# 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 10^{12} 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 10^{12}

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.

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