Interactive Video Script Template
Lesson Objective
Course
Semester
Unit
Lesson
Math 8
A
2
6
Students will use basic exponent properties to generate equivalent forms of
expressions involving exponents.
CLIP A (Introduction)
Visual
<Image>
Audio
Well, now we're cooking! You know the
three secret ingredients in any great power
problem.
http://www.morguefile.com/archive/display/89
8830
<All fade out>
<Image appears. Text is overlaid in the
margin above as follows>
1)
𝒂𝒎 ∙ 𝒂𝒏 = 𝒂𝒎+𝒏
You've seen that when we multiply two
powers with the same base, we keep the
base and add the exponents.
http://www.morguefile.com/archive/display/84
7872
<Image appears. Text is overlaid in the
margin above as follows>
That if we want to find a power of a power,
we keep the base and multiply the
exponents.
1|Page
2)
(𝒂𝒎 )𝒏 = 𝒂𝒎∙𝒏
http://www.morguefile.com/archive/display/84
7881
<Image appears. Text is overlaid in the
margin above as follows>
3)
𝒂𝒎
𝒂𝒏
= 𝒂𝒎−𝒏
And finally, that when we divide two powers
with the same base, we keep our base and
subtract the exponents.
http://www.morguefile.com/archive/display/84
7875
<Image>
Of course, these are shortcut facts
http://www.morguefile.com/archive/display/87
0149
<Image>
that simply make sense when we consider
powers in their expanded forms.
http://pixabay.com/en/cookbook-recipesfood-cooking-book-539686/
<Image>
We should never forget why these are true!
2|Page
http://www.morguefile.com/archive/display/92
1481
<Image appears. Text is overlaid in the
margin at right as follows>
But these rules will allow us to simplify crazy
problems like this
54
( 3 )−6 × 52
5
http://www.morguefile.com/archive/display/92
5798
<Previous screen remains. Replace/Flash
text quickly one by one>
54
( 3 )−6 × 52
5
At lightning speed!
(51 )−6 × 52
(51 )−6 × 52
5−6 × 52
5−6 × 52
< Image appears as follows with text
overlaid>
Voila!
= 𝟓−𝟒
http://www.morguefile.com/archive/display/91
4045
<All fade out>
3|Page
<Image appears. (Example only. Not
Copyright free.)
In this lesson, you'll need a
http://www.whsd.org/uploaded/documents/di
strict/profdev/math_grade8.pdf
Add rectangle with red border. Reference for
what to frame below>
<Image>
full cup of each of these three central power
properties,
so let's make sure we've got these
ingredients ready to go.
http://www.morguefile.com/archive/display/80
0396
Question A
Stem: When we divide two powers with the same base, what should we do with the
exponents?
Answer Choices:
A.
B.
C.
D.
Add
Divide
Multiply
Subtract
4|Page
Correct Response (D)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip E)
CLIP B (DOK1)
Visual
<Image>
Audio
It's one thing to know the rules, but it's
another to be able to follow them!
http://commons.wikimedia.org/wiki/File:US
_Navy_060509-N-3560G010_Culinary_Specialist_3rd_Class_Guan
gfeng_Zhou_assigned_to_Naval_Mobile_
Construction_Battalion_Four_(NMCB4)_prepares_ingredients_to_be_used_in_
a_competition_dinner.jpg
< Text appears as follows to the left, with
the following text and image to the right*>
Let's simplify this one-step problem.
7−4
7−6
http://www.whsd.org/uploaded/documents/
district/profdev/math_grade8.pdf
*Image on right is example only, not
copyright free.
<Previous image remains. Transparent
rectangle with red border frames the
formula that reads
𝑎𝑚
𝑎𝑛
The third formula applies here:
= 𝑎𝑚−𝑛 >
5|Page
<Previous image remains. Both 7's
change font color to blue>
we have the same base in both powers,
<Previous image remains, but blue font
color is removed from 7's. Now blue font
color is added to the fraction bar>
and we are dividing.
<Previous image remains, but blue font
color is removed from fraction bar. Text is
added in a line below previous as follows>
7−4
7−6
The guide says: keep the base and
subtract the exponents!
= 7−4−(−6)
<Previous screen remains. The following
line of text is added below the previous>
= 7−4+6
Remember, subtracting negatives is the
same as adding a positive!
<Previous screen remains. The following
line of text is added below the previous>
= 72
Negative four plus six is positive 2.
Question B
Stem: Which of the following statements is false?
Answer Choices:
A. 7−6 × 7−8 = 7−14
B.
C.
5−3
=
53
5
6
=
6−4
−4
D. 8
5−6
69
× 82 = 82
Correct Response (D)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to clip F)
6|Page
CLIP C (Increased DOK2)
Visual
<Image>
Audio
Our master chefs have told us time and
again, anything to the zero power is one.
But why?
http://pixabay.com/en/chef-decoratingcupcakes-preparation-577824/
<Image><Example only, not copyright
free>
We can apply exponent properties to
prove it must be true!
http://www.whsd.org/uploaded/documents/
district/profdev/math_grade8.pdf
< Text appears as follows>
𝑥𝑛
𝑥𝑛
Say we had this division. Before we
begin,
<Previous screen remains. Both 𝑥 𝑛 have
font color changed to blue>
notice that this is a number divided by
itself.
<Previous screen remains, but blue font
color is removed. Text is added to the
right of previous as follows>
𝑥𝑛
=1
𝑥𝑛
We know this will always be one, no
matter the number!
<Previous screen remains. Another copy
But what if we also applied exponent
properties?
of
𝑥𝑛
𝑥𝑛
appears in a line below the previous.
7|Page
"Exponential Properties" image also
appears to the right. See reference
below>
𝑥𝑛
=1
𝑥𝑛
𝑥𝑛
𝑥𝑛
<Previous image remains. Transparent
rectangle with red border frames the
A division problem,
𝑎𝑚
formula that reads 𝑎𝑛 = 𝑎𝑚−𝑛 >
𝑥𝑛
=1
𝑥𝑛
𝑥𝑛
𝑥𝑛
<Previous screen remains. The following
text appears to the right of the second
= 𝑥 𝑛−𝑛 = 𝑥 0
𝑥𝑛
>
𝑥𝑛
<Previous screen remains, but redbordered rectangle fades out. Change first
𝑥𝑛
𝑥𝑛
With the same base, so subtract the
exponents.
Interesting! If the value of this expression
is one
and = 1 to green>
<Previous screen remains. Change = 𝑥 0
to green>
and x to the zero power,
<Previous screen remains, but everything
fades out except 𝑥 0 and = 1. These two
elements move to center-screen and read
as follows>
𝑥0 = 1
then x to the zero power is one!
<All fade out>
Question C
Stem: Select the correct order of the statements of the proof that anything to the zero power is
one:
1. Because the division is equal to one and equal to 𝑥 0 , we know that 𝑥 0 must also be one.
𝑥𝑛
𝑥
2. We create a division of two identical powers ( 𝑛 )
8|Page
3. We know that any number divided by itself is one. Then, applying the division property of
powers with the same base, the division results in 𝑥 0 .
Answer Choices:
A. 2, 3, 1
B. 3, 1, 2
C. 1, 2, 3
D. 2, 1, 3
Correct Response (A)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip G)
CLIP D (Increased DOK3)
Visual
<Image>
Audio
Part of great understanding is being
able to explain your reasoning.
http://commons.wikimedia.org/wiki/File:US_
Navy_070508-N-1786N015_Culinary_Specialist_2nd_Class_Keeva
n_Haynes_talks_to_culinary_students_from
_San_Diego_High_School_about_how_a_N
avy_ship_prepares_food_for_more_than_1,
000_people_three_times_a_day.jpg
<All fade out>
<Completely new screen. Text appears as
So, what if someone presented the
follows toward the top, with = aligned exactly following work to you?
in the center of the screen>
52 × 53 = 255
<Previous screen remains. = is replaced
with ≠ that is red in font color>
This statement is not correct.
9|Page
<Previous screen remains. Text appears as
follows>
52 × 53
= (5 × 5) × (5 × 5
× 5)
≠
Expanded form shows this very clearly.
255
= 25 × 25 × 25 × 25
× 25
< Text appears as follows toward the top,
with = aligned exactly in the center of the
screen>
24 + 22 = 26
Take this declaration.
<Previous screen remains. + sign changes
to blue font color>
We haven't seen laws of addition with
exponents.
<Previous screen remains. = is replaced
with ≠ that is red in font color>
And there is a reason. This is not true.
<Previous screen remains. Text appears as
follows>
24 + 22
26
≠
An evaluation here may be helpful.
= 16 + 4
= 64
<Previous screen remains, but last line of
text fades out. New line of text replaces, as
follows>
24 + 22
26
≠
= (2 ∙ 2 ∙ 2 ∙ 2)
+ (2 ∙ 2)
=2∙2∙2∙2∙2∙2
<Previous screen remains. Two arrows
appear as follows>
≠
24 + 22
26
= (2 ∙ 2 ∙ 2 ∙ 2)
+(2 ∙ 2)
Or perhaps an argument involving
factors, like this.
You simply cannot add the factors of
two things that do not have the exact
same factors in common!
= 2∙2∙2∙2∙2∙2
<All fade out>
Question D
Stem: Suzie claims that (43 )6 is 49 . Do you agree or disagree with her response? Choose the
best explanation.
Answer Choices:
10 | P a g e
A. I believe Suzie is correct because the 6th power outside the parentheses means that we
will multiply 6 additional factors of four to the original 3 factors of four.
B. I believe Suzie is incorrect because the law of division of exponents says that we keep
the base the same and subtract the exponents.
C. I believe Suzie is incorrect because, reading this statement, we will have three factors of
four repeated 6 times, resulting in 18 factors of four, not 9.
Correct Response (C)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip H)
CLIP E (Remedial 1)
Visual
<Image appears *Example only, not
copyright free>
Audio
Because these properties are so central to
your work with powers,
http://www.whsd.org/uploaded/documents/
district/profdev/math_grade8.pdf
<Image>
The key is being able to interpret what
each formula is telling us.
http://commons.wikimedia.org/wiki/File:Flic
kr_-_Official_U.S._Navy_Imagery__Chef_Robert_Irvine_talks_with_Navy_co
oks..jpg
< Text appears as follows>
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
Take the first property.
<Previous screen remains, but color
accents are added as follows>
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
Let's try to put the first part of the equation
into words.
11 | P a g e
<Previous screen remains, but color
accents are modified as follows>
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
We have a multiplication of two powers
that have the same base.
<Previous screen remains, but previous
color accents are modified as follows>
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
To find out how this can be simplified, we
check the other side of the equation.
<Previous screen remains, but previous
color accents are modified as follows>
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
The base remains the same, and the
original exponents are added together!
Question E
Stem: Examine the second formula (𝑎𝑚 )𝑛 = 𝑎𝑚∙𝑛 . How would you describe this formula in
words?
Answer Choices:
A. When we divide two powers with the same base, we keep the base the same and
subtract the exponents.
B. When we multiply a power 𝑎 𝑚 by n, we also multiply the exponent m by n.
C. When we multiply two powers with the same base, we keep the base the same and add
the exponents.
D. When we raise a power 𝑎𝑚 to the n power, we multiply the two exponents, m and n.
Correct Response (D)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip F)
12 | P a g e
CLIP F (Remedial 2)
Visual
<Image>
Audio
Let's cook up a solution
http://www.morguefile.com/archive/display
/622650
<Text appears as follows to the left, with
the following text and image to the right*
(*example only, not copyright free)>
to this next problem.
(−2)−4 ÷ (−2)−5
http://www.whsd.org/uploaded/documents/
district/profdev/math_grade8.pdf
<Previous image remains. Transparent
rectangle with red border frames the
We can see the third item can help us.
𝑎𝑚
formula that reads 𝑎𝑛 = 𝑎𝑚−𝑛 . A new line
of text appears below previous. See
reference below>
(−2)−4 ÷ (−2)−5
= (−2)−4−(−5)
<Only -4-(-5) of previous screen remains;
all other information fades away as if a
mirage. -4-(-5) grows in size and moves
center slightly right screen>
Now, if you get stuck adding and
subtracting integers,
13 | P a g e
<Previous screen remains. A number line
appears to the left of -4-(-5). See
reference below>
a number line can help.
−4 − (−5)
<Previous screen remains. Text is added
in the line below -4-(-5) as follows>
−4 +
First, subtraction can be converted to
addition.
<Previous screen remains, but is covered
with a transparent gray rectangle,
shadowed out. An opaque blue rectangle
rises from the bottom of the screen,
containing the following text>
𝑎 − (+𝑏)
= 𝑎 + (−𝑏)
Remember, subtracting a positive is like
adding a negative,
<Previous screen remains. New line of
text added to the blue rectangle below
previous, as shown below>
𝑎 − (+𝑏)
= 𝑎 + (−𝑏)
𝑎 − (−𝑏)
= 𝑎 + (+𝑏)
and subtracting a negative is like adding a
positive!
<Blue rectangle slides down and out of
sight. Transparent grey rectangle
covering previous text fades out and
disappears>
<Previous screen remains. The number 5
fades in after the -4+ in the last line of
text>
Now, let's read the problem.
<Previous screen remains. Show number
line and a dot at -4>
It says, begin at negative 4,
14 | P a g e
<Previous screen remains. A bold line
extends from -4 to 1 with an arrow, and a
final red dot appears on 1, as shown
below>
then climb up five steps.
<All fade out>
<Completely new screen. Text appears as
follows>
(−2)−4 ÷ (−2)−5
Problem solved: positive one!
= (−2)−4−(−5)
= (−2)1
<All fade out>
15 | P a g e
Question F
5−2
Stem: Simplify 5−3 .
Answer Choices:
A. 51
B. 5−1
C. 5−5
D. 56
Correct Response (A)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to Intervention Alert,
bringing students back to clip B)
CLIP G (Remedial 3)
Visual
<Image>
Audio
A proof is the tool that a mathematician
has on-hand to show that an idea is true.
http://www.morguefile.com/archive/display
/669062
<All fade out>
<Image fades in very slowly>
Mathematicians are still creating new
proofs
http://www.morguefile.com/archive/display
/729214
<Image fades into the next very slowly>
<Image fades in very slowly>
today to make discoveries!
16 | P a g e
http://pixabay.com/en/lantern-dark-cavernglow-metal-556852/
<All fade out>
<Completely new screen. Text and
formula guide* appear as follows
*example only, not copyright free>
Let's get a feel for proof by looking at a
specific case: showing that five to the zero
power is one.
50 = 1
<Previous screen remains. Text added as
follows below previous>
56
56
For instance, take this expression.
<Previous screen remains. Transparent
rectangle with red border frames the
By the rule for dividing powers with the
same base,
formula that reads
𝑎𝑚
𝑎𝑛
= 𝑎𝑚−𝑛 .>
<Previous screen remains. Text added to
the right of
56
56
this results in five to the 0 power
as follows>
= 56−6 = 50
<Previous screen remains. New text
added to the line below previous as
follows>
56
56
Let's re-examine the original division.
<Previous screen remains. New text
added to the right of previous as follows>
=1
We also know that anything divided by
itself must be 1.
17 | P a g e
<Previous screen remains. New line of
text added as follows below the previous>
∴ 50 = 1
So, five to the zero power must be one.
Question G
45
Stem: What results when you simplify 45 using the law of division of powers with the same
base?
Answer Choices:
A. 40
B. 410
C. 0
D. 10
Correct Response (A)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP H (Remedial 4)
Visual
<Image>
Audio
Let's apply some of what we've learned
about powers to the real world.
http://commons.wikimedia.org/wiki/File:US
_Navy_060509-N-3560G062_Culinary_Specialist_%27s_Zhou_ass
igned_to_Naval_Mobile_Construction_Bat
talion_Four_(NMCB4)_celebrate_capturing_1st_place_during
18 | P a g e
_a_competition_dinner.jpg
<All fade out>
<Completely new screen. Image appears
with text/table overlaid as follows>
1 Kilobyte
1 byte
Computers use bits and bytes. With this
information, how many bits are in one
kilobyte?
210 bytes
23 bits
http://www.morguefile.com/archive/display
/723701
<All fade out>
<Completely new screen. Text appears
as follows>
210 ∙ 23
Multiplication will help to solve this.
<Previous screen remains. New text
appears to the right of the previous as
follows>
= 230
But what if someone said that this would
result in two to the thirtieth power? Would
you believe them?
<Previous screen remains, but = changes
to a ≠ in red font>
Of course not!
<≠ 230 fades out, but 210 ∙ 23 remains>
<Previous screen remains. New text
added below as follows>
= (2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2) ∙ (2 ∙ 2 ∙ 2)
We have 10 factors of 2 and another three
factors of two,
<Previous screen remains. New text
added in new line below as follows>
213
which gives us thirteen factors of two total,
<Previous screen remains, but font color
of all exponents change to blue, and 13 is
replaced with 10+3, as shown below>
210 ∙ 23
= (2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2) ∙ (2 ∙ 2 ∙ 2)
210+3
<All fade out>
and the property of multiplication of
powers!
<Completely new screen. Text appears
as follows>
213 = 8192
So there are eight thousand one hundred
ninety two bits in a kilobyte. Wow!
19 | P a g e
Question H
Stem: A megabyte contains 220 bytes. As we saw, a kilobyte contains 210 bytes. To find out
how many kilobytes are in a megabyte, we can perform the following division: 220 ÷ 210.
Choose the correct solution.
Answer Choices:
A. There are 22 , or 4, kilobytes in a megabyte.
B. There are 210 , or 1024, kilobytes in a megabyte.
C. There are 10 kilobytes in a megabyte.
D. There are 2 kilobytes in a megabyte.
Correct Response (B)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip G)
20 | P a g e