Interactive Video Script Template
Lesson
Objective
Course
Semester
Unit
Lesson
Algebra I
A
I
9
Students will state the simplest radical form of a square or cube
root of a number.
CLIP A (Introduction)
Visual
<Insert text below with audio cues.>
√25 = 5 because 5 ∙ 5 = 25
3
√125 = 5 because 5 ∙ 5 ∙ 5 = 125
Audio
In previous lessons, you learned how to
simplify square roots that are perfect
squares and cube roots that are perfect
cubes.
In the first example, 25 is a perfect square
because five times five equals 25.
In the second example, 125 is a perfect
cube because five times five times five is
125.
<Remove previous image and insert
images below with audio cues.>
The prime factors of 25 are 5 and 5.
√25 = √5 ∙ 5 = 5√1
Each pair can be moved outside of the
radical.
<Remove previous image and insert
image below. Follow audio cues.>
<Add an ‘s’ to each side of the square>
Pairs of prime numbers that are located
inside a square root radical can be
removed from the radical sign and kept
outside. Since the square root of 1 is 1
and 1 times 5 equals 5, the square root of
25 is 5.
The square root is an operation that is
based upon the relationship between the
sides of a square and its area. If the area
of a square is 16 square units, what is the
length of each side?
s
s
Area = 16 sq.
units
s
s
<Add the text below the square with audio
cues.>
𝐴=𝑠∙𝑠
𝐴 = 𝑠2
16 = 𝑠 2
√16 = 𝑠
4=𝑠
<Replace the “s” with a 4 by each side of
the square above.>
Knowing that the area is equal to the
length of a side squared, we can use the
square root operation to find the length of
a side of the square given the area.
Since the area of the square is 16, each
side of the square must be 4 units in
length. Here we used the square root
operation to find the length of the side.
<Remove previous image and insert
radical symbol and arrow box.>
The square root sign is called a radical
sign. The square root operation is the
opposite of squaring a number.
<Add additional text when read.>
Radical Sign
√𝑛 2 = 𝑛
√16 = 4
<Remove previous an insert below with
audio cues.>
The prime factors of 125 are 5, 5, and 5.
3
√125 =
3
√5 ∙ 5 ∙ 5 = 5√1
Each group of three can be moved
outside of the radical.
Triads of cubed numbers that are located
inside a cube root radical can be removed
from the radical sign and kept outside.
Since the cube root of 1 is 1 and 1 times 5
equals 5, the cube root of 125 is 5.
<Insert image below.>
<Fade in the 4s on each side of the cube
with audio cue.>
4
The cube root is an operation that is
based upon the relationship between the
sides of a cube and its volume. If the
volume of a cube is 64 cubic inches, what
is the length of each side of the cube?
Volume = 64
cubic inches
4
4
<Add images below with audio cues.>
Radical Sign
The cube root determines what number
times itself three times is equal to the
value inside the radical sign.
Root Being
Found
3
3
√64 = 4
3
√𝑛3 = √𝑛 ∙ 𝑛 ∙ 𝑛 = 𝑛
<Fade in under previous equation.>
3
3
√64 = √4 ∙ 4 ∙ 4 = 4
The radical sign for a square root does not
have a number on the symbol. This is
because the two is understood if a number
is not present.
Since we are calculating the cube root, a
small three is placed on the radical sign.
If the volume of a cube is 64 cubic inches,
then each side of the cube is 4 inches in
length.
The cube roots of certain integers, called
perfect cubes, are integers. When we
found the length of one side of the cube
was 4, that meant that 64 is a perfect
cube.
Question A
3
Stem: Which of the following is the value of √27?
Answer Choices:
A.
B.
C.
D.
3
9
12
18
Correct Response (A)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip E)
CLIP B (DOK1)
Visual
Audio
<Insert list of numbers, all in blue.>
<With audio cue, make numbers 1, 4, and
9 bold and red. Add text below numbers.>
𝟏, 2, 3, 𝟒, 5, 6, 7, 8, 𝟗, 10, …
Only some of the square roots are of
perfect squares. Most square roots have
other values.
Therefore, it is more likely that when you
calculate a square root, it will not be a
perfect square.
Perfect Squares
Other Values
<Insert title and equations one at a time
with audio cues. Pause on this screen for
3 seconds.>
A number is called a perfect square if the
square root of the number is an integer.
The numbers 1, 4, 9, 16, 25, 36, 49, 64,
81, and so on are all perfect squares.
Common Perfect Squares
√1 = 1
√16 = 4
√49 = 7
√4 = 2
√25 = 5
√64 = 8
√9 = 3
√36 = 6
√81 = 9
<Remove previous and insert below with
audio cues.>
√400
20 ∙ 20 = 400
√400 = 20
<Insert list of numbers, all in blue.>
<With audio cue, make numbers 1 and 8
bold and red. Add text below numbers.>
𝟏, 2, 3, 4, 5, 6, 7, 𝟖, 9, 10, …
Perfect Cubes
Non-Perfect Cubes
We are going to simplify the square root of
400.
Since 20 times 20 equals 400, the square
root of 400 equals 20. This is an example
of using a perfect square.
Only some of the cube roots are perfect
cubes. Most cube roots have other
values.
Therefore, it is more likely that when you
calculate a cube root, it will not be a
perfect cube.
<Remove previous and insert chart
below.>
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
<Remove previous and insert text below
with audio cues.>
3
√343
7 ∙ 7 ∙ 7 = 343
The common perfect cubes are shown in
this chart. When you see one of these
values inside a cubed root radical, the
cubed root is an integer.
We are going to simplify the expression
the cube root of 343.
Since 7 times 7 times 7 equals 343, the
cube root of 343 equals 7. This is an
example of using a perfect cube.
3
√343 = 7
Question B
Stem: Which value is a not perfect square or perfect cube?
Answer Choices:
A.
B.
C.
D.
125
250
512
900
Correct Response (B)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP C (Increased DOK2)
Visual
Audio
<Insert text below with audio cues.>
Every integer can be written as a group of
unique factors. When a number is a
composite number, it can be factored into
more than two factors.
16: 1, 2, 4, 8, and 16
17: 1 and 17
When the number is a prime number, the
only factors of the number are itself and
one.
<Remove previous and fade in below with
audio cues.>
When only prime numbers can be
multiplied together to equal a given value,
we call it the prime factorization.
Prime Factorization
As you can see, we have done this with
four, eight, and sixteen since two is a
prime number.
4=2∙2
8=2∙2∙2
16 = 2 ∙ 2 ∙ 2 ∙ 2
<Remove previous and fade in below with
audio cues.>
34 = 2 ∙ 17
12 = 2 ∙ 2 ∙ 3
25 = 5 ∙ 5
Every composite number can be written as
a unique combination of prime factors.
Prime factors can be repeated when
finding the prime factors of a composite
value.
Question C
Stem: Which of the following is the prime factorization of 24? Remember, the answer
must only include prime numbers and must multiply to equal 24.
Answer Choices:
A.
B.
C.
D.
2 ∙ 12
2∙2∙2∙3
8∙3
2∙2∙3∙3
Correct Response (B)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip G)
CLIP D (Increased DOK3)
Visual
<Insert text and image with audio cues.>
√25 = 5
Audio
When the square root of a perfect square
is calculated, the answer is an exact
value.
<Insert created image.>
The square root of twenty-five is five. This
is one example of an exact value of a
square root.
<Fade out previous, fade in below.>
The square root of seventeen is four point
one two three one zero five six.
√17 = 4.1231056 …
<Insert created image.>
The square root of seventeen is an
irrational number and therefore, the
decimal value is an approximate value.
<Remove previous and insert image.>
http://pixabay.com/en/hand-wood-fingersnails-work-287041/
<Fade in created image and text with
audio cues.>
There are times that an approximate value
of a square root is acceptable to use. A
carpenter wants to make a shelf to place
in the corner of his living room.
The shelf will be triangular in shape and
will be 2 feet along one wall and 3 feet
along the other wall. The length of the
front edge is the square root of 13.
Bob cannot use the exact measurement
because he can only cut a piece of wood
to a few decimals places in terms of
accuracy.
√13 = 3.6055512 …
<Insert image below with audio cues.>
Exact Value
When making calculations in math class,
we want to use the exact values as much
as possible.
This is because when we find the decimal
version, we lose accuracy, which can
result in incorrect answers.
√13 = 3.605512 …
Approximate Value
Question D
Stem: Which value is the most accurate way of writing √19 ?
Answer Choices:
A.
B.
C.
D.
4
4.35
4.35889894 ….
√19
Correct Response (D)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip H)
CLIP E (Remedial 1)
Visual
<Add text below with audio cues.>
√36 = 6 because 6 ∙ 6 = 36
3
√216 = 6 because 6 ∙ 6 ∙ 6 = 218
Audio
Square roots that are perfect squares and
cube roots that are perfect cubes can be
simplified into integers.
In the first example, 36 is a perfect square
because 6 times 6 is 36.
In the second example, 216 is a perfect
cube because 6 times 6 times 6 equals
216.
<Remove previous image and insert below The prime factors of 36 are 6 and 6. Pairs
with audio cues.>
of prime numbers that are located inside a
square root radical can be moved to the
outside of the radical sign. Since the
square root of 1 is 1 and 1 times 6 equals
6, the square root of 36 is 6.
√36 = √6 ∙ 6 = 6√1
=6
Each pair can be moved outside of the
radical.
<Remove previous image and insert below The prime factors of 27 are 3, 3, and 3.
with audio cues.>
Groups of three identical numbers inside a
cube root radical can be moved from the
3
radical sign to the outside of the radical
sign.
3
√27 =
√3 ∙ 3 ∙ 3 = 3√1 = 3
Since the cube root of 1 is 1, and 1 times
3 equals 3, the cube root of 27 is 3.
Each group of three can be moved outside Each group of three can be moved outside
of the radical.
of the radical.
<Remove previous image and insert below Let’s simplify the expressions together.
with audio cues.>
Since 7 times 7 is 49, the square root of
49 is seven.
√49 = √7 ∙ 7 = 7
3
3
√343 = √7 ∙ 7 ∙ 7 = 7
Multiplying seven by 49 is 343, therefore,
the cube root of 343 is 7.
Question E
Stem: Which of the following is the value of √625 ?
Answer Choices:
A.
B.
C.
D.
5
15
25
35
Correct Response (C)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP F (Remedial 2)
Visual
<Show text on the screen with audio
cues.>
Audio
A perfect square is a number whose
square root is an integer.
A perfect square is a number whose
square root is an integer.
1, 4, 9, 16, 25, 36, 49, 64, …
These are all examples of perfect squares.
<Insert created image. Pause on this
screen for 5 seconds.>
Notice that they form a diagonal line on a
multiplication table. That is because
perfect squares are the product of the
same integer squared.
<Fade out previous and insert image
below.>
A square root can be simplified into an
integer if the value inside the radical sign
is a perfect square.
√𝑛 2 = 𝑛
√81 = √9 ∙ 9 = 9
<Fade out previous and insert image
below.>
Similar to perfect squares, the cube root of
certain integers, called perfect cubes, is
also an integer.
3
√𝑛3 = 3√𝑛 ∙ 𝑛 ∙ 𝑛 = 𝑛
9 is the cube root of 729 because 9 times
9 times 9 equals 729.
<Fade in under previous equation>
3
3
√729 = √9 ∙ 9 ∙ 9 = 9
<Remove previous. Insert chart below and
pause on this screen for 3-4 seconds.>
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
Some common perfect cubes are shown
here. When the cube root of one of these
numbers is calculated, the result is always
an integer.
Question F
Stem: Which value is not a perfect square or perfect cube?
Answer Choices:
A.
B.
C.
D.
144
400
600
1331
Correct Response (C)
(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
Audio
<Insert table. Add text with audio cues.>
Composite
4
6
9
Prime
2
3
7
<Remove previous and insert created
images with audio cues.>
Every integer can be written as a group of
factors. A number with more than two
factors is called composite.
If a number only has two factors, itself and
one, then the value is prime.
You can factor a number using a factor
tree.
Thirty-six can be divided by four to get the
factors four and nine.
Since 4 and 9 are not prime numbers, they
can be further simplified. Four is
equivalent to two times two and nine is
equivalent to three times three.
Factors
of 36
Prime
Factors
of 36
Therefore, the prime factors of thirty-six
are two, two, three, and three. We call this
the prime factorization.
36 = 2 ∙ 2 ∙ 3 ∙ 3
<Insert created image with audio cues>
In the previous example, thirty-six could
have been factored by three and leaving
twelve and then further factored using
primes.
Notice that the prime factors are the same,
two, two, three, and three. Even when
different factors are used, the prime
factors are unique and do not change.
36 = 2 ∙ 2 ∙ 3 ∙ 3
Question G
Stem: Which of the following is the prime factorization of 18?
Answer Choices:
A.
B.
C.
D.
2∙9
2∙3∙3
6∙3
2∙2∙3
Correct Response (B)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP H (Remedial 4)
Visual
Audio
<Inert text and created images with audio
cues.>
Sometimes a square root can be simplified
to an exact value and other times we can
only approximate the value of a square
root.
√49 = 7
The square root of forty-nine is seven,
which is an exact value.
<image>
√7 = 2.65575131106 …
<image>
Other times, the square root appears as
an irrational number, which can only be
approximated on the number line. Recall
that an irrational number cannot be written
as a fraction using only integers.
The square root of seven equals 2 point
six four five seven five and so on. This is
an approximation for the value of the
square root of seven.
The application, or how we intend to use
the value, can dictate whether we need an
exact or approximate value. The next two
examples will demonstrate these
differences.
Soda
<Insert created image.>
<Insert created inage. Show several cans
inside box.>
A soda company wants to bundle cans of
soda inside of a box. They want the box
to hold thirty-six cans and they want the
box to be a square shape How should
they arrange the cans?
<Slide equation under box at audio cue.>
√36 = 6
Since the box has to be square shaped,
we can take the square root of thirty-six to
see there should be 6 rows of 6 cans.
<Remove previous image and sketch
created image with audio cue. Sketch a
box around the cans and label each side
with a “6.”>
6
6
<Insert created image.>
The company wants each can of soda to
have approximately the square root of 140
ounces.
Soda
Since the square root of 140, is 11 point
8321, each can would have approximately
11.8 ounces of soda. It is not possible to
have the exact amount of soda.
<Slide equation under can with audio
cue.>
√140 = 11.8321 …
Question H
Stem: Which value is the most accurate way of writing √21 ?
Answer Choices:
A.
B.
C.
D.
4
4.58
√21
4.582575694 ….
Correct Response (C)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip G)