CLIP A (Introduction)

advertisement
Interactive Video Script Template
Lesson Objective
Course
Semester
Unit
Lesson
Math 8
A
2
7
Students will express very large numbers using scientific notation.
CLIP A (Introduction)
Visual
Audio
<Text appears digit by digit>
2,349,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000
Here is a number. A very, very big number.
<Previous screen remains. Below
previous, the following text is added>
÷
643,000
<All fade out>
Please divide this number by six hundred
forty three thousand.
<Image>
Ready? Go!
http://pixabay.com/en/olympics-2004athens-greece-10-84221/
<Image>
Okay, we're kidding. Let's face it
http://pixabay.com/en/shadow-shadow1|Page
play-man-person-536/
<Image>
performing this operation would take a very
long time.
http://www.morguefile.com/archive/display/
729215
<Image>
However, you are about to see that there is
another way.
http://www.morguefile.com/archive/display/
934874
<Image>
A much easier way.
http://pixabay.com/en/children-childchildren-portrait-110963/
<Image appears. Text fades in one
number at a time until all 3 numbers
appear>
You see, huge numbers are all around us.
5,430,230,394,124
789,239,123,234,324
45,239,120,340
http://pixabay.com/en/tree-branch-mazestrong-big-huge-338432/
<Image appears. Text overlay fades in
They’re in computers and the quantities of
2|Page
after image>
data they process,
5,430,230,394,124
http://www.morguefile.com/archive/display/
10837
<Image appears. Text overlay fades in
after image >
In our world population,
789,239,123,234,324
http://pixabay.com/en/skyscraper-homescity-america-450793/
<Image appears. Text overlay fades in
after image >
and even when discussing gigantic objects
in space!
45,239,120,340
http://commons.wikimedia.org/wiki/File:A_N
ew_View_of_the_Tarantula_Nebula.jpg
<Image>
Mathematicians and scientists have united
to create a new way of writing numbers.
http://commons.wikimedia.org/wiki/File:Tec
3|Page
hnician_performing_drug_synthesis.jpg
<Text appears as each word is spoken>
Scientific Notation
They call it scientific notation.
<Image>
And, you guessed it; it involves powers!
http://pixabay.com/en/lightning-strike-nightstorm-bolt-583713/
<Text appears>
2,349,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000
<Text slides out bottom>
Scientific notation turns this insane number
<Text slides in from top>
2.349 × 1048
Into this.
<Text appears>
2,349,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000
÷
643,000
<Text slides out bottom>
And this outrageous operation
<Text slides in from top>
(2.349 × 1048 ) ÷ (6.43 × 105 )
into a simple division with powers of the
same base.
<Previous text changes to white font color
and remains on screen. Zooms out as
image fades in. See reference below>
Scientific notation is truly out of this world.
4|Page
(2.349 × 1048 ) ÷ (6.43 × 105 )
http://commons.wikimedia.org/wiki/File:Gal
axies_in_Hiding_(Unannotated).jpg
Question A
Stem: Which of the following numbers is written in scientific notation?
Answer Choices:
A. 540,670,000
B. 300,000,000 + 240,670,000
C. 540,670,000.00000
D. 5.4067 × 108
Correct Response (D)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip E)
5|Page
CLIP B (DOK1)
Visual
<Image>
Audio
Before we proceed, let's learn some
critical vocabulary.
http://www.morguefile.com/archive/display
/141416
<Completely new screen. Text appears
as follows top-center screen>
Scientific Notation
First, when we say scientific notation,
<Previous screen remains. Text appears
as follows below previous>
5.47 × 106
we mean numbers written like this.
<Previous screen remains. Text color of
5.47 changes to red. Additionally, a red
arrow appears from 5.47and points to new
text as follows>
5.47 × 106
They have two parts to them: a coefficient,
which is a number between 1 and 10
written in front,
1 < Coefficient < 10
<Previous screen remains, but the
1 < Coefficient < 10 text and arrow
disappear. Red color font also removed
from 5.47. Now, text color of 106 changes
to blue, and a blue arrow appears from
106 and points to new text as follows>
and a power of ten.
5.47 × 106
Power of ten
<All fade out>
<Completely new screen. Text appears
as follows>
5,470,000
Now, this is another way we could write
this same number. This looks more
familiar, doesn't it?
6|Page
<Previous screen remains. Font color of
5,470,000 changes to green. New title
appears where "Scientific Notation" was
previously. Text as follows>
We call this standard notation.
Standard Notation
𝟓, 𝟒𝟕𝟎, 𝟎𝟎𝟎
<All fade out>
Question B
Stem: Please select the two words to correctly fill in the blanks.
In the number 6.54 × 109 , 6.54 is called the (1)____________. 6,540,000,000 is the way
to write the number in (2)___________________.
Answer Choices:
A. (1) coefficient; (2) scientific notation
B. (1) coefficient; (2) standard notation
C. (1) scientific notation; (2) standard notation
D. (1) standard notation; (2) coefficient
Correct Response (B)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to clip F)
7|Page
CLIP C (Increased DOK2)
Visual
<Text appears as follows>
1.91 × 108
Audio
While the coefficient tells us about the
finer details of the number,
Coefficient
<Remove red font color and red arrow.
Add blue arrow, text, and font color as
follows>
1.91 × 108
the power of ten
Power of ten
<Previous screen remains. Text appears
as follows below "Power of ten">
(Order of magnitude)
determines the order of magnitude,
<Previous screen remains, but 108 grows
larger and larger>
meaning how large the number is!
<All fade out>
<Completely new screen. Text appears
overlaid on the image as follows>
For instance, just looking at the
4.5 × 105 meters
http://www.morguefile.com/archive/display
/163466
<Previous screen remains. 105 font color
turns blue.>
power of ten tells us that the Grand
Canyon is
<Previous screen remains. New line of
text appears below previous text as
follows>
4.5 × 𝟏𝟎𝟎, 𝟎𝟎𝟎 meters
<All fade out>
hundreds of thousands of meters long!
8|Page
<Completely new screen. Table appears
as follows>
Power
of ten
Expanded Form
Let's study powers of ten.
Value
101
102
103
104
105
<Previous screen remains. All text of "10"
turns blue in color>
The base is ten.
<Previous screen remains, but blue font
color of 10 is removed. Now, exponents
turn red and text appears in Expanded
Form column as follows>
The exponent tells us how many times to
repeat the factor.
Power
of ten
101
102
103
104
105
Expanded Form
Value
= (10)
= (10)(10)
= (10)(10)(10)
= (10)(10)(10)(10)
= (10)(10)(10)(10)(10)
<Previous screen remains, but red font
color is removed. Text appears in Value
column as follows>
Power
of ten
101
102
103
104
105
Expanded Form
= (10)
= (10)(10)
= (10)(10)(10)
= (10)(10)(10)(10)
= (10)(10)(10)(10)(10)
Finally, we evaluate. Notice a pattern?
Value
= 10
= 100
= 1000
= 10000
= 100000
<Previous screen remains, but red font
The exponent reflects the number of zeros
color returns to exponents and now is also after one in each evaluation.
added to any "0" in the value column. See
reference below>
Power
of ten
101
102
103
104
105
Expanded Form
= (10)
= (10)(10)
= (10)(10)(10)
= (10)(10)(10)(10)
= (10)(10)(10)(10)(10)
Value
= 10
= 100
= 1000
= 10000
= 100000
<All fade out>
9|Page
Question C
Stem: Which of the following numbers represents a correct evaluation of 105 ?
Answer Choices:
A. 50
B. 10,000
C. 100,000
D. 111,110
Correct Response (C)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip G)
10 | P a g e
CLIP D (Increased DOK3)
Visual
<Image>
Audio
Let's shine some light on the mystery of
http://www.morguefile.com/archive/display/877713
<Previous screen remains. Text appears
as follows in the flashlight beam of the
image>
scientific notation. It's not as complicated
as you might think!
Scientific
Notation
<All fade out>
<Completely new screen. Text appears
as follows top-center>
3,000,000
Let's begin by saying this number aloud:
<Previous screen remains. Text appears
as follows below previous>
Three million
Three million, right?
<Previous screen remains, but numbers
and "Million" text fly out to the left>
This means that there are three millions
collected together,
<Following text flies in from the right>
3 × 1,000,000
like multiplying three by one million!
<Previous screen remains. Text appears
in a line below previous as follows>
3 × 10?
Wait: can't one million be written as a
power of ten?
<Previous screen remains, but the
following text changes color to red>
3 × 1,000,000
We count 6 zeros,
<Previous screen remains, but exponent
which means ten to the sixth power.
11 | P a g e
replaces ? in red as follows>
3 × 106
<Previous screen remains, but a blue
bordered transparent circle appears
around 3 × 106>
Congratulations! This is scientific notation.
<All fade out>
Question D
Stem: Which of the following correctly shows how one may write 4,000 (or four
thousand) in scientific notation?
Answer Choices:
A. 4000 = 4000 × 1
B. 4000 = 2000 + 2000
C. 4000 = 4 × 100 = 4 × 102
D. 4000 = 4 × 1000 = 4 × 103
Correct Response (D)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip H)
12 | P a g e
CLIP E (Remedial 1)
Visual
<Image>
Audio
Scientific notation is where our
understandings of powers and the real
world collide!
http://pixabay.com/en/space-universeouter-space-planet-92348/
<All fade out>
<Text appears as follows>
23,634,000,000,000,000
When an extremely large number
<Previous screen remains. Text appears
below previous as follows>
=
2.3634 × 1016
is written in scientific notation, it's
representing the same value,
<Both numbers fades out, but = sign
remains>
<Previous screen remains with just =. The
following text above =>
Laughing out loud
but in a much
<Previous screen remains. The following
text below =>
LOL
<All fade out>
shorter way.
13 | P a g e
<Image>
Even your calculator uses scientific
notation!
http://www.morguefile.com/archive/display
/102119
<All fade out>
<Image>
When calculators return extremely large
results,
Screen shot
<All fade out>
<Image>
they come back looking
Screen shot
14 | P a g e
<Previous screen remains. The following
text covers over and replaces 1.17e+33 in
the image>
= 1.17 × 1033
<All fade out>
something like this.
Question E
Stem: Scientific notation is...
Answer Choices:
A. A longer way of writing large numbers.
B. A shorter way of writing numbers by adding them repeatedly.
C. A shorter way of writing numbers that involve powers.
D. A special type of handwriting that scientists use.
Correct Response (C)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip F)
15 | P a g e
CLIP F (Remedial 2)
Visual
<Image>
Audio
Let's master the vocabulary we need to
complete the objective.
http://pixabay.com/en/scrabble-gameboard-game-words-243192/
<All fade out>
<Completely new screen. Text appears
as follows in the left part of the screen>
Scientific Notation
Scientific notation refers to our new way to
write very large numbers,
8.234 × 109
<Previous screen remains. Image
appears in the right part of screen>
used regularly in science!
http://pixabay.com/en/biology-researchlaboratory-220005/
<Image fades out>
<Previous screen with number remains.
Text color of 8.234 changes to red. Text
appears directly below the number as
follows>
(Coefficient)
<Image also appears in the right part of
The coefficient is connected with
16 | P a g e
the screen>
http://www.morguefile.com/archive/display
/857775
<Previous screen remains. Text color of
109 changes to blue. Text appears to the
right of (Coefficient) as follows>
×(Power of ten)
the power of ten in this multiplication.
<Previous screen remains, but image of
plugs in outlet is replaced with the
following>
They go together to explain the number.
Scientific notation will always have these
two pieces.
http://pixabay.com/en/connect-connectioncooperation-20333/
<All fade out>
< New text appears>
8,234,000,000
Now we're very familiar
<Previous screen remains. Image
appears in the right part of the screen>
with seeing numbers this way, meaning
17 | P a g e
http://pixabay.com/en/book-bored-collegeeducation-15584/
<Previous screen remains. Text appears
where "Scientific Notation" was previously
written>
Standard Notation
standard notation.
<All fade out>
Question F
Stem: Which of the following is a correct explanation of standard notation?
Answer Choices:
A. Standard notation is the new way for writing numbers. It looks like this: 4.9 × 102.
B. Standard notation is the number multiplied by a power of ten in scientific notation.
It looks like this: 4.9.
C. Standard notation is the way we are used to seeing numbers written. It looks like
this: 4,900.
D. Standard notation is when we indicate positive or negative numbers with a symbol
in front of the number. It looks like this: +4.9, -4.9.
Correct Response (C)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to Intervention Alert,
bringing students back to clip B)
18 | P a g e
CLIP G (Remedial 3)
Visual
<Image>
Audio
You're on the path to success with
scientific notation!
http://pixabay.com/en/bowling-pins-ballplaying-alley-596766/
<Image>
Memorizing how to evaluate powers of ten
will help you get there!
http://commons.wikimedia.org/wiki/File:Bo
wlingball.JPG
<All fade out>
<Completely new screen. Text appears
as follows>
101
102
103
104
105
Remember, powers are repeated
multiplications.
<Previous screen remains. 102 turns bold
and green>
Take ten squared.
<Previous screen remains. In the two
cells to the right of 102 , the following text
appears>
= 10 ∙ 10
= 100
Ten times ten is one hundred.
19 | P a g e
<Previous screen remains, but green color It turns out that a very cool pattern forms
accents and bolding is removed. The
in our results.
table is filled in as follows>
= 10
= 10
101
= 10 ∙ 10
= 100
102
= 10 ∙ 10 ∙ 10
= 1000
103
= 10 ∙ 10 ∙ 10 ∙ 10
= 10000
104
= 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 = 100000
105
<Previous screen remains. Exponent
color changes to red as follows in first
column>
101
An exponent of one
<Previous screen remains. Text color
changes to red as follows in third column>
= 10
means one zero,
<Previous screen remains. Text color
changes to red as follows in first column>
102
two means
<Previous screen remains. Text color
changes to red as follows in third column>
= 100
two zeros,
<Previous screen remains. Text color
changes to red as follows in the third row>
= 10 ∙ 10 ∙ 10
= 1000
103
three means three zeros,
<Previous screen remains. Text color
and so on.
changes to red as follows in the fourth and
fifth columns>
= 10 ∙ 10 ∙ 10 ∙ 10
= 10000
104
5
= 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 = 100000
10
<All fade out>
20 | P a g e
<Image appears. Text is overlaid as
follows.>
Be careful! This only works when the
base is 10!
Pattern only occurs
with base 10!
http://pixabay.com/en/site-warning-lightroad-works-541197/
<All fade out>
Question G
Stem: Which power of ten results in 1,000?
Answer Choices:
A. 102
B. 103
C. 104
D. 105
Correct Response (B)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip F)
21 | P a g e
CLIP H (Remedial 4)
Visual
Audio
<Text appears as follows>
2.5 × 10𝑛
Consider the coefficient two point five.
<Previous screen remains, but text is
modified as follows>
2.5 × 10 =
Two point five times ten results in
<Previous screen remains, text appears to
the right of previous as follows>
25
<All fade out>
twenty five!
<Image>
Want to know a secret?
http://www.morguefile.com/archive/display/66095
<All fade out>
<Completely new screen. Text appears
large and center screen>
2.5 × 10
Multiplying by ten
<Completely new screen. Text and arrow
appear as follows>
2.5 = 25.0
is the same as moving the decimal point to
the right one space!
× 10
<All fade out>
<Completely new screen. Text appears
as follows>
2.5 × 10 = 25.0
25.0 × 10 = 250.0
Let's imagine multiplying by ten again.
<Previous screen remains. Text appears
to the right of the last line of previous>
250.0
We'll reach two-hundred fifty!
22 | P a g e
<Rearrange previous to show:>
2.5 × 10 × 10 = 250.0
We multiplied by two factors of ten total in
this problem.
<Previous screen remains, but text is
modified as follows>
2.5 × 102 = 250.0
Just like multiplying by ten-squared!
<Previous screen remains, but arrows are
added as follows>
2.5 × 102 = 250.0
Or moving the decimal twice.
<All fade out>
Question H
Stem: Following the reasoning in the clip, how can we find 2.5 × 103?
Answer Choices:
A. This will simply be 2.5. The coefficient does not change.
B. We can move the decimal point in 2.5 to the left three spaces, reaching 0.0025.
C. We can move the decimal point in 2.5 to the right three spaces, reaching 2500.
D. We can move the decimal point in 2.5 to the right two spaces, reaching 250.
Correct Response (C)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip G)
23 | P a g e
Download