Teachers > Instructional Television > Lesson Plans > Divide and Conquer: Equivalent Fractions


How Close Can You Get? Estimating

Master Teacher: Susan Deese-Laurent
Subject: Science, Mathematics
Grades : E, M
Series: The Eddie Files: Episode 2 - Going to the Dogs
Math Talk Episode 15 - Close Enough - Estimating 


Pre-viewing Activities

Focus for Viewing

Viewing Activities

Post-viewing Activities

Action Plan





Image of Jar of CandyIn the following lesson, students take part in a number of real-life estimation activities. Initially, they work collaboratively to figure out how many crackers are in a large container. They learn about the process of chunking, or using a smaller unit to estimate larger amounts.

Then, they view a video and see how often people use estimation at their jobs. They watch Eddie visit a number of people who talk about how and when they use estimating. These people include a boy who is particularly interested in bats and how to insure the continuation of this species of animal.

While viewing a second video, students work on figuring out appropriate estimations to real-life problems posed on a mock talk show.


Learning Objectives

Students will be able to:

  • recognize when an estimate is appropriate.
  • determine the reasonableness of a solution.
  • list several examples of how estimation is used in real-life situations.
  • determine and record a plan for using estimation to figure out a large number problem.
  • demonstrate an understanding of how to use the process of "chunking" to make more accurate estimates for large numbers of objects.
  • describe the environment in which bats live.
  • list facts about bats, including information pertaining to their eating habits, population, how they help mankind, and body makeup.


  • large glass or plastic container to hold snack food, i.e., 10-gallon fish container
  • enough goldfish crackers (or other snack food) to fill the above container
  • 5 to 6 smaller square or rectangle-shaped containers, all same size
  • chart with Chinese Numerals recorded on it
  • calculators, 1 for each group of 2 to 3 students


Previewing Activities

Note to the teacher: You will not be showing the first part of the video, The Eddie Files #2, to the students. However, it would be beneficial to preview it yourself to get an idea on how the following previewing activity will work.

In order to introduce the concept of "chunking" to help estimate large numbers of objects, do the following activity with students prior to viewing the video. Tell students that you would like to share a snack with them today; however, you have a problem to solve first. Show them a large container, i.e., a glass container such as a 10-gallon fish tank, filled with goldfish crackers (or other type of snack food; size to be determined by your students' ages and number sense). Tell them that you want to give everyone approximately the same number of crackers, but to do this, they need to figure out about how many crackers are in the container.

Have up on the board the number in Chinese Numerals that tells how many crackers are actually in the container. Post a chart of the Chinese Numerals (see Appendix #1) so students can later figure out what the large number is.

Ask students to give you estimates on how many crackers they think are in the container. Record their estimates on a chart, without names, and ask questions such as the following:

  • Which estimate is the greatest number? The least?
  • Can somebody read this number?
  • How many more than this estimate is this one?
  • Is this estimate an even or odd number? How do you know?
  • What would you get if you added this estimate and this one?
  • Would anyone like to explain how they came up with their estimate?
Discuss with students why it was perhaps difficult to come up with a close estimate for how many crackers are in the container. (Nothing to gauge their estimates toward).

Hand out one small container to each group of 4 students and ask them to use these containers in some way to come up with a more accurate estimate. Have students think about this and begin working. When a group comes up with the idea of using the smaller container as a gauge and counting how many crackers it will hold, have them share this idea with the whole group. This is using the idea of "chunking" to make more accurate estimations with large numbers of items. After students have figured out more accurate estimations, tell them the actual number of crackers has been up on the board the whole time; but they have to figure it out using the Chinese Numerals posted on the chart (see Appendix #3).

Discuss the process of using "chunking" and how it helped them.


Focus for Viewing

To give students a specific responsibility while viewing parts of The Eddie Files , have them pay particular attention to how people in different careers use estimating to come up with information needed to do their jobs.

Tell students that in a second video, Math Talk, #15: Close Enough - Estimating, they will be given an opportunity to use some of the strategies they see in the first video to figure out accurate estimations to real-life problems.


Viewing Activities

Fast forward The Eddie Files , #2 video to just after the part when Ms. Tolivar tells her students that there are 4,263 cat biscuits in the container. Start video where she tells them they are going to have weekend work.

Pause video after Ms. Tolivar says to Eddie, "And Eddie, you have to figure out how many doooooogs there are in New York City." Ask students for ideas as to how they might figure out how many dogs there are in New York City.

Resume video. You will see Eddie using tally marks to try and figure out how many dogs there are in New York City.

Pause video after Eddie says, "And people talking about dogs." Ask students what they think about this method. Will it work? Why or why not?

Resume video. The scene is now at Vincent's camera shop.

Pause video after Vincent states, "Of course not...he doesn't have time for that!" Ask students how they think the major figured that out. Discuss their strategy ideas. Then say, "Let's see what else Vincent has to say."

Resume video up to the part where the woman veterinarian is shown.

Pause video after Eddie says, " Anyway, she has her own clinic in Brooklyn." Ask students to predict ways in which a veterinarian might use estimating (scheduling appointments as to how many animals they can see in a day, ordering medicines).

Resume video and see the remainder of the section on the veterinarian and on into the part about John and his work with bikes.

Pause video right after John ends by saying, "Why don't you hand me that wrench over there while I kill these bugs." Tell students they'll now see how Jan, a bug grower and researcher, uses estimation often in her work. Have them pay attention to why she needs to estimate.

Resume video and see Jan explain her work using tiny wasps to kill bugs that are harmful to plants and people.

Pause video when Eddie closes his file on bugs and says, "Don't study bug file before dinner," and have students share ideas about how and why Jan used estimation in her work.

Resume video and see a section on bats and estimation.

Pause video after bat section is over (Eddie shows a photograph of the boy who studies bats) and ask students to restate why the boy was interested in finding out how many bats were in the cave (to make sure the species does not become extinct). Discuss with students why his strategy was a good one (or not such a good one).

Resume video and see section where Eddie is still counting dogs and having nightmares. The setting returns to Ms. Tolivar's classroom.

Pause video after Ms. Tolivar says, "Eddie...I'd like you to tell us..how did you come up with the number of dogs in NYC." Ask students if they have any ideas as to how Eddie came up with his estimation and what the number might be. Optional: This would be an excellent time to stop the video and have students write in a journal explaining their ideas. Have students share what they wrote prior to resuming video.

Resume video to hear Eddie share his estimation and how he went about getting the number of 350,000 dogs. (Eddie's figuring went like this: 1 dog for every 20 people, 7 million people = population of NYC, 7 million divided by 20 = 350,000 dogs)

Stop video when Eddie says (at the end), "I have a feeling tomorrow is going to be a big day."'

Note to teacher: Prior to the lesson, fast forward the Math Talk, #15 video to the place after the explanation by the parrot of how the two boys figured out how much paint to purchase. (You may wish to show that part of the video at another time; it includes a neat rap song and real-life example of estimating). It will be at the place where the "Close Call" show begins and the cartoon lady says, "Here's a game from Square 1 TV called "Close Call"....it's also about estimation."

Explain to the students that they will be working in pairs, or small groups, to figure out some estimating problems that kids are solving on the video. (Make calculators available if you think it is appropriate for your students.) There are three real-life estimating problems presented on the video. You can set up a contest situation, as they do on the video, where students receive points for answers depending on how close they are to the actual answer. If this does not fit your classroom practices, students can work each problem and then share strategies and answers with no points attached.

Start video where a man is reading a paragraph from an enlarged book. He presents a problem for students to work on that involves figuring out how many letters there are on a whole page of a book given only the information that there are 173 letters in the first paragraph and 35 lines of type on the page.

Pause video when the man says, "I'm Arthur Howard and now I'd like to introduce my co-host Louisa Lashin." Have students use the information presented to come up with accurate estimations. While they are working, fast forward video to where you see the two hosts walking over to an orange juice stand.

Stop video. Once all groups have their estimates, allow time for them to share strategies and answers. Then tell students that the actual number of letters on the page was 1,540 and see how close their estimates were. (Assign points depending on how close answers were, if you are following this format).

Resume video to see the second problem about oranges and juice.

Pause video right after answer to the problem. As students are working, fast forward video to where the two hosts are reading a card with the third problem on it (right before the picture flashes to the baby chicks). Follow the same procedure as above with students. (The closest estimate given on the video was 395 oranges).

Resume video for third and last problem. (There are 11 chicks inside the small square, so how many are inside the entire pen?)

Pause video after the problem is stated. Have students begin working as before. As they work, fast forward video to where the two hosts are looking at a card again and the screen flashes back to the chicks.

Stop video. After students have worked out their estimates, shared, and discussed strategies, resume video to show the hosts presenting the answer of 141 baby chicks being in the pen. Stop video.


Post-viewing Activities

As a follow-up to the section on bats, have students conduct research on these mammals. Write to the following organization for information about bats:
Bat Conservation International
P.O. Box 162603
Austin, TX 78716


Action Plan

Create a survey for students in another class, designed to find out what they do to help animals in their yard or neighborhood survive during the winter. For example: Do they have such things as bird feeders, suet bags, or peanut butter pine cone feeders? 

Write a letter to an animal activist group who works to protect natural habitats. 

Find out about homeless shelters in your community. Make a cassette tape of students reading pertinent holiday poetry, short stories or original writings. Offer the tape to the shelter as a "human" connection to the survival theme.



Create an estimation corner in the classroom where you put out, on a regular basis, different objects for students to estimate. Use a same-sized container, such as a gallon jug, in which to put various- sized objects on different days. Keep a chart that lists what the objects were, the high and low estimates, and the actual amount; this gives students a point of reference for making more accurate estimations.

Have students create real-life problems where estimation is needed to figure out a solution. Have them solve each others' problems.

Social Studies:
Tell students that people who manage cities often need to use estimation when figuring out answers to questions like, "How many people travel to work on a train or a bus each day?" Have students think of a problem they might have to find a solution to if they were the mayor of a city. After recording their problems, have them solve them by coming up with a plan. Then, have students write a report to present to the class, including the solution and how they arrived at their accurate estimation. An example might be, "Think of a way you could estimate the total number of people who drive their own car, i.e. they do not car pool to work each day."



Additional Video Resources
NatureWorks - Episode 5. Migration

Print Resources
Clement, Rod. Counting On Frank. Milwaukee: Gareth Stevens Publishing, 1991.

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: The Council, 1989.

Schwartz, David M. If You Made A Million. Scholastic, Inc.: New York, 1989.
How Much Is A Million? Scholastic, Inc.: New York, 1985.

Stenmark, Jean Kerr. Family Math . Regents, University of California, 1986.

Wells, Robert E. Is A Blue Whale The Biggest Thing There Is? Albert Whitman & Co.: Illinois, 1993.


NH Framework Correlations

3a. Curriculum Standard: Students will demonstrate an increasing ability to recognize patterns and products of evolution, including genetic variation, specialization, adaptation, and natural selection.
3b. Curriculum Standard: Students will demonstrate an increasing ability to understand how environmental factors affect all living systems (i.e. individuals, community, biome, the biosphere) as well as species to species interactions.
3d. Curriculum Standard: Students will demonstrate an increasing ability to understand fundamental structures, functions, and mechanisms of inheritance found in microorganisms, fungi, protists, plants, and animals.

1a. Curriculum Standard: Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content.