ESTIMATION INVESTIGATION
Grades 4-6
In this lesson and its extension activities, students will
explore
the concept of estimation. The lesson integrates viewing sequences and
hands-on
investigations to help the students solve problems involving estimation.
Opportunities are provided which allow students to investigate various
strategies
for arriving at an estimate. Students will work cooperatively to measure,
make comparisons, make predictions, and verify results. This
investigation
may be done in one lesson or it may be divided into two sessions as time
dictates.
The Eddie Files # 102: Estimation: Going to the
Dogs
Students will be able to:
1. give an operational definition of "estimation" .
2. identify situations in which estimation is appropriate.
3. apply a variety of strategies in order to solve problems involving
estimation.
4. explain the process used to arrive at an estimate.
5. name ways estimation is used in various careers.
6. evaluate the importance of estimation.
Texas Assessment of Academic Skills (TAAS, Grade 4
Science Objectives:
#6: Identify a problem, formulate a hypothesis, design and conduct a
scientific
investigation.
#8: Related and/or apply scientific and technological information to
daily
life.
Math Objectives:
#8: Use multiplication to solve problems.
#10: Estimate solutions to a problem situation.
#11: Determine solution strategies and analyze or solve problems.
#13: Evaluate reasonableness of a solution.
NCTM Standards for Grades K-4:
Standard 1: Mathematics as Problem Solving
Standard 4: Mathematical Connections
Standard 5: Estimation
Standard 11: Statistics and Probability
NCTM Standards for Grades 5-8:
Standard 7: Computation and Estimation
Per class:
- 1 pound of peanuts (in the shell) in a clear bag
- 1 quart jar filled with jellybeans
- various measuring cups (1/2 cup; 1 cup; 1/4 cup, 2 cup, etc.)
- 1 teacher-made poster giving equivalent measurements (to be posted
in the room)
- 2 sticks of modeling clay
- 4 popsicle sticks
- 11 yards of yarn
- dried lima beans (100)
- unpopped popcorn (1 cup-approximately 1300-1800 kernels/cup)
Per group of 4-5 students:
- disposable cup (5 oz. paper cups work well)
- 1/2 cup of jellybeans
- 3x5" index cards (one per student)
- estimate/estimation
- reasonable
- pint
- quart
- benchmark
To introduce the concept of estimation, hold up a bag
containing
one pound of peanuts in their shells. Say, "The cafeteria has asked
us to help with a problem. They would like to sell peanuts during lunch
as an extra snack. They can buy the peanuts in one pound bags, but they
need to separate them into smaller bags before they sell them. The
cafeteria
manager has asked us to tell her how many peanuts are in a one pound bag,
so she can decide how many to put in each smaller bag. Take a close look
at this bag, and tell me how many peanuts you think are in it. (Allow
students
time to respond.) What are some of the things you did in order to arrive
at the number you gave me? (Allow response time, accepting all estimates
that the students can justify.) What would have made your job easier? (to
get a closer look at the bag, to have some method for establishing a
benchmark
by which to then arrive at an estimate) If everyone works together to
help
count, we can find out if our answers are close."
Have the students work in groups of 4 or 5. Use a 1/2 cup measure, and
give
each group 1/2 cup of the peanuts. Allow time for each group to count
their
peanuts. Ask them to choose one member of their group to record their
number
on the chalkboard. After each group has recorded its number, add to get
the total number of peanuts.
Ask, "Would every one pound bag of peanuts contain the same number
that ours did? (no) What could we do to be more certain of our answer?"
(count several bags) [Note: You may want to allow your students to eat
the
peanuts, or you may collect them and re-bag them.]
To give students a specific responsibility while viewing the
video, say, "We are going to go with a student named Eddie as he enters
his math class. Today his teacher, Ms. Tolliver, is giving a lesson on
estimation.
If you listen carefully, you should be able to discover what "estimation"
really means. Watch to see what strategies the students use in order to
try and solve a problem. After math class is over, we will follow Eddie
as he works on a homework problem. Watch to see how the people he
encounters
use estimation in their jobs."
BEGIN the video with the title screen on which you see
"Eddie Files". PAUSE after you hear Eddie say, "Maybe
he could have helped me with my assignment in Ms. Tolliver's class."
You see a chalkboard on which is written "What do you think this means?"
followed by a series of symbols. Say, "Look at this sign carefully
and remember it. As we watch this video, see if you can find out how this
fits with the problem Ms. Tolliver's class has been asked to solve."
RESUME the video.
PAUSE when you hear Eddie say, "What a way to start a math class,"
and you see a full picture of the container of cat biscuits. Ask, "Can
you think of some ways you might approach this problem?" Allow time
for students to respond. Accept all reasonable responses. "Let's listen
to the students as they give their estimates." RESUME video.
PAUSE when you hear the students giving their estimates and the
final
student says, "Twenty million." Ask, "What estimates did
you hear the students give? (100,000; 10,000; 80,000; 20,000,000) What
was
the lowest estimate? (10,000) What was the highest? (20,000,000) Why do
you think there was such a wide range? What could the students do to get
a better estimate? Watch and listen to some of the techniques Ms.
Tolliver's
students use." RESUME the video.
PAUSE when you hear Eddie say, "In our own round about way,
we finally came up with some pretty good estimates." Ask, "What
techniques did the students use? (group counting, high tech, little bin
in big bin) Now that they've taken a closer look at the problem, do you
think their estimates will be more accurate? Let's see what estimates
they
came up with." RESUME video.
PAUSE when you hear Ms. Tolliver say, "All this time you've
had the answer right in front of you." Ask, "What estimates did
Ms. Tolliver's students give this time? (2,760; 1,000; 3,000) What is our
range this time? (between 1,000 and 3,000) Ms. Tolliver said that the
answer
was right in front of the students. Where do you think the answer has
been?
Let's find out how many cat biscuits were actually in that bin."
RESUME
video.
STOP after you hear Eddie say, "We learned a lot about estimation
that I never knew before. But it wasn't over yet."
Say, "You are now going to practice estimating just as Ms. Tolliver's
students did. Instead of estimating cat biscuits, however, you will look
at this jar and try to tell me how many jellybeans I have placed in it.
I will tell you that this is a quart jar. Ms. Tolliver gave her students
some smaller containers to help with the problem, so here are some
smaller
containers of jellybeans that might help you. I also have placed some
measuring
cups at the work station if you need to use them in any way. Let me give
you one other word of advice. Do you remember that Ms. Tolliver had the
answer posted right in front of the students? Well, I don't have the
answer,
but I do have information posted in the room that will give you the help
you need."
On a work station in the room, have several measuring cups so that
students
have a standard with which to work. Also have posted the teacher-made
poster
which gives equivalent measurements for ounces, pints and quarts. Give
the
students time to work with the materials and arrive at an estimate. Have
students share their estimates.
Say, "Ms. Tolliver is going to give assignments to some of the students
in her class. Watch and find out what those assignments are."
BEGIN
the video.
PAUSE when you hear, "And Eddie, you have to find out how many
dogs we have in New York City." Ask, "What were the assignments
given by Ms. Tolliver? (how many sneakers, how many apartments, how many
dogs in New York City) What do you know about New York City? It's a very
large city. There are approximately seven million people living there. Do
you think Eddie's job will be an easy one? How would you go about working
on this assignment? Watch to see some of the problems Eddie faces with
his
assignment and what he does to try and solve these problems."
RESUME
video.
PAUSE when you see the store with the sign "Professional Photo
Supply" and you hear Eddie say, "So, I stopped by Vincent's to
get some film and some advice." Ask, "What problems has Eddie
encountered? (dogs everywhere, unable to count each one) Eddie may need
to get some help from experts. Watch to see what advice Vincent gives."
RESUME video.
PAUSE when Vincent leans forward and says, "I wouldn't be much
help to you with the dogs, anyway - I'm a cat person." Ask, "What
advice did Vincent give Eddie? (It's not practical to count large
numbers.
Estimate.) What examples did he give of instances where estimation was
necessary?
(headlines about subway commuters; astronomers counting stars; the number
of raisins in Raisin Bran; the amount of water in the Hudson River) What
did Vincent say estimation was?" (Take what you know and make a smart
guess.)
Say, "Next Eddie will visit a veterinarian. How do you think a
veterinarian
uses estimation? Let's watch and find out." RESUME video.
PAUSE when you hear Eddie say, "I've got a whole file on people
who work with animals and Dr. Dendtler, she's right at the top." Ask,
"How did Dr. Dendtler use estimation? (scheduling; how many pets she
can see in a given amount of time; ordering medications)
Say, "Next Eddie will visit Jan Dietrick. She has an unusual job. Watch
to find out what her job is and how she uses estimation." RESUME
video.
PAUSE after Jan Dietrick says, "Everything I've learned has
helped me do what I want to do now..." and you see squirming larvae.
Ask, "What is Jan Dietrich's job? Now turn to your neighbor and discuss
the ways Dietrich used estimation."
While the students are discussing the last segment of the video with
their
partner, FAST FORWARD and PAUSE the video after you see an
evening picture of bats in flight followed by Eddie's desktop covered
with
photographs. Say, "What did you and your partner believe to be some
of the ways Jan Dietrich used estimation? (one room contains millions and
millions of bugs; one sheet contained approximately 100,000 wasp eggs;
one
gallon contains about 72,000 ladybugs) Let's see how Ms. Tolliver's
students
completed their week-end assignments. Do you remember how many people I
said made their homes in New York City? (7 million) Remember that Brandon
was to estimate how many sneakers were in New York City. How many would
you estimate? How would you go about arriving at an estimate? Eddie was
to find out how many dogs lived in the city. How many would you estimate?
What strategy would you use to get that estimate? Let's watch to find out
their answers and how they got their estimate." RESUME the
video.
STOP the video after you hear Ms. Tolliver say, "Great Eddie.
Three hundred thousand. That's a wonderful estimate." Ask, "How
close were you to the number Brandon and Eddie gave? What information did
they have that we didn't have?" (Each had a sample to base his answer
on.)
Select an area for the post-viewing activity, and prepare the
"park" area before presenting the following scenario to the class.
It should be an area that is not likely to be disturbed, and it should be
an area where there is little ground cover. The parking lot, a bare spot
on the playground, or a little used hall inside the building work well.
Mark off an area that is six feet wide and ten feet long. "Rope"
off the area by placing half a stick of modeling clay at each corner.
Insert
a popsicle stick into the clay, and string the yarn from stick to stick
to create a fence around the perimeter. Use 100 lima beans to represent
the cougars and 1 cup of popcorn kernels (between 1300 and 1800 is a good
range) to represent the rabbits. Spread the beans and popcorn evenly over
the "park" area. You may wish to prepare some signs designating
this as "Big Bend National Park" to add to the activity. Each
student will need a 3" x 5" index card upon which to record the
solution to the problem in this activity.
Upon completion of The Eddie Files video, say, "You've seen the way
two people use estimation in their jobs. Now, I've got a job for you. The
National Park Service has just hired you to help solve a problem. There
is a large area in south Texas called Big Bend National Park. The park
has
had quite a bit of rain this past year. Because of that, the grass is
green
and the rabbit population has increased dramatically. Because food is so
plentiful, the cougars that live in the mountains of the park and
surrounding
mountains have been thriving. The Park Service is concerned that the
large
cougar population might become a danger to the people who enjoy the park.
They would like for you to investigate this situation and help them
decide
if they need to trap some of the cougars and move them to more isolated
areas where they won't endanger humans. If they move the cougars,
however,
what will happen to the rabbit population? (Their numbers will increase.)
They will have no predator to control their numbers."
"You will work in teams of three to estimate the number of rabbits
and the number of cougars in the park area. In order to do this, we will
need to travel to the park. So, if you will follow me, I will help with
the transportation."
Take the students to the area marked off as the "park". Explain
that the lima beans represent the cougars in the park, while the popcorn
kernels represent the rabbits. Give each team time to devise a strategy
and complete an estimate. Have each student record their estimates on a
3 x 5 card and post them on the chalkboard upon re-entering the
classroom.
Discuss the results. Some questions for discussion might be: "Which
animal population was easiest to estimate? Why? (Students will come
closer
to an agreement on the cougar population, and have a wider range for the
rabbit population.) What is our lowest estimate? What is our highest
estimate?
Why didn't we agree? What kind of difficulties would real animals present
that we did not have with our pretend animals? Can we get a class average
of the number of cougars using the numbers each team gave? Can we get an
average for the rabbit population? Using our averages, how many rabbits
are there for every cougar?"
Have the students work in groups to write to the rangers at
Big Bend National Park to ask how they would handle a problem such as the
one the students were faced with in the simulation. Also have the
students
ask how the rangers arrive at estimates for the numbers of animals in
their
park.
Superintendent
Big Bend National Park, Texas 79834
Other inquiries could be sent to the following: state parks and wildlife
agencies asking how they estimate animal and bird populations for given
areas; city animal control facilities to inquire about how estimates are
made regarding the number of stray animals in the city; car manufacturers
to ask how they estimate the number of automobiles they should produce
for
any given year; your local school district to find out how they estimate
the number of students who will attend school the next year; and/or your
public library to ask how they estimate the number of books they need to
purchase or replace each year.
Interview the school cafeteria manager to determine how she/he estimates
the amount of food to order for school lunches.
Have the students interview their parents to find out how they use
estimation
in their everyday lives.
Writing: Have the students open their reading book to a
specific
page. Have them estimate the number of e's they will find on that page.
Then, have the students write a "how-to paper describing the
process they used for arriving at their answer.
Reading: For one week, have the students search newspapers to find
headlines
in which an estimate is involved. Post the articles on a bulletin
board.
Math: On a sheet of paper, have them create the following chart.
Object My Estimate Actual Number
book shelves
light bulbs
windows
electrical outlets
pictures on the wall
chairs
tables
After creating the chart, have the students close their eyes and think
about
the rooms of their home. Have them record their estimates for the items
listed in the chart. For homework, they will count the items and list the
actual number they find. In class the next day, discuss their findings.
Was their estimate accurate? Were they over or under the actual number.
You may wish to create a graph to show the class total for the items
listed.
Science: Estimate how long it would take to walk to the moon. First have
the students use the library to find the distance from earth to the moon.
Then help students determine their walking speed. Time the students as
they
walk around a measured track, around a measured area of the playground,
or down a city block that has been measured. The students must also
decide
if they will determine the time of their walk based on continuous
walking,
or if they will take time to eat, sleep, rest. Have the students work in
teams to calculate the time it would take for their walk.
4 oz. = 1/2 cup
1 cup = 1/2 pint
1 pint = 1/2 quart
1995-1996 National Teacher Training Institute / Austin
Master Teacher: Gayle Evertson
Lesson Plan Database
NTTI
Thirteen Ed Online
wNetStation