The Exponential Clothesline

Many students have difficulty
expressing large numbers using
exponential notation . The exponential
clothesline helps to pre -assess student
understanding of exponents by
providing a visual representation of
exponential notation ( powers of ten ).
The Exponential Clothesline
Conversion Table will also pre -assess
and refresh student understanding of
fractions and decimals .

Provide each group of students with the following materials:

One 5-meter piece of clothesline (or string)
Fourteen (14) clothespins (or paper clips)
Fourteen (14) index cards with the following numbers identified as follows:
0 written in red,

1, 2, and 3, in blue,
and 10¹² in green,
and 10^-4 in black

Numbers written in black on different colored index cards are more visual, and any
incorrectly placed numbers are immediately recognizable in a large classroom. The
Number and Exponent Cards described above are also available in pdf format for you to
download.

Depending on your group, you may wish to provide some larger (or smaller) exponents
or include a set of numbers with exponents such as and 2 x 10^-2.

Give each group of students the clothesline, clothes pins, and a set of numbered index
cards. Randomly distribute the cards as evenly as possible within each group. Have the
students string the clothesline, and ask the student in each group with the number 0 to
attach that index card approximately one-sixth of the way from the left end of the
clothesline. The Students with the number 1 should attach it 25-cm to the right of the
number 0.

Explain to the students that their clothesline represents a number line and that they are
going to add whole numbers and numbers expressed in scientific notation to the number
line. Ask the students who have numbers 2 and 3 in each group to place their numbers on
the clothesline. Most students will correctly place whole numbers on the number line.
Give the students the task of placing the remaining numbers on the number line in their
correct locations. [It is important to explain to your students that this number line is not
to scale.] Most groups will discuss and accurately place and 10¹²
and other higher powers of ten ; however when they begin to place the negative exponents
on the clothesline, most students will place them to the left of 0, which is a common
mistake.

The negative exponents actually fall between 0 and 1. Encourage the
students to make changes if they think any of the numbers are not in the
correct order . If any of the groups think that their number lines are
correct and there are still numbers placed out of sequence, hand out the
Exponential Clothesline Conversion Table. The purpose of the
conversions is to express the exponents as whole numbers, fractions and
decimals . After the final conversion of the exponents to decimals,
students who have the negative exponents incorrectly placed usually
begin to see that negative exponents are still greater than 0 and rearrange
their number lines accordingly.

Use the completed Exponential Clothesline Conversion Table to enter
into a discussion about what scientific notation is and why it is useful.