Estimation Contest

Sandra A. King-Bryson          Saucedo Magnet School
                               2850 W. 24th. Blvd.
                               Chicago, Il. 60623
                               (312) 534-1770

Objective:

Students will gain a more concrete understanding of the subtle difference 
between a guess and an estimate. 

Materials Needed:

Large box of Cheerios or other similar cereal
32 oz. or 48 oz. container (translucent or transparent)
Cups for each student or group of students (an odd size cup will offer the 
  greatest challenge, i.e. 6.8 oz. or 7 oz.)
Paper plates
Paper and pencil

Strategy:

Estimation is a powerful mathematical idea to be used both in solving problems 
and in checking the reasonableness of results.  When the student wants to know 
about how long it will take to earn enough babysitting money to buy a new 
bicycle he or she can estimate the answer.  Estimation should be used to solve 
problems for which exact answers are inappropriate and to check computation 
results.

We all make estimates everyday.  How long will it take you to walk to school, 
how much food should I put on my plate for dinner, how many times will Mother 
call me before she comes to look for me, etc.?

The Estimation Contest is a fun and easy way to allow the students to make 
"educated guesses".

1)  Fill the large container (32 or 48 oz.) with the Cheerios or similar cereal.  
    Try to use only whole pieces, not broken ones.  Count the number of pieces.
    
2)  Write the number of pieces and put this information in a safe place.  (Do 
    not put this information on the container).

3)  Give each child, or group, a paper plate, a cup, paper and pencil.  Tell the 
    students the capacity of the cup (7 oz., 8 oz., etc.).  Tell the capacity of 
    the large container.

4)  Give each child more than enough cereal bits to fill their cup.

5)  Ask students to estimate the number of cereal bits in the large container.  
    They may use whatever measuring devices they think will help them get the 
    best estimate.


Example:   You have a 48 oz. container filled with Cheerios and the students are 
           given a 6 oz. cup:
           
       VOLUME OF CONTAINER = number of 6oz. cups required to fill the
          VOLUME OF CUP      large container

       Therefore: 48 oz. = # of 6oz. cups required to fill large container
                   6 oz.
                               The number would be 8
            
       8 cups X 223 cereal bits in a cup = 1,784 cereal bits in the 48 oz.
                                           container

Questions:

1.  How could you make your estimate more accurate?

2.  Given a weighing apparatus, could you estimate the weight of the cereal bits 
    in the large container?

Extension:

Show children the difference between a guess and an estimate.  Set up several 
guessing stations in your classroom.  One might be guessing the length of a 
piece of rope, another might be guessing the amount of popcorn kernels in a 
container, another might be guessing the amount of liquid in a container, etc.  
Point out to the students that when they guess they really aren't basing the 
guess on any factual information.  Explain that an estimate is based on some 
amount of knowledge or facts that can be obtained. 

Acknowledgements:

M. Matyas and J. Combs, "Proyecto Futuro". American Association for the 
Advancement of Science (AAAS).