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.

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.
Standard 1: Mathematics as Problem Solving
Standard 4: Mathematical Connections
Standard 5: Estimation
Standard 11: Statistics and Probability

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

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