UBD Learning Plan
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UBD Learning Plan Topic: Addition and Subtraction of Radical Expression
Year: Second Year Demonstrator: Rayson C. Alfante (BSEdIII)
STAGE 1 Established Goals: The learner demonstrates understanding of the key concepts of radical expressions.
Transfer Goals: Students will be able to independently use their learning to solve radical expression and solves it by applying a variety of strategies with utmost accuracy.
Essential Understanding: Essential Question: Students will understand that only How do you determine whether the similar radicals having same index and radicals can be added and subtracted? radicand can be added or subtracted but radicals that are not similar or dissimilar should first be simplified.
Students will be able to: Students will know: describe a radical expression the concept of radical expressions add and subtract similar radical adding and subtracting similar expression radical expression simplify dissimilar expression into the process of simplifying similar radical expression dissimilar radical expression into similar radical expression
STAGE 2
Product or Performance Task: involve radical expression are solved using addition and subtraction should be simplify if it is dissimilar radical expression
Evidence at the level of Evidence at the level understanding: of performance: Learners should be able to Assessment of demonstrate understanding by problems formulated covering the six (6) facets of based on the understanding: following: problems Explanation: Discuss ways of solving involved similar and dissimilar radical radical expression using addition and expression subtraction. problems are Criteria: solved using a

Clear Coherent Justified
Interpretation: Figure out the procedure in simplifying and solving radical expressions. Criteria:  Creative  Illustrative  Accurate Application: Use the best method in simplifying and solving radical expression. Criteria:  Accurate  Appropriate  Efficient Perspective: Compare and contrast the procedures in solving similar and dissimilar radical expression Criteria:  Clear  Credible  Insightful Empathy: Solve and simplify similar and dissimilar radical expression. Criteria:  Accurate  Clear  Understandable Selfknowledge: Recognize the right solution to a given problem regarding radical expression. Criteria:  Appropriate  Illustrative  Accurate
variety of strategies with utmost accuracy
STAGE 3 I. PROCEDURE A. Daily Routine 1. Putting class in order 2. Prayer 3. Greetings 4. Checking of attendance B. Motivation
Teacher’s Activity Class, do you know how to play the boat is sinking?
Student’s Activity Yes, Sir!
O.k. Today you will play the boat is sinking but let’s have a new version. Instead of telling directly the desired group let’s put a new changes. I will tell the desired group in the form of perfect number. What you’re going to do is find first its square root. Class, do you understand?
Yes, Sir!
Kindly move your chair to the side.
(The class will move their seat)
The boat is sinking into √144. . . . √100 . . . √64 . . . √49 . . . √25 . . . √16 . . . √25 . . . √9 . . . √4
(The class will group)
O.k. class, did you enjoy our game? Thank you for your actively participation and cooperation.
Yes, Sir!
C. Lesson Proper The activity that we’ve done is very much related tom our topic for this day. It is called “Radical” specifically the “Addition and Subtraction of Radical Expression”. But before that, I will discuss some concepts about radicals. The nth root of a number x can be written in symbol as √ The character √ is
called the radical sign. The expression x inside the radical sign is referred to as radicand. The symbol n is called the index. Are you familiar with the radicals? How about in adding and subtracting
Yes, Sir! No, Sir!
it? In adding and subtracting radicals it should have the same index and radicand which is called similar radicals. The following pairs expression are similar: 2√ , √ √ 2x2 √
, ,
radical
18x3√
,
√
of
9x2y2 √
√
O.k. class, did you understand?
Yes, Sir!
Who can give another example? Very Good! Another one. Nice answer! Another. Very Good!
Yes, __________
It seems that you really understand the similar radical expression. Let’s proceed in adding and subtracting it. Here are some examples on how to add and subtract radical expression. Example: Combine into single radical a. 4√ + 3√ = (4+3) √ = 7√ b. 3√
 6√
= (36) √ = 3 √ c. 5√
+√
= (5+1) √ =6 √ d. 3x2  √
 2x √
Yes, __________ Yes, __________
= (3x2 – 2x) √ Class, did you understand?
Yes, Sir!
O.k. try to solve this following problem. Combine into a single radical. a. 2√ + √ b. 4√  9√ c. 4x√ d. 13√
 3x√  b√
+ 5a√
Kindly solve the letter a into the board. . . . the letter b . . . the letter c . . . the letter d
Yes, __________ Yes, __________ Yes, __________ Yes, __________ Expected Answer: a. 2√ + √ = (2 + 1) √ = 3√ b. 4√  9√ = (4  9) √ = 5 √ c. 4x√
 3x√
= (4x – 3x) √ = 7x √ d. 13√  b√ + 5a√ = 13 – b √ + 5a √ Kindly explain your answer for letter
(The students will explain her work)
a. Very Good! . . . for letter b Excellent! . . . for letter c Very Good! . . . for letter d Excellent! O.k. class, did you know how to add and subtract similar radical expression? Let’s proceed in adding and subtracting dissimilar radical expression. Dissimilar radical expression doesn’t
(The students will explain his work) (The students will explain her work) (The students will explain her work)
Yes, Sir!
have same index and radicand. In adding and subtracting dissimilar radical expression you must first simplify to make it similar radical expression. Let’s consider the following examples: Examples: Make each pair of radical expression similar. a. √ , √ =√ , √ = 2√ , √ b. √ , 2√ = 3√ , 2√ = 3(2)√ , 2(4)√ = √ , 8√ c. √ =
√
=
√
,
√
√
, ,
√
O.k. class, did you understand? Try these following problems on your seat. a. √ + √ √ b. x√  2√ c. √ + √ d. √
 √
Yes, Sir!
+ √ √
Who want to solve for letter a? . . . for letter b? . . . for letter c? . . . for letter d?
Yes, __________ Yes, __________ Yes, __________ Yes, __________ Expected Answer: a. √ + √ √ =√ + √ = 4√ + 3√ = 2√ b. x √
 2√
 √ √ + √
= x√  2√ + √ = x(2)√  2(3x)√ + 4 √ = 2x √  6x √ + 4√ = 4x √ + 4 √
c. √
+ √
=√ + √ = 3√ + 2√ =3+2√ = 5√ d. √
 √
= 21√  4a√ = (21 – 4a – 1) √
√  √
Kindly explain your answer for letter a. Very Good! . . . for letter b Very nice answer! . . . for letter c Excellent! . . . for letter d Very Good! O.k. class, did you understand how to add and subtract dissimilar radical expression? Because you’ll really understand how to add and subtract similar and dissimilar radical expression, let’s have an activity. Are you familiar with the mechanics in quiz bee using cardboard to show the answer? So I will group you into 8 groups. Start counting You may now go to your respective groups. Each of the group will have a cardboard and chalk. What are you going to do is to show your answer once you heard times up. You only have one (1) minute for every problem to solve. I have a tabular sheet to tabulate your scores. One point for every problem. The group that will earn high score from the ten (10) problems will declare as winner and have a reward. O.k. class, understand?
(The students will explain her work)
(The students will explain her work) (The students will explain her work) (The students will explain her work)
Yes, Sir!
Yes, Sir!
1, 2, 3, 4, 5, . . .
Yes, Sir! Problem 1: 3√ Time is up! Show your answer Problem 2: 6√  4√ + 2√
Expected Answer: 1. 2√ + 5√
Time is up! Show your answer Problem 3: √
+ 2√
2. 2√
+ √
Time is up! Show your answer Problem 4: √ + √ Time is up! Show your answer Problem 5: 5√ + 3√  2√ Time is up! Show your answer Problem 6: 3 + √ Time is up! Show your answer Problem 7: 1  √ +√ Time is up! Show your answer Problem 8: 2√ + √ Time is up! Show your answer Problem 9: 5√  2√ Time is up! Show your answer Problem 10: 1+√ Time is up! Show your answer
3.
√
+
4. 4√ 5. 3√
+ 3√
6. 3 + √ 7. 1  11√ 8. 4√ 9. 10√  10√ 10. 4
Because the Group ______ earned the high (The students will perform the I score, so you are the winner for this Math LOVE MATH clap.) Radical Quiz Bee. Here is your reward. Because all of you participated in our activity, everybody standup and let’s have I LOVE MATH clap for job well done. D. Generalization Now again class, describe a radical Sir, radical expression has the expression? following parts: radicand, radical sign and index. Very Good! O.k., how to add and subtract similar Sir, in adding and subtracting radical and dissimilar radical expression. expression, the radical should have same index and radicand but if it is dissimilar, you must simplify it to become similar radical expression. “You’ve got it class! II. EVALUATION In ½ sheet of paper, answer the following radical expression. 1. 2. 3. 4. 5.
√
7√ +3√ +3√ 2√ + 8√  √ √ + √ x√ + √ + √ (The students will start answering)
Are you all finished class? O.k., please pass your paper in front properly.
Yes, Sir!
III. ASSIGNMENT In ½ sheet of paper, answer the following radical expression. 1. √ + √  √ 2. 2√  3√ √ 3. 45√ + 6√ + 2√ That’s all for today! And now let’s call this day “A DAY” Goodbye class!
“A DAY” Goodbye Sir!
Materials needed: Manila paper, scotch tape, chalkboard, chalk, cardboard, colored paper Reference: Diaz, Zenaida E. et. al., Intermediate Algebra
Prepared by:
RAYSON C. ALFANTE (BSEdIII) Checked and Approved by:
DR. CECILIA G. SALAZAR (Professor in Principles of Teaching II)
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