Power Up: Using
Review decimal notation by logging onto the Converting
fractions to decimals
website. Provide students with a FOCUS FOR MEDIA
INTERACTION by asking students to determine which numerical place they might
find the number 8 in the number 432.567108? (The eight would be found
in the millionths place in the preceding number. Explain to students that
the term decimal has as its root dec- which means ten. Explain to students
that decimal notation is a base-10 system that changes numbers either by
multiplying or dividing by factors of 10.)
Check for student understanding by asking students to determine which number
is found in each of the remaining numerical place"holders".
(Each integer has an associated value based on the number 10; the 4
is in the 100s place. The 3 is in the 10s place. The 2 is in the ones place;
the 5 in the tenths place, the 6 in the hundredths place, the 7 in the thousandths
place, the 1 in the ten-thousandths place, the 0 is in the hundred-thousandths
place and the 8 in the millionths place).
Create a number line. On a large writing space draw a horizontal line with
arrowheads on each end similar to the one shown below. At the midpoint of
the line, mark a point for zero. At equal intervals to the right of the
zero, add additional points. At equal intervals to the left of the zero,
add additional points.
students to identify the placement of each of the following integers on
the number line: -3, -2, -1, 1, 2, 3. (The negative integers should
be placed to the left of the zero place with the –1 closest to 0,
followed by –2 and –3. The positive integers should be placed
to the right of the zero with 1 closest to the o, followed by 2 and 3.)
Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to recall
from the previous website the"place value" of the zero on the
number line shown. (Explain to students that the number line system
is a model for using numbers. When combined with the concepts associated
with decimals—base-10 numbers—the number line becomes an important
frame of reference for different models in mathematics.)
Provide students with additional practice by providing real-life examples
of positive and negative integers. Ask them to consider on which side of
the zero they might find a variety of different numbers.
| Real-life examples of negative numbers
||Overpayment: Customer paid over total amount due
||Checking account: Account deficient by $2.75
|| -5° C
||Temperature is 5 degrees below 0°C
||Incline grade -9
||Exercise machine is simulating the action of walking
down a hill with a 9% decline (about 16°)
Identify a rationale for using other ways besides decimals to express numbers.
Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to record
the distance between Earth and the Sun. LOG onto The Zany World of Basic
Math, Module 6: Working with Decimals; segment 6,"Scientific Notation"
(prior registration required). Click on the streaming icon
for high-speed playback
connection speeds. PLAY the segment by clicking on the triangular radio
button located under the screen. PAUSE the segment using the radio button
left of the play button when the narrator states the distance between Earth
and the Sun. You will see a blue screen with an arrow between an Earth icon
and a Sun icon. Write the answer on a large instructional writing space.
(The distance between Earth and the Sun is approximately 144 billion meters.)
Ask a student to place an asterisk (*) after the ones place in the number
144 billion (144 000 000 000) on the large instructional writing space.
(1*44 000 000 000)
. Distribute the"Number line paradigm"
handout. Ask students to describe how the asterisk and the zero are similar.
Ask students to write an example for each number type shown on the handout.
(Answers will vary but an example of a negative number is –35
(a negative number is a number less than zero); an example of a negative
number with a magnitude less than 1 is –0.005; a positive number with
a magnitude less than 0.005; a positive number with a magnitude greater
than 1 is 927.)
Discover scientific notation. Provide students with a FOCUS FOR MEDIA INTERACTION
by asking them to define scientific notation. PLAY segment from the beginning
by clicking on the solid square then by clicking on the triangular radio
button under the screen. PAUSE segment when the image of Earth and the Sun
appears on the screen. (Scientific notation is a power of ten system
where a very large or very small number is represented by a number between
1 and 9.999 multiplied by 10 expressed to an integral power.)
On the large instructional writing space, write down the three parts of
any number expressed in scientific notation:
between 1 and 9.999 which represents the
magnitude of a number
, always 10
(Power of 10); if the actual value of the number
has a magnitude greater than 1, the power of ten is positive. If the actual
value of the number has a magnitude less than 1, the power of ten is negative.
FAST FORWARD the downloaded segment to the"Amnesia Alert" (2:01-2:15).
Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to complete
the statement:"To use scientific notation for large numbers the exponent
…" (The number is positive.)
: Identify additional contexts for scientific notation. Provide students
with a FOCUS FOR MEDIA INTERACTION by asking them to identify at least two
uses of scientific notation in real life calculations. LOG onto the Institute
for Energy and Environmental Research
website. (On the site there
are several examples of use of scientific notation: reporting volumes of
radioactive waste—note the magnitudes of the numbers are represented
in the last column; size of atomic particles, astronomical distances.)
Check for student understanding by asking them to name the three parts of
a number written in scientific notation. (Coefficient between 1 and
9.999, a multiplier which is always 10 and an exponent/power on the ten
which determines the number of spaces moved and the direction in which a
decimal is moved to represent the actual value of a number.)
students with a FOCUS FOR MEDIA INTERACTION by asking them to review the
information provided on the Institute
for Energy and Environmental Research
Divide class into four large groups. Distribute the"Working
" handout and advise students to record their responses
at station III on a separate sheet of paper for collection and review. All
students will circulate through all four groups round-robin style. Give
each group 7 minutes at each station. Ask students to record their web-based
scores from stations I and IV on their answer sheet with their other responses.
Circulate around the room to check for student understanding and to monitor
Widener University: Scientific notation Decimal notation conversion
"Working with Decimals" handout (pages 3 and 4 of Viewing
Upon completion students can review decimal calculations and rounding.
GED Connection: Mathematics (2001) Cathy Fillmore Hoyt, PBS LiteracyLink,
pages 259 (#13-#19), 267 (#12), 268 (#19)
AAA Math: Scientific notation drill (timed)
Explain to students that calculators are often equipped to handle calculations
involving scientific notation. Check for student understanding by asking
them the mathematical name/operation/function for"power of ten".
(Exponentiation is the function associated with the"power of ten".)
Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to identify
the button they think might be used to represent power of ten on a calculator.
LOG onto the Online
. (Answers will vary; there are two buttons
associated with"power of ten": LOG and EXP. The INV button
when pushed simultaneously with the LOG button, accesses the 10x function
on the calculator. To be used for scientific notation, a student must first
type in a coefficient before typing INV+LOG followed by the number for the
exponent. The second (preferred) method for expressing a number in scientific
notation using a calculator requires a student to hit the coefficient followed
by the EXP button and the exponent.)
||6.12 + INV + LOG + +/- 4
||6.12 + EXP + +/- 4
|42 000 000 000 000
||4.2 + INV + LOG + 13
||4.2 + EXP + 13
Review the answers to the worksheets from Step 1 using the online calculator.
Use Method II above to enter student responses then hit Enter. The answer
provided on the calculator should match the original question from the"Working
with decimals worksheet" #1-4.
Visit the PBS LiteracyLink companion website (Registration required) at
to become more familiar with the GED Math Test. Practice taking tests after
reviewing concepts in math, science, language arts and social studies.
Practice writing numbers in scientific notation using real data provided
by science. Gather examples of the use of scientific notation in science
using nuclide data
GED Connection Program 38: Introduction to Algebra (Broadcast date:
February 12, 2004); Watch an additional presentation of uses of scientific
notation and decimals in this program.
Scientific notation worksheet
Review and practice conversion between decimal and scientific notation
after printing a copy of this worksheet.