THE
TURKEY FARM
GRADES: 48
Every week I try to incorporate a cooperative
lesson into our math class. I teach 6th grade math and have about 43
students per period, so I must be prepared! This is a simple yet fun
activity where students will find the mean, median, and mode of a given
set of numbers.that I just did with my classes. It turned out great!
MATERIALS:
 worksheet
 calculator
 marker
 crayons
 2 sheets of construction paper
 scissors
 glue
 small paper plate
METHOD:
 I distribute a worksheet
that has a story that I made up : "Your group owns a turkey
farm. The newly elected President has chosen your farm to supply
them with 5 turkeys for their special Thanksgiving dinner. Only
the 5 heaviest turkeys will be chosen."
 George 25lbs
 Millie 22lbs
 lulu 24lbs
 kiki 30lbs
 chi chi 24lbs
 wonka 14lbs
 Kyle 23lbs
 boo 28lbs
 The students choose the 5 heaviest and find
the mean, median, and mode.
 The students then construct a turkey using
the information and supplies given.
 Paper plate is the body where the mean, median,
and mode are written
 The 2 sheets of construction paper are used
for feathers. the 5 weights are written on each one in order from
least to greatest.
 The feathers are glued onto the paper plate,
a copy of a turkey head is given and colored, and also attached to
the plate
 Any extra details are added by the group members
 I place
it them on a bulletin board that reads, "Who
let the turkeys out?"
My students had a great time doing this project!
Submitted by,
MAIRA MAGUIRE
CENTENNIAL MIDDLE SCHOOL
MIAMI, FL
mywonka@aol.com
GETTING
TO KNOW YOU GRAPHING JOURNAL
GRADES: 38
This lesson is a good one to do during the first
week of school as it helps breaks the ice for your class and introduces
or reinforces various forms of graphs.
MATERIALS:
 graph sheets
 pencils or crayons
METHOD: overhead.
 On the first day the 3 bar graphs we make
are: hair color, types of pets, and the year each child entered our
school for the first time.
 When we make the double bar graph we use information
gathered
 The first week of school I teach 5 major
forms of graphs. I do one forcle graphs. Each day I have the
class make 3 graphs. The first one we all make together, the
second one is guided,m a day. The first day I teach single
bar graphs. Then double bar graphs, single line graphs, double
line graphs, and cir and the third graph is made independently.
To gather the information post the question and record the data
on the board or
by the row. One of these is the number of brothers
and sisters per row. This is set up across the xaxis using these identifiers:
row 1 brothers, row 1 sisters, row 2 brothers, etc. Other graphs
of this type that we do are # of aunts and uncles and # of cats and
dogs.
 Single line graphs are very simple to do and
there is a variety of info to be gathered. When we do double line
graphs, we use information gathered by gender. The ones we are doing
this year are birth month, favorite color, and height. Use two different
colors to form the lines.
 Our final graphs are circle or pie ones. I
created mine on the computer so that I could have a circle divided
with the number of sections that correlated with the number of kids
in my class. We are doing favorite soda pop, favorite outdoor activity,
and favorite dessert.
 At the end of the week we have accomplished
several major objectives. The class is now ready to use this essential
tool throughout the year instead of waiting for the math book to
introduce this. Also, put all of the wonderful graphs into a portfolio
or journal which will be wonderful for Back to School Night. You
can also use this data for a number of writing and language activities
(biographies, interviews, web pages, etc.)
submitted by
SHELLEY BOWEN
MITCHELL K6 SCHOOL
WINTON, CA
fambowen@cyberlynk.com
SOME IDEAS FOR SIMPLIFYING YOUR
MATH CLASS
GRADES: 412
MATERIALS:
METHOD:
 When teaching requires the use of tools, such
as rulers, compasses, protractors, etc., try to get the whole class
to have the same instrument. I had some class funds to use recently
& bought enough protractors & compasses for everyone in the
class to use. They will be reused from year to year. When I went to
teach the lesson, I didn't have to run around the room trying to show
everyone how "theirs" worked. Also – try to use clear
protractors. The new purple & green plastic ones are cute, but
hard for beginners to use.
 Another idea for protractors: Use a small
drill (like a Dremel tool) to put a small hole at the crosshairs.
Some protractors come with a hole already there. Tie a string through
the hole. When the knot is lined up over the crosshairs, the student
can then pull the string up along the angle side they are measuring & the
string points to the correct number of degrees.
 Use the overhead! Write to the publisher to
get permission to make overhead transparencies of difficult lessons.
This way everyone can watch what you're doing on the overhead. (I
had a couple of difficult lessons on scale drawings & map distances
that I taught this way. They weren't difficult lessons – just
difficult to teach when everyone couldn't see what I was doing).
Make a ruler out of transparency film or photocopy onto a transparency.
Slide overhead transparencies into clear plastic sheet protectors.
They can then be stored in a 3ring binder, and the sheet protectors
can be easily written on & erased.
 Use examples from real life, whenever possible.
For a lesson on sales tax, photocopy a receipt from a recent purchase.
Have the students figure out if the tax was correct. Copy your electric
bill & talk about the way kilowatts are measured & billed.
For a lesson on scale drawings, visit a new home development & take
a copy of the floor plans of a new house. I found a really neat book
about the way carpenters have to use math – such as measuring
the angle & pitch of a staircase, etc. Challenge the students
to think of a profession that doesn't use math (farmers have to measure
acreage, pounds of fertilizer, etc., lawyers have to be able to bill
accurately, etc. Every job requires that employees be able to check
to see if their paycheck is correct!)
 Take math grades once a week instead of daily.
I correct math lessons orally daily, usually with students marking
their own mistakes, but I only collect them weekly – usually
on test days. Of course I have to watch for cheating, but I know
my kids' ability pretty well & it becomes obvious to spot. I
record the grades while the students are testing. Since my school
uses workbooks & I do not allow the students to tear out the
pages, this is the only way I have found to be able to glance over
their work for neatness, completeness, similar errors, skipping problems,
etc. without keeping their books overnight. I also clip the corners
of pages I've checked to help me go the the right lesson next time.
 Use manipulatives, even in middle school &
high school. I was a straightA student, but didn't really understand
most math concepts until a college professor let us "play"
with his 5th grade manipulatives. Use fraction pieces, counters, graph
paper, etc. Go ahead & make 5 groups of 4 with edible manipulatives
like Cheerios. It's the first time I really understood the concept
of multiplication! Use "fun" manipulatives like m&m's,
Skittles, pennies, etc. – they don't have to be boring bean counters.
submitted by
C. DAMIGO
no school listed
SAN JOSE, CA
thedamigos@aol.com
DAILY STORY PROBLEM
GRADES: 38
This approach to story problems made a tremendous
difference in my classroom this year. Test scores shot up both on proficiency
tests and standardized tests. Although the instructions are designed
for an elementary selfcontained classroom, they can easily be adapted
for middle school and departmentalized programs.
MATERIALS:
 tagboard
 small incentive charts
 stickers
METHOD:
 While this will take some preparation time,
the payoff is worth it! I have a daily story problem that is written
on tagboard to put up in my class every morning. (It is worth the
effort to put these on tag because there is no effort in future years
to keep this going.)
 The problem is read aloud no matter what the
grade level and students have until after lunch to solve the problem.
 Children keep a file folder with their answer
papers inside. I give a new sheet a week and make sure the children
are aware of having substantial space to work.
 All answers must have labels i.e. feet, puppies,
centimeters, etc.
 After lunch, 3 or 4 students go to the board
to solve the problem. They talk aloud as to how they solved the problem.
 When children use different methods to reach
the same answer, we spend time discussing how and why that works.
 Each child has an incentive chart up in the
class. Each day 2 students are assigned the task of collecting those
papers with correct answers. A sticker is put on the chart for each
student who was correct. When a child gets 20 stickers, he/she gets
a prize and a new chart goes up on the wall.
HELPFUL HINTS:
 I do not discourage children from talking
to each other about ways to attempt to solve the problem. They may
not copy each other though.
 I do not make up nonsense problems. If we
are studying a specific unit, I look for information about that to
create my problems. So, we did 3 weeks of problems about ancient
Egypt and 3 weeks of insect problems.
 I vary the targeted math skill. So in one
week, we may do one long division, one simple fraction, two on working
with money, and one on decimals.
 I make sure that once and awhile the daily
problem is very simple so that everyone is having success.
 I also made up a lot of trivia problems using
the Guiness Book of World Records. My kids enjoyed reading about
things like the largest pizza ever made.
Finally, the students' ability to locate and
use mathematical language improved tremendously. Many of my kids are
second language learners and need constant practice in looking for
key vocabularyin addition to the daily review and practice of math
skills.
submitted by
SHELLEY BOWEN
MITCHELL SCHOOL
ATWATER
shellyb@cyberlynk.com
THE BASIC PRACTICE MODEL
GRADES K12
The Basic Practice Model is the traditional behavioral
approach utilized by many school districts which is a standard, traditional,
direct lesson plan where the teacher presents to the whole class and
the students practice. Many administrators evaluate teachers with this
model in mind, so it is a good idea to have some good lessons prepared
that utilize it. Besides, in this "day of constructivism," this
model has its place and use.
Here are the steps:
 ORIENTATION: Teacher establishes content,
continuity with previous activities and future activities, establishes
the objective of the lesson.
 PRESENTATION: The teacher presents both visually
and orally to the whole class; students listen and watch.
 STRUCTURED PRACTICE: Teacher essentially presents
again with the students working along with the presentation.
 GUIDED PRACTICE: Students work on another
example while teacher circulates and offers assistance.
 INDEPENDENT PRACTICE: Students do another
example without assistance.
 FEEDBACK: Hey, you "gotta" reflect
and debrief.
submitted by
ROB SCHUCK
PACOIMA MIDDLE SCHOOL
LOS ANGELES, CA
rschuck@glendale.edu
SETTING A FOUNDATION FOR PROBLEM
SOLVING
GRADES 312
The beginning of the school year is a crucial
time to begin the problem solving processa process that is a central
component of all new Math texts adopted today. The following are a
number of stages, approaches and steps for problem. They should be
discussed with the students, and if possible, put onto charts for display
throughout the year. Examples should be chosen in accordance with the
age and level of your students.
6 STAGES OF THE PROBLEM SOLVING PROCESS
 Define the problem
 Brainstorm possible solutions
 Evaluate and prioritize the possible solutions
 Choose the best solution
 Determine how to implement the solution
 Assess how well solution solved the problem
7 APPROACHES TO PROBLEM SOLVING
 Guess and check
 Find a pattern
 Use a systematic list (charts & tables)
 Use a drawing or a model
 Eliminate possibilities
 Work backwards
 Use a similar, simpler problem
5 STEPS TO PROBLEM SOLVING
 Read and understand the problem
 Organize the information
 Determine the operations needed, establish
equation
 Solve and check answer
 State and label your answer
submitted by
ROB SCHUCK
PACOIMA MIDDLE SCHOOL
LOS ANGELES, CA
rschuck@glendale.edu
THE FOLLOWING ARE SOME VERY POPULAR
PROBLEM SOLVING LESSONS THAT WE RAN LAST YEAR. THESE ARE AN EXCELLENT
WAY TO CONDITION YOUR STUDENTS INTO HIGHER LEVEL THINKING SKILLS FROM
THE BEGINNING OF THE YEAR!
TEACHING THE "GUESS AND
CHECK" METHOD
GRADES 312
Guess and check is an important critical thinking
process that is becoming increasingly prevalent within new math texts.
It is usually introduced in some form in third grade, and is used in
some form all the way up through senior high.
There are four major steps involved in the "Guess
and Check" method:
 Make a plan
 Create a chart or table
 Eliminate possibilities
 Look for a pattern
The following are a number of examples you can
use. (Additional examples can be found in virtually any math text book).
They are listed in developmental order, less sophisticated to those
more sophisticated. Pick those most appropriate to your students. (The
numbers can easily be changed to provide additional examples).
With practice your students will develop a self
confidence that will enable them to obtain solutions ranging from a
variety of correct answers to one correct answer. This will serve as
a preparation for high order thinking skills as those used in Algebra,
Geometry, etc.
EXAMPLE 1
Using pennies, nickles and dimes, how many different
combinations can be used to obtain 25 cents? (HINT: there are 12 ways)
Make a chart with pennies, nickles, dimes and
"total" as column headings.
TEACHER NOTE: This problem introduces all four
of the steps and adherence to ONE CONDITIONthe combination must
total 25 cents. The students should be able to put these combinations
in any order they choose. As they practice this type of problem,
they will find that using a particular system or order, (i.e. concentrating
on pennies from greatest to least) will emerge as a faster, more
accurate method. Initially, in the earlier grades, students should
use actual coins and record their findings.
EXAMPLE 2
Using nickles, dimes and quarters, how many different
combinations (where at least one of each coin is used), can make 50
cents? Before you start, make a prediction. Compare your prediction
to your findings.
TEACHER NOTE: There are only 2 combinations.
This example introduces TWO CONDITIONSat least one of each coin
AND a total of 50 cents.
EXAMPLE 3
Using 17 coinsincluding AT LEAST ONE NICKLE,
DIME AND QUARTERhow many different combinations can be used to make
$2.25? Before you start, make a prediction. Compare your prediction
to your findings.
TEACHER NOTE: There are only 3 combinations.
This example introduces THREE CONDITIONSat least one of each coin,
17 coins AND a total of $2.25.
EXAMPLE 4
Using 17 coinsincluding AT LEAST ONE NICKLE,
DIME AND QUARTERhow many different combinations can be used to make
$2.25WHERE THERE ARE 4 MORE DIMES THAN NICKELS? Before you start,
make a prediction. Compare your prediction to your findings.
TEACHER NOTE: There is only 1 combination.
This example introduces FOUR CONDITIONSat least one of each coin,
17 coins, a total of $2.25 AND a relationship of one variable (dimes)
to another (nickles).
submitted by
ROB SCHUCK
PACOIMA MIDDLE SCHOOL
LOS ANGELES, CA
rschuck@glendale.edu
USING A SYSTEMATIC APPROACH TO
THE GUESS AND CHECK METHOD
GRADES 312
Last time we traced the developmental stages
of guess and check ("Teaching the Guess and Check Method"),
utilizing four components. These components involved:
 Making a plan
 Creating a chart or table
 Eliminating possibilities
 Looking for a pattern
The purpose of these components is to demonstrate
to the student that through an organized, systematic process,
answers to seemingly "impossible" problems can be found.
The key is the systematic approach, because all four components
evolve around the system.
Having already explored the wonderful world of
coin problems, the following examples are concerned with consecutive
numbers and age problems. Also available are very basic problem solving
examples that highlight each of the seven approaches originally addressed
two weeks ago ("Setting a Foundation for Problem Solving").
EXAMPLE 1
5 years ago, Jay was seven times older than Mary.
In five years, Mary will be half as old as Jay (or Jay will be twice
as old as Mary). How old is each now?
Make a horizontal chart with the following headings.
(discuss the construction of the heading with the students):
J5YAM5YAJ7XOLDER?JNOWMNOWJIN5YMIN5YM1/2J?
KEY:
J5YA (John's age 5 years ago)
M5YA (Mary's age 5 years ago)
J7XOLDER? (Is John 7 times Mary's age?)
JNOW (John's age now)
MNOW (Mary's age now)
JIN5Y (John's age in five years)
MIN5Y (Mary's age in five years)
M1/2J? (Is Mary half of John's age?)
TWO POSSIBLE ANSWERS: (Numbers are in order of
the columns above)
71YES1261711NO
142YES1972412YES
Therefore, Jay is 19 and Mary is 7
EXAMPLE 2
Make a chart similar to the one above.
Let's make up a consecutive number problemyour
choice.
GUESS AND CHECKFINAL PROJECT
MULTIPLE VARIABLES AND CONDITIONS
GRADES: 612
This is the last of the problem solving contributions
that will be submitted, unless there is a sudden outcry for more! more!
more! I hope that what has been presented so far has been of use for
some of you. So...for the grand finale of problem solving utilizing
the guess and check (trial and error) method, I present to you the
infamous chickens, pigs, and sheep problem.
TEACHER NOTE: Remember that
the
"guess and check" method utilizes four components. These components
involve:
 Making a plan
 Creating a chart or table
 Eliminating possibilities
 Looking for a pattern
The purpose of these components is to demonstrate
to the student that through an organized, systematic process, answers
to seemingly "impossible" problems can be found. The key
is the systematic approach because all four components evolve around
the system. Also, by using a systematic approach, it becomes increasingly
easier to eliminate possibilities. This is especially true of the problem
presented here.
THE PROBLEM: You are given $100
to buy 100 farm animals (at least one each of three animalschickens,
pigs, and sheep). If chickens cost 10 cents, pigs cost $2, and sheep
cost $5, how many of each animal must you purchase so that the total
is 100 animals for $100?
THE CHART: There should be five
(5) column headings to represent the problem components. You might
want to add a few more to make the students check to see which direction
they need to make their "guesses".
CHICKENS (.10)PIGS ($2)SHEEP ($5)100
ANIMALS?$100
CHICKENS: 35 ($3.50)
PIGS: 40 ($80)
SHEEP: 25 ($125)
100 ANIMALS?: YES
$100: NO ($208.50)
CHICKENS: 50 ($5)
PIGS: 35 ($70)
SHEEP: 15 ($75)
100 ANIMALS?: YES
$100: NO ($150)
TEACHER NOTE: These two lines
represent a wealth of information. In addition to each column beginning
to show a potential pattern of direction for future guesses, a viewer
should be able to see the plan I am using. Also, what possibilities
have already been eliminated? What other possibilities can be eliminated
as a result? If your students become frustrated with their own attempts,
you might consider using these two lines (or your own) to help them
get back on track.
THE SOLUTION: Do you really
want me to tell you? Okay, I'll meet you half way. The number of chickens
is a multiple of 10 (Why must this be so?). It is not 50 chickens.
The number of pigs feet is almost = the number of chickens. There are
less sheep than the other two animals (approximately 1/7 of chickens
and 1/2 of pigs).
submitted by
ROB SCHUCK
PACOIMA MIDDLE SCHOOL
LOS ANGELES, CA
rschuck@glendale.edu

