Guide Index If Only They Could Talk! Who Needs Words, Anyway? Number Crunchers Figure That One Out No Fools About Tools Thinking About Thinking Viewer Challenge

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.

National Science Education Standards
Related Frontiers Show and Activity
Activity: M&M Math
Extensions

 BIOLOGY/LIFE SCIENCE primates MATH binary numbers PSYCHOLOGY learning

NATIONAL SCIENCE EDUCATION STANDARDS

 SCIENCE AS INQUIRY / LIFE SCIENCE 5-8: Structure and Function in Living Systems, Reproduction and Heredity, Regulation and Behavior, Diversity and Adaptations of Organisms 9-12: Biological Evolution, Behavior of Organisms
 HISTORY AND NATURE OF SCIENCE 5-8: Science as a Human Endeavor, Nature of Science 9-12: 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:
1. Place an M&M in the 1 column. In expanded notation, this would be expressed as (1 x 1) = 1.

2. Clear off the 1 column. Place an M&M in the 2 column: (1 x 2) + (0 x 1) = 2.

3. Add an M&M to the 1 column: (1 x 2) + (1 x 1) = 3.

4. Clear off all M&Ms and place an M&M in the 4 column: (1 x 4) + (0 x 2) + (0 x 1) = 4.

5. 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

1. 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?

2. Do you think the rhesus monkeys seen on Frontiers are really counting the apple pieces? Explain.

3. 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?