square
is not a number that can be expressed as the ratio of two whole numbers.).
In essence, this showed the existence of irrational numbers. This discovery
disturbed Greek mathematicians and the Pythagoreans themselves, who believed
that whole numbers and their ratios could account for geometrical properties.
Pythagoreans believed that all relations could be reduced to number relations
("all things are numbers").
The Pythagoreans knew, as did the Egyptians before them, that any triangle whose sides were in the ratio 3:4:5 was a right-angled triangle. The so-called Pythagorean theorem, that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, may have been known in Babylonia, where Pythagoras traveled in his youth. The Pythagoreans, however, are usually credited with the first proof of this theorem.
Much of the Pythagorean doctrine that has survived consists of numerology and number mysticism, and the influence of the belief that the world can be understood through mathematics. That belief was extremely important to the development of science and mathematics.
Proving the Pythagorean Theorem
The following figure is the typical figure used to prove the Pythagorean theorem that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. c2 = a2 + b2
1. If the right triangle ACB were isosceles, the figure would appear as follows.
Show how with the addition of three lines the proof of the theorem is as simple as 2 + 2 = 4.
2. The following figure was used by President Garfield in proving the
Pythagorean theorem. His method is based on the fact that the area of
the trapezoid ACED is equal to the sum of the areas of the three right
triangles ACB, ABD, and BED.
Prove the Pythagorean theorem using President Garfield’s method.
3. A Hindu mathematician named Bhaskara used the following figure to prove
the Pythagorean theorem by showing the sum of the area of the small square
and the area of the four congruent right triangles equal the area of the
large square.
13
Adding Math to the Doplar Effect Lesson(To the Doplar Effect lesson as seen in the science section, add the following math)
Content area: … and math: distance formula, multiplication, and calculator
Goal: … and calculate the distance traveled by the car during the time of the beep at each speed.
Materials: add stop watch and calculator
Target audience: pre- or GED math students
Min/max: same
Delivery: back at classroom, have students time length of beep using stop watch. Then determine distance car traveled using time of beep, speed, and distance formula.
Evaluation: check math
S. Ratelle
14
A non-math lesson I would use would be about life science. The class would talk about what life science is and look at and discuss a diagram of a plant cell. The class would seperate into groups and answer multiple choice questions about the cell. Then the answers would be discussed in class. This lesson could be developed into a math lesson in keeping with the plant discussion. First, the class would review addition, subtraction, multiplication, and division of whole numbers. Then each student would be given a diagram of a garden containing certain dimensions. The student would be responsible for planning the garden using math to space the plants, plan borders, figure out how deep to dig holes, and even how long to build a fence around the garden. This lesson could vary in difficulty depending on the learners abilities. For example, in addition to using whole numbers, fractions and measurements could be used. This lesson connects the scientific makeup of plants too!
mathmatically constructing
an area for plants to grow in. This shows the students that what they
are learning is useful in the "real world".
Submitted by : Lisa Michalochick
15
Goal/Objective— To emphasize the importance of planning in order to accomplish any goals—long range or short range
Introduction— Financial planning is a skill that is vital to successful daily living. The purpose of this lesson is to provide the students with opportunities to use Math in planning for their goals.
Activity--
To view a proposed plan for budgeting for a family vacation
Sam Ford’s Monthly Net Income is $1,540.00. This is a family of 4,whch includes 2 children and 2 adults. Sam is presently the only breadwinner.
| Rent | $500.00
|
|
Food |
$450.00
|
|
Utilities |
$280.00 |
| Entertainment/Recreation |
$
50.00 |
|
Insurance |
$
120.00 |
| Clothing |
$ 50.00 |
| Miscellaneous |
$ 75.00 |
| |
|
| $1525.00 |
Sam and his wife Jane are determined to visit Disney world during the last week in April of 2003. They have $15.00 left after the expenses are paid. The present cost for this trip is approximately $3,522.00. This includes airfare, hotel, spending money, food, as well as, the entrance fees to the parks—for everyone in his family. Sam feels he should add at least $1,500.00 to include the rising costs for next year.
1.How many months/weeks
does Sam have in order to complete his goal?
2.Do you feel that Sam should include a goal such as the above in his
budget?
3.Why, Why not? 4.How much would Sam and his wife need to save each week/
month for this project?
5. What price does Sam estimate the total cost of his vacation?
6. What % of Sam’s yearly net income will this vacation cost?
Evaluation-
Students will work in groups composing written “real world” problems and using a combination of written (language mechanics) , and problem solving math skills to compute their answers.
Some of their real life compositions would probably include the following: weight loss, computing gasoline/mileage, doubling recipes ,carpeting, painting etc.
*Teacher will assist students where needed ,with the help of student tutors, in the correct formulation of their work.
*Teacher will give written tests which will incorporate the GED goals for MATH
Sylvia Bey #10
16
I had
class look through various grocery store ads and calculate cost per ounce
for various items to determine which stores had best buys and also whether
it was best to purchase two small items or one larger item. We also discussed
whether BOGO items are always good buys.
Could assign essay discussing their findings or comparing and contrasting
prices at various stores. Could also discuss benefits of stocking up on
items or of "cherry picking" for sale items.
17
Rich Yates
Materials:
Science article by
Jeremy Lovell : "World Facing Critical Choices on Environment"
Global Environmental Outlook - 3 Report: Chapter 5: page 2: "Alleviating
Poverty"
US Census Bureau estimate of World Population
Pertinent information
from GEO-3 Report:
Alleviating Poverty: "The international community has set a target
of halving by 2015 the proportion of the world population (currently 22
per cent) which survives on less than US$1 a day. The day-to-day lives
of the majority of the poor are much more closely linked to the state
of the environment than is the case for the better off -- a healthy, productive
environment is one of the stepping stones out of poverty. As long as millions
of the world's population remain poor, and the environment stays on the
periphery of mainstream policy making, sustainable development will be
an unachievable goal."
US Census Bureau World Population Estimate 5/28/2002 3:39:29 GMT (EDT+4): 6,227,123,864
1. What is 22% of the world's current population?
2. What would 11% of the world's population be?
3. Given the GMT time of 3:39:29 am 5/28/02, what would this be in EDT (Eastern Daylight Time)?
4. How would you spend
your dollar for the day if that's all you had to spend for the day?