Interactive Video Script Template
Lesson
Objective
Course
Semester
Unit
Lesson
Algebra I
A
I
4
Students will place a list of rational and irrational numbers in the
correct order according to value and plot them on a number line.
CLIP A (Introduction)
Visual
Audio
<Insert created table with audio cue.>
Rational Numbers
2
3
−4
3
Irrational Numbers
√5
2𝜋
2
5
<Insert created number line below the
table with audio cue.>
Previously, you learned how to order and
plot rational numbers on the number line.
It is possible to order rational and irrational
numbers together and to plot rational and
irrational numbers on the number line.
<Add and highlight each step with audio
cues.>
Covert each value to a
decimal.
To compare irrational numbers, we should
convert them to decimals to approximate
the value.
Compare the decimals
to each other.
Once all values are in decimal form, they
can be compared.
Write the numbers in
order as requested.
Place the following values in order from
least to greatest.
√5
2√3
3𝜋
4
Once they are compared, you can write
the values in the order that was requested.
Let’s practice together. We will place the
following values in order from least to
greatest.
<Add table to previous screen.>
Original Form
√5
2√3
3𝜋
4
Decimal Form
2.23607
3.4641
2.35619
Add image with audio cue.>
http://commons.wikimedia.org/wiki/File:Cal
culator_with_pi.JPG
<Highlight the decimal portion of the
numbers in the table>
Original Form
√5
2√3
3𝜋
4
Using the information above, we will
convert each value to a decimal using a
calculator.
Decimal Form
2.23607
3.4641
2.35619
When making calculations with pi, you can
use the number 3.14.
As you can see, you only need to include
some of the decimal digits for the
numbers.
<Replace previous screen with three
numbers below and follow audio cues.>
2.23607
2.35619
We need to compare the digits before we
can order the values.
3.4641
<Highlight the first 2, 2, and 3 in the
values>
Two of the decimals have a two in the
ones place while the other has a three.
<Enlarge the fraction 3.4641>
The value with the three is the largest.
<Highlight the 2 in the tenths place of
2.23607 and the 3 in the tenths place of
2.35619>
Looking at the remaining decimals, we
now go to the tenths place. One has a 2
and the other has a 3 in the tenths place.
Three is greater than 2 .
<Insert the “<” signs with audio cue.>
2.23607 < 2.35619 < 3.4641
So when we compare the decimal values
this is what we get.
<Insert text below with audio cue.>
The order is:
The original values from least to greatest
would be the square root of 5, three pi
divided by four, and then 2 times the
square root of three.
√5
3𝜋
4
2√3
Question A
Stem: Place the following values in order from least to greatest.
2.25
2√2
√6
Answer Choices:
A.
√6
2.25
2√2
B.
2.25
2√2
√6
C.
2√2
√6
2.25
2.25
√6
2√2
D.
Correct Response (D)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip E)
CLIP B (DOK1)
Visual
Audio
<Insert created Image. Show arrow with ?
to represent possible data point
placement.>
Just like rational numbers, irrational
numbers can be plotted on a number line.
To plot irrational numbers on a number
line, we first have to find the decimal
equivalent for each value.
√2
?
<Insert text below. Follow audio cues.>
Let’s try one together. We want to plot
these three values on a number line:
√5
2√3
3𝜋
4
The square root of 5.
<Highlight √5 >
Two times the square root of three.
<Highlight 2√3>
<Highlight
3𝜋
4
And three times pi over 4.
>
<Add the table to the previous screen.>
Original Form
√5
2√3
3𝜋
4
Decimal Form
2.23607
3.4641
2.35619
Just as in the previous example, we
calculated the decimals forms of the
values, as shown in the table.
<Add each point to the number line as it is
read. >
<Add and label the first point as√5>
<Add and label the third point as 2√3 >
<Add and label the middle point as
3𝜋
>
4
We are now ready to plot the irrational
numbers on the number line.
The value of the square root of 5 should
be plotted about one quarter of the way
between 2 and 3.
The value of two times the square root of
three is almost halfway between 3 and 4.
The value three pi divided by 4 is about a
third of the way between 2 and 3.
Question B
Stem: Which number line shows the correct location of the following points?
√7
√10
√2
2.45
Answer Choices:
A.
B.
C.
D.
Correct Response (A)
(Video progresses to clip C)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP C (Increased DOK2)
Visual
Audio
<Insert created image>
It is possible to order irrational values
when a calculator is not available. What is
needed is a good knowledge of the perfect
squares.
<Add text below at audio cue.>
Perfect squares are values whose square
roots are integers.
√𝑛2 = 𝑛, where n is an integer.
<Remove previous image and replace with You can use the perfect squares, like
text below.>
those shown here, to determine the
square root value. Then you can compare
√1 = 1
√9 = 3
√4 = 2
values or place the each value on a
√16 = 4
√36 = 6
√25 = 5
number line.
√49 = 7
√64 = 8
√81 = 9
<Fade out previous image and replace
with each line of text below at audio
cues.>
What is the approximate value of the
square root of 27?
√27?
√25 < √27 < √36
5 < √27 < 6
√27 is approximately 5.2.
To solve this problem, find the perfect
square immediately above and below the
value 27. The value of the square root of
27 is between the square root of twentyfive and the square root of thirty-six.
The square root of 25 is 5, and the square
root of 36 is 6. Therefore, the square root
of 27 is between 5 and 6.
Since 27 is closer to 25 then 36, the value
of the square root of 27 is closer to 5.
Question C
Stem: Which of the following is the closest approximation of √42?
Answer Choices:
A.
B.
C.
D.
6.25
6.50
6.75
6.90
Correct Response (B)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip G)
CLIP D (Increased DOK3)
Visual
Audio
<Insert created image but without the data
point. Show arrow with ? to represent
possible data point placement>
Since we can approximate square roots
without a calculator, we can also
determine roughly where the value lies on
the number line.
√7
?
<Add text to image above, one line at a
time with audio cue.>
Where should the point that represents the
square root of seven be located on the
number line?
√4 < √7 < √9
The square root of seven is between the
square roots of the perfect squares 4 and
9.
2 < √7 < 3
Therefore, the square root of 7 is between
2 and 3.
√7 ≈ 2.6
<Add the number line to the screen
underneath the last calculation.>
Since 7 is closer to 9 than 4, the number
should be slightly higher than 2.5. The
square root of 7 is approximately 2.6.
We can plot 2.6 on the number line to
represent the square root of 7.
Question D
Stem: The square root of which integer could be represented by the plot below?
Answer Choices:
A.
B.
C.
D.
5
8
12
18
Correct Response (D)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip H)
CLIP E (Remedial 1)
Visual
Audio
<Fade in text.>
What is the order of the following values
when placed from greatest to least?
Comparing irrational numbers to put them
in order from least to greatest or greatest
to least is similar to the process used
when comparing and ordering rational
numbers.
√3
6
5
√2
<Remove previous text an insert text and
table with audio cues.>
There are three steps to order rational and
irrational numbers. First, convert all of the
values into decimals.
Step 1: Convert the values into decimals.
Original Form
Decimal
1.732…
√3
6
1.2
5
1.414…
√2
<Keep table on the screen. Slide up the
following text from the bottom.>
Step 2: Compare the sets of values.
1.732 … > 1.2
1.2 < 1.414 ….
<Add to existing…slide up from the
bottom.>
Step 3: Write the values in order.
1.732 … > 1.414 … > 1.2
or in original form:
√3 < √2 <
6
5
Second, compare each combination of
decimal values to determine which is
greater.
Finally, write the values in order as
requested in the problem. Write the
values in the original form.
Question E
Stem: Place the following values in order from least to greatest.
2√5
4.65
√17
Answer Choices:
A.
2√5
√17
4.65
B.
2√5
4.65
√17
C.
√17
4.65
2√5
D.
√17
2√5
4.65
Correct Response (D)
(Video progresses to clip B)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP F (Remedial 2)
Visual
Audio
<Add table.>
Original Form
√3 (Irrational)
6
(Rational)
5
Decimal
1.732…
1.2
1.414…
√2 (Irrational)
<Keep the table and add the number line
below it. Bold each decimal value in the
table as it is read and placed on the
number line.>
<Plot each value as it is read. 1.732
followed by 1.2 and then 1.414. Label
each point with the original form from the
table.>
When plotting rational and irrational
numbers on a number line, it is easier to
convert all of the values into the same
form. The easiest form to use for all types
of numbers is decimal equivalents. This is
because all types of numbers can be
written as a decimal.
Once the values are written as decimals,
they can be plotted on a number line.
The value one point seven three two is
slightly to the right of 1 point 7.
<Pause between each point>
The value one point two is on the second
tick mark to the right of 1 point zero.
<Pause.>
6
5
√3
√2
The value 1 point four one four is slightly
to the right of one point four.
Question F
Stem: Which number line shows the correct location of the following points?
√6
2√2
2.1
Answer Choices:
A.
B.
C.
D.
Correct Response (B)
(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
<Insert text.>
The perfect squares:
Audio
When you do not have a calculator
available, you can still approximate an
irrational value as a decimal by using
perfect squares.
1, 4, 9, 16, 25, 36, … , 𝑛2
<Fade out previous text and fade in text
below with audio cues.>
√21.
√16 < √21 < √25
4 < √21 < 5
√21 = 4.6
<Insert created number line.>
Let’s approximate the value of the square
root of 21. This is an important skill as we
are often required to make calculations
involving square roots without access to a
calculator.
First, we look for the perfect squares
below and above 21. The square root of
21 is between the perfect square root of
16 and the perfect square root of 25.
Therefore, the square root of 21 is
between 4 and 5.
Since 21 is slightly more than halfway
between 4 and 5, it is approximately 4.6.
This approximation can be used to order
numbers or plot them on a number line.
On the number line, 4 and sixth tenths
would be slightly past the halfway mark
between 4 and 5.
Question G
Stem: Which of the following is the closest approximation of √78?
Answer Choices:
A.
B.
C.
D.
8.00
8.25
8.50
8.75
Correct Response (D)
(Video progresses to clip D)
Incorrect Response (other responses)
(Video progresses to clip F)
CLIP H (Remedial 4)
Visual
Audio
<Insert created image but change labeled
points to “3, 3 ½, 4.” Show arrow with ? to
represent possible data point placement.>
When you do not have a calculator
available, you can still approximate where
the value is on the number line by using
perfect squares.
√12
?
We are going to estimate the square root
of forty-eight and plot it on a number line.
√48
√36 < √48 < √49
The square root of forty-eight is between
the perfect square roots of thirty-six and
forty-nine.
6 < √48 < 7
So the square root of 48 is greater than 6
and less than 7.
√48 ≈ 6.9
Since 48 is so close to 49, the square root
of 48 is about 6.9.
<Insert image and pulse plot point at 6.9.>
Now, the value can be plotted on the
number line at 6.9; just to the left of 7.
Question H
Stem: The square root of which integer could be represented by the plot below?
Answer Choices:
A.
B.
C.
D.
36
42
45
50
Correct Response (C)
(Video progresses to Success Alert)
Incorrect Response (other responses)
(Video progresses to clip G)