K-High Session Guide
Episode 6
EPISODE TITLE:
THEME:
CRITICAL ISSUE:
MATH COMPONENT:
I.
OBJECTIVES
At the end of the lesson, the students should be able to:




II.
TREE PLANTING
Environment
Nature and Industrialization
Approximating Square root
define square roots;
identify the different parts of a square roots;
solve for the square of a number;
identify the use of square root in reality.
SUMMARY OF THE EPISODE
This episode features basic concepts on square root with emphasis on extracting the root of perfect
squares. It also explains how the concept is applied in getting the area of a given figure and in
approximating square roots of numbers with large values. This episode also explains how the
concept is applied in the process of transforming ecological sites into industrialized zones
III.
SUGGESTED ACTIVITIES
A. Pre-viewing
1.
Share an article to the students as a motivation.
Are you the Perfect Greek Model?
Rational and radical numbers and expressions have interesting connection to art, architecture, and
science. The golden ratio, phi,
Ρ
1 5
 1.618034 , one of the most commonly known
2
number which involves an integer, a square root, and a ratio, is most often encountered in many
fields, such as art, architecture and science. This golden ratio is connected to the famous Fibonacci
sequence (1, 1, 2, 3, 5, 8, 13, 21 …). If you get the ratio of the 6 th and the 7th, 8th and the 7th, 9th and
the 8th, etc, numbers in the series, you will get more or less the golden ratio. In the book, Da Vinci
Code, phi is mentioned in page 100, and its connection to science and mathematics was discussed.
Greek architects and artists used this golden ratio during the Renaissance time. In architecture, the
golden ratio is most often encountered in the form of a golden rectangle, a rectangle with dimensions
in the golden ratio. This has been considered visually appealing, and hence has been used by Greek
architects and artists during Renaissance time. One of the famous examples of the golden rectangle in
classic architecture is the Parthenon in Greece. In the arts, the golden ratio has influenced Leonardo
da Vinci’s illustration for the book De Divina Proportione by Luca Pacioli and also other Greek
works in sculpture.
K-High Session Guide
Episode 6
2.
Connect the article to square roots. Inform the students that the term square root is all
about radical expression. Then introduce radical expressions by explaining the basic
terms on exponents.
Exponent – a number used to tell how many times a number is used as a factor.
Base – a number to which an exponent refers.
Power – a number that can be expressed by means of a base and an exponent.
power
32
exponent
 32  3  3  9
base
3.
Ask the students to answer the following numbers orally.
Find the square of the following numbers:
4.
a. 2 2
c. 4 2
e. 6 2
g. 8 2
i. 10 2
b. 32
d. 52
f . 72
h. 9 2
j. 112
Connect radical expressions to square roots by telling the students that a square is a
figure with 4 right angles and 4 sides with equal lengths. To find the area, we multiply
the length of one side by itself. Given the figure below, we square the number that
represents the length of a side. So 49 is the square of 7. We call 7 a square root of 49,
because 7 square is 49. ( 7 2  49 )
7
7
5.
Define square roots
Square roots
a2  b .
b  a if a 2  b .
The number a is a square root of b if
In algebraic notation,
6.
Discuss with the students the different parts of a radical expression.
Radical symbol
b a
Principal root
radicand
7.
Mention to the students that every positive number has two square roots – one positive
and one negative. Express that the principal root is always positive.
K-High Session Guide
Episode 6
8.
Give examples.
Find the indicated square root.
b. 121
a. 100
Solution:
a.
b.
c.
d.
9.
c. 0
10
-11
0
d .  256
e.
f.
e. 361
-16
19
Impress the students that square roots are a common approximation problem and can be
somewhat challenging since some educated guessing is involved. Tell the students that
the good thing about it is that they can often get the answer in a somewhat close range.
Inform them that this method is very similar to finding the exact value of a square root.
10. Discuss with the students the steps in getting the approximate square root of a number.
1.
2.
3.
Mentally take off 2-digits at a time, starting from the right, until you are left
with a manageable square root. Usually we want 3 or 4 numbers to work with.
Judging from the value under the square root make an educated guess.
Add 1 zero to the end for every 2-digits you took off from step 1.
Example:
a. 139456
 Taking off 2-digit at a time, we are left 1394
 We know 352 = 1225 and 402 = 1600. 1394 is closer to 1225 than it is to
1600, so we might want 37.
 Add one 0 since we took off two numbers
 We get 370
 The answer can be between 355 and 392
b.
2349761
 Taking off 2-digit at a time, we are left with 243. (note that there were 4
digits taken off)
 We know that 152 = 225 and 162 = 256. Now we must make an educated
guess. 243 is between 225 and 256 so we could use 15.5 for the middle.
 If we do we would get 1550 for the answer. (notice instead of just adding
two 0’s we moved the decimal over 1 and added 1 zero)
 The answer can be between 1483 and 1640.
11. Inform the students that if a number is a perfect square, then we know what the ending
digit will be of the answer by looking at the ending digit of the question.
IF THE NUMBER ENDS IN:
0 – then the ending digit is a 0
1 – then the ending digit is 1 or 9
4 – then the ending digit is 2 or 8
5 – then the ending digit is a 5
6 – then the ending digit is 4 or 6
9 – then the ending digit is 3 or 7.
K-High Session Guide
Episode 6
12. Tell the students that more examples will be discussed in the episode that they are going
to watch.
B. Viewing Proper
C. Post- viewing
1.
To assess the students’ learning, ask the following questions:
a.
b.
2.
Give additional exercises:

3.
Find the square roots of each number.
1. 625
6. 1458
2.
3.
4.
5.
7.
8.
9.
10.
400
1296
1600
64000
4537
54321
212269
43567810
To summarize, ask the students the following questions:
a.
b.
IV.
How was square roots used in the episode?
What important role did it play in this particular episode?
What are the rules in getting the principal square root of a number/variable?
How can we use the knowledge and skill in approximating square roots in our daily
life?
SYNTHESIS/VALUING
In approximating the square root of any number, we must choose between two numbers close to its
value which, when squared, would give us a hint on the square of the given number. We must be
mindful though in choosing between these two numbers in order to come up with an accurate
answer.
In life we are also presented with a lot of choices. Today, as modern technology and globalization
has become a trend and a necessity, our government and other people in authority are forced to
compete with other countries in terms of technology and industries which affects the environment
and our natural resources. This entails much critical thinking as they need to weigh the pros and
cons of both choices and consider its effect not just to the people of today, but more importantly,
to the children of tomorrow.
References:
Chua, Simon L., Josephine Lorenzo-Sy Tan, Andrew D. del Mundo. Understanding Elementary
Algebra I. Quezon City: SIBS Publishing House Inc., 2004. Print.
Oronce, Orlando A., Marilyn O. Mendoza. e-Math Intermediate Algebra II. Quezon City:
Rex Printing Company, Inc.2007. Print
Jones, Dewayne. Math Magic: Number Sense Revealed. May 23, 2004. March 14, 2011
<http://www.math-magic.com/approx/square_roots.htm>.