



Animal Einsteins: Number Crunchers 
Throughout much of human history, it's been assumed that the use of numbers is unique to people. Recent studies have cast doubt on that assumption, however, as animal behaviorists like the ones seen on this show demonstrate that primates can manipulate numbers. Watch as rhesus monkeys test their math skills and a chimpanzee works with fractions.
Curriculum Links
National Science Education Standards
Related Frontiers Show and Activity
Activity: M&M Math
Extensions
Answers
CURRICULUM LINKS
BIOLOGY/ LIFE SCIENCE
primates 
MATH
binary numbers 
PSYCHOLOGY
learning 
NATIONAL SCIENCE EDUCATION STANDARDS
SCIENCE AS INQUIRY / LIFE SCIENCE 
58: 
Structure and Function in Living Systems, Reproduction and Heredity, Regulation and Behavior, Diversity and Adaptations of Organisms 
912: 
Biological Evolution, Behavior of Organisms 
HISTORY AND NATURE OF SCIENCE 
58: 
Science as a Human Endeavor, Nature of Science 
912: 
Science as a Human Endeavor, Nature of Scientific Knowledge 
RELATED FRONTIERS SHOW AND ACTIVITY
ACTIVITY: M&M MATH
Numbers play a significant role in human communication. We humans use a base 10 (decimal) system of numbers that is presumed to have originated because we have 10 fingers and 10 toes. In this system, place values are expressed in powers of 10. Other cultures in history developed various counting systems using other bases. The early Mayans used a base 20 system; ancient Romans used a base 12 system.
Computers use a language called the binary system. Only the numbers zero and one are used to signify a switch being turned off or on. In a binary system, place values are expressed in powers of two. In this activity, you'll use a model to understand the binary counting system.
MATERIALS
 paper
 pencil
 M&Ms candy (or other small items)
PROCEDURE
In a decimal system, you multiply by 10 for each place you move to the left of the decimal point. To visualize the decimal system, create a chart four columns wide. Label the columns with place values from left to right as follows: 1000, 100, 10 and 1. You'll use M&Ms or other small placeholders to help you count. To represent the number 1412, place one M&M placeholder in the 1000 column, four M&Ms in the 100 column, One M&M in the 10 column and two M&Ms in the 1 column. You can use your chart to help write out the number in expanded notation: (1 x 1000) + (4 x 100) + (1 x 10) + (2 x 1) = 1412
Counting in the binary system is a little more challenging, because this system uses only two numbers: zero and one. To visualize this system, make a chart seven columns wide, as shown here:
Label the columns with place values in powers of two, from left to right: 64, 32, 16, 8, 4, 2 and 1. Draw one circle in each column as shown. In this model, like in the decimal model, your M&M placeholder indicates the number one; an empty space represents zero. To count from one to five, express numbers as follows:
 Place an M&M in the 1 column. In expanded notation, this would be expressed as (1 x 1) = 1.
 Clear off the 1 column. Place an M&M in the 2 column: (1 x 2) + (0 x 1) = 2.
 Add an M&M to the 1 column: (1 x 2) + (1 x 1) = 3.
 Clear off all M&Ms and place an M&M in the 4 column: (1 x 4) + (0 x 2) + (0 x 1) = 4.
 Add an M&M to the 1 column: (1 x 4) + (0 x 2) + (1 x 1) = 5.
Using your chart, figure out how to finish counting to 10 and write the answers on your paper, using both expanded notation and binary numbers. What base 10 number is represented by the base 2 (binary) number 10101, as shown below?
To find the answer, use expanded notation:
(1 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (1 x 1) = 21
What base 10 numbers are represented by the base 2 numbers 1100, 1110, 11011, 100101, 1010101? What's the highest base 10 number you can express using the binary number chart above?
QUESTIONS
 The decimal (base 10) system is believed to have originated because humans have 10 fingers and 10 toes. What base system might a giraffe use? What about a chimpanzee? If nonhuman animals possess a sense of math, do you think they count the same way we do?
 Do you think the rhesus monkeys seen on Frontiers are really counting the apple pieces? Explain.
 It's been said that crows can count hunters in a field, and are able to distinguish between four and five hunters. How would you design an experiment to test this?
EXTENSIONS
 Create a way to use binary numbers to represent the alphabet. Send a coded message to a friend.
 Find out more about the Mayan and Roman base systems. Why do you think they developed as they did?
ANSWERS
Click here to see the answers.




Scientific American Frontiers
Fall 1990 to Spring 2000
Sponsored by GTE Corporation,
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