Sample first year mathematics ipp lesson plans

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Ignatian Pedagogical Paradigm Lesson Plan (First Entry)
Subject: Mathematics 1: Beginning Algebra (I–St. Garnet)
Prepared by: Rommel M. Gonzales

Date of coverage: 3 Periods June 19, 2008 2 periods June 23, 2008 2 periods
June 20, 2008 1 period June 24, 2008 1 period

Content Coverage: Chapter 1: The Real Number System
1.1. The Real Number System
1.2. Properties of Real Numbers

Learning Objectives Experiences/Strategies/Reflection/Action/Evaluation/Assignment
June 19 Objectives:
At the end of the two periods, the
learners should be able to:
PRELECTION:
Presentation of the Problem for the Day:
“Ann as P150.00. She went to a bookstore to buy 5 pieces of Cartolina at P8.00 each and 3 pieces pentel pen at P32.00
each. Her classmate shared half of the expenses for the Cartolina and P50.00 for the pentel pen. How much was left of
Ann’s money?”

ACTIVITIES/STRATEGIES (EXPERIENCE)
1. Small Group Activities
1. solve a problem in many ways • The class will be grouped into 11 groups of 4 members each.
possible through collaborative work; • Instructions will be given to them.
• Guide questions for discussion will also be given out:
a. What are the given information in the problem? How much is the money of Ann? How much did her
classmate contribute?
b. What are the expenses?
c. In how many ways can you solve the problem?
• The groups will be given 30 minutes to accomplish the tasks.

2. Presentation of Solutions and Processing
2. distinguish from among the (Classroom Discussion)
solutions and answers the most
• Each group will be asked to post their output on the board. Outputs will be categorized according to similarity
reasonable solution/s and correct
of final answers, regardless of the different solutions.
answer.

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• Reporter of each group will present the solution/s.
• Clarificatory questions may be asked as the reporters present.
• For the processing, the following questions may be asked:
a. How many different solutions are there? Do they share the same answer despite the differences in
solutions?
b. How different is one solution from the other?
c. Why are other groups having different solutions and answers?
d. Which of the outputs give us the most reasonable solutions and correct answer? Why?
• The teacher will explain the connection of the whole activity to the topic on Real Number System.

3. Synthesis: In Grade School, the manner we look at a problem may be very narrow or myopic, with certain structures
to follow. As you move higher with learning Mathematics, it is very possible that we can look at a problem in many
perspectives and offer different solutions to it, but with the same answer in the end. Just like what this activity has
shown us today.

3. share feelings or emotions about
working first time with group mates REFLECTION/ACTION:
and about going in front and report to Guide Questions:
the whole class the group’s output. a. How is it working with group members?
b. Why is it there are members who would point at one person for the solution and answer? (optional)
c. Were the solutions and answers a group’s decision or a decision of selected few?
d. Was there a point in your discussion that you did not agree with each other? Why? How did you resolve it?
e. For those who reported their group’s output, how does it feel to be in front of the whole class? Was it your first
time or you did it already in the past?
f. How does it help you?

EVALUATION:
The presentations of the group will be the evaluation for the day.

MATERIALS TO BE USED:
1. USAID Instructional Materials
2. Manila Paper
3. Crayons
4. Masking tape

June 20 Objectives:
At the end of the period, the learners
should be able to:
PRELECTION
1. recall the previous day’s activity

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and the different discussion points 1. Recall of previous day’s activity: Teacher has consolidated the different most reasonable solutions and correct
raised; answer. On a manila paper, the teacher has written the given information and below it are the different solutions.
2. Link between the problem and the hierarchy of real numbers.
ACTIVITIES/STRATEGIES

2. identify the different kinds of 1. Classroom Discussion:
numbers in the previous day’s • The different kinds of numbers based on the problem given – whole numbers, fractions, decimals
problem; • Hierarchy of Real Numbers (with their corresponding symbols and sample elements), through inductive
procedure, namely:
- The set of counting numbers or the set of positive integers
- The set of whole numbers or the set of nonnegative numbers
- The set of negative numbers, to include the set of nonpositive numbers
- The set of integers
- The set of non-integers
- The set of rational numbers
- The set of irrational numbers
- The set of real numbers
• The following questions may be asked:
a. What kinds of numbers were present in the problem given the previous day?
b. Can you give more examples of each kind?
c. When you were in Grade 1, for instance, what were the first numbers you became very familiar with?
d. When you were in Grade 4, for instance, what were the new sets of numbers that you were made familiar
with? In Grade 6?
e. REFLECTION: Which of these sets of numbers you are comfortable working with? You find difficulty
dealing with? Why?
f. Take a look at the hierarchy of real numbers. Where do all these numbers you mentioned fall? What do we
3. define each set of numbers based call these numbers in general?
on the given hierarchy; • Number Association: Learners will associate the different sets of numbers in the hierarchy based on the
examples they will give. Then, they will start defining for themselves each of the sets of numbers.

4. establish the relationships among 2. Synthesis/EVALUATION: Given the hierarchy of real numbers, the learners will be asked to explain the
the different sets of numbers given the relationships among these sets of numbers. Questions, like the following will be asked. Or they will asked to describe
hierarchy of real numbers. the relationships.
a. Are all counting numbers whole numbers? Support your answer.
b. Are integers rational? Support your answer.
Or:
a. All counting numbers are whole numbers.

1. Manila paper containing the different solutions to the problem and the hierarchy of real numbers

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2. Reference: Acelajado, Maxima J., “Algebra: A Problem-Solving Approach (Second Edition).” Belgosa Media
Systems, Inc. Makati City, 2002.
3. Student’s Textbook
June 23-24 Objectives:
learners should be able to: PRELECTION

1. familiarize with the different 1. Idea organizer outlining the different axioms and fundamental properties will be presented to the class. Students
axioms and fundamental properties will be informed that these will be the nature of the numbers that we will be working with, the first of which will be the
on real numbers, equality, and set of real numbers.
order;

1. Work by Dyad
2. define each property of real • Students will work by dyads. Each of them will be given handout containing the properties of real numbers. As
numbers; they study each property, they will be asked to make their own examples (at least two) that will further
illustrate the property. Also, they will be asked to identify some similarities and differences among properties
(or distinct properties), in terms of their application in the four fundamental operations.

2. Classroom Discussion/Processing
• Board work: Pairs will be asked to define each property and provide two examples for each.

• In the processing of information obtained from previous activities, the following will be used to help students
put the different properties in categories. In doing so, students will be helped in gaining familiarization and
understanding of the properties (POINT FOR REFLECTION: Familiarization or association can bridge
understanding. Remember how a child develops concepts of a particular thing).

Write YES or NO.
•

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Questions
O P E R A T I O N S

Addition
Subtraction
Multiplication
Division

1. In which operation/s does closure exist? Show why it exists.

2. In which operation/s does commutativity exist? Show why it
exists.

3. In which operation/s does associativity exist? Show why it
exists.

4. In which operation/s does identity exist? What is the
3. categorize properties according corresponding identity element? Show why it exists.
to their existence in the four
fundamental operations; 5. In which operation/s does inverse exist? What is the
corresponding inverse element? Show why it exists.

6. Under which operation/s does distributivity exist? Show why
it exists.

4. apply the properties to new Following questions may be asked:
mathematical statements or a. What does each property mean? Can you give examples?
expressions. b. Why do some properties exist under certain operations?
c. How does each property operate under certain operations?
• Some Reflection Questions:
a. Where do we see each of the properties in our day to day experiences?
b. What is the identity/image that you would like to project now that you are in the High School? What

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was the image you projected when you were younger? Is it worth keeping or changing? Why?

3. Synthesis: In the end students must be able to come up with a generalized approach to looking at the different
properties of real numbers. This will be done through a concept map.
Properties of Real Numbers

Closure Commutative Associative Identity Inverse Distributive
Property Property Property Property Property Property

Note: Students will continue this map by supplying the operations where the property exists, its definition and one
example.

EVALUATION: Quiz will follow after the discussion, where students will be asked to identify the property that each
statement describes.

MATERIALS USED:
1. Manila paper (visual aids containing matrices and concept map)
2. Handouts (taken from a reference material)
3. Reference: Acelajado, Maxima J., “Algebra: A Problem-Solving Approach (Second Edition).” Belgosa Media
Systems, Inc. Makati City, 2002.
4. Student’s textbook

ASSIGNMENT: Each pair will be asked to make 50 square tiles of two contrasting colors. The dimension of each tile
will be 1x1. This will be used for the next topic on Integers.

Ignatian Pedagogical Paradigm Lesson Plan (Second Entry)

Date of coverage: June 25, 2008 2 periods
June 26, 2008 2 periods


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1.3. Integers
1.4. Operations on Integers
1. Addition of Integers
2. Subtraction of Integers

June 25 Objectives
students should be able to:
PRELECTION:
A comic strip will be presented to the class.
Question: What do you see in the strip? What can you say about the comments made by the characters?


1. Classroom Discussion
1. define the concept of integers and • Pose on the board a very simple equation: 5 – 3 = ______. Then, ask them what kind of number the difference is
positive and negative integers and property it holds.
operationally;
• Pose on the board another simple equation: 3 – 5 = ______. It may be that they can give the correct answer. Then
ask them what kind of number the difference is. Is the property in number 1 holding true for this?
• Ask the students to think of real life situations that can be associated with the equation in number 2.
• Present to the students the HISTORICAL HIGHLIGHT in relation to INTEGERS.
• Show to the class basic concepts of integers using the real number line.

2. discuss the wide application of • Share with them the uses of integers in the following applications (POINT FOR REFLECTION):
integers in the real world; a. Credits and Debits
b. Temperature
c. Sports
d. Time
e. Altitude
3. describe conditions or situations • Exercise: Students will be asked to identify the integer that each of the situations or conditions represents.
using positive and negative
integers; • After which, the teacher may say that the four basic operations are also performed on integers. Lets find out
how addition and subtraction are performed using tiles.

2. Work by Dyad: Addition and Subtraction with Black and Red Tiles (or their equivalents)
• Each pair will receive a Math Activity Worksheet. They will follow instructions as stipulated in the worksheets.
They will use their tiles as their main manipulative. It will be a guided instruction for them as the teacher will
help them go through the process.

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• Questions to be asked:
a. How do you form the addition equation using the tiles? How do you add the integers using the tiles?
b. How do you form the subtraction equation using the tiles? How do you subtract integers using the tiles?
c. What concept is developed when we add integers? Subtract integers?

3. Synthesis: Given the models for addition and subtraction of integers, come up with the rules on how to add and
4. develop rules for addition and subtract integers.
subtraction on integers.

ACTION: Please refer REFLECTION part above.
• Young as you are, you have already experienced difficult moments or moments when you felt so down and sad.
On the other hand, you have also experienced the happiest moment in your life or the most enjoyable moment
in your life that you keep forever.
5. apply the rules of addition and • Recall these moments in your life. Then, make a symbol or drawing that will represent these two opposing
subtraction of integers. moments. Narrate the experience. Share your learning from the experience.
• Expected output: Essay with illustration

4. EVALUATION (Work by Dyad): Each dyad will receive an exercise worksheet containing items where they will
apply the rules on addition and subtraction of integers. The worksheet also includes problem sets.

1. Math Activity Worksheet
2. Acetates containing the Comic Strip, uses of integers
3. Colored chalk
4. Manila Paper
5. Reference: Bennett and Nelson, “Mathematics: Conceptual Approach.” Von Hoffmann Press, Inc., Mc Graw
Hill, 2001.
6. Student’s textbook

Ignatian Pedagogical Paradigm Lesson Plan (Third Entry)

Some updates: The days with no lesson plans were the days when students were doing series of exercises. Please refer to exercise
worksheets.

July 03-05, 2008 --> High School Faculty and Staff Retreat

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Date of coverage: July 09, 2008 Wednesday 2 periods
July 10, 2008 Thursday 2 periods

1.2. Operations on Integers
3. Multiplication of Integers
4. Division of Integers
July 09-10, 2008 Objectives
At the end of the four periods, the
PRELECTION:
Recognizing Patterns: Students will be shown with sets of number sentences and will be asked to observe some
patterns. From there, students will be asked to develop rules for multiplication and division of integers.


1. develop rules for multiplication • From the recognizing pattern activity, students will be asked to come up with rules for multiplication and
and division of integers; division of integers.
Question: From the sets of number sentences, what patterns do you see in terms of the signs of the products and
quotients?

• The students will be asked to compare the rules formulated on their own and those found in the book. Examine
for any differences or similarities.
(Reflection) Question: Which sets of rules are easier to remember? Rules for addition, subtraction,
multiplication, or division? Why?
2. apply the rules of multiplication
and division to different situations;
2. Dyad Work: Exercise Worksheets
• Each pair will receive a Math Activity Worksheet. They will follow instructions as stipulated in the exercise
worksheet. They will be asked to determine the truthfulness or falsity of each of the statements. Moreover, if
the statement is false, they will be asked to provide a counterexample.
3. Teams-Games-Tournament (TGT)
• The class will be divided into small groups called teams, according to seating arrangements.
• Each member of the team will be designated with a number.
• For every number that will be called, the representative of each group having the number will go to the board,
in their designated places and answer the question that will be raised.

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• Each item is worth 2 points.
• The group to garner the highest number of points will emerge the winner.
3. decide which sets of rules for
integers are difficult to remember 3. Synthesis statements:
and what can be done about the • In multiplying two integers, find the product of their absolute values.
difficulty? a. If the integers have the same sign, their product is positive.
b. If the integers have different signs, their product is negative.

• The quotient of two integers with the same sign is positive real number.
• The quotient of two integers with different signs is a negative real number.

ACTION: Please refer to the REFLECTION QUESTION part above.
Questions:
1. Why do you consider the set/s difficult to remember? Why do you consider the others easier to remember?
2. What would you do so as to remove the difficulty?

EVALUATION (Work by Dyad):
I. Computational Exercises: Answer exercises found in the textbook, pages 108-110 (even-numbered items
only).
II. Quiz the following day

1. Exercise worksheet
2. Textbook
3. Sets of number sentences

NOTE: The students were given a problem set on the application of rules for addition and subtraction of integers a
week ago which they need to accomplish in one week. Please see attached sheets for the problem set. This is to help
students improve their skills on problem solving. As much as possible, a problem will be used as prelection, the so-
called problem solving strategy.

Ignatian Pedagogical Paradigm Lesson Plan

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Date of coverage: 2 Periods July 14, 2008 Monday

Content Coverage: Chapter 2: Algebraic Expressions
2.1. Historical Development of Algebra
2.2. Constants, Variables, Exponents, and Algebraic Expressions

July 14, 2008 Objectives
PRELECTION:
1. discuss the historical Questions: 1. Who was Francois Viete? What was his contribution to the world?
development of Algebra and how it 2. Who was Al-Khowarizmi? What was his contribution to the world?
has evolved;
Tasks (by 4s): Get to know them more. Do the following:
1. Find the picture of these two important people.
2. Find out their family background. Make it brief.
3. Find out their life story. What motivated them to do the things they had done?
4. Reflection: If you are to present their lives to the youth today, what characteristics of each will you
highlight which can serve as inspiration for the youth?

Note: The teacher will explain to the class on how to come up with the output.


1. Classroom Activity (Dyad): Number-Pattern Experiment
• Students will be asked to make an experiment that involves just a sheet of paper. By repeatedly folding the
paper in half, an interesting number-pattern will emerge. The basic question will be: What is the relationship
between the number of folds and the thickness?
• The dyads will be guided on how to do the experiment. In the end, they must discover that: The thickness
doubles with each successive folds.
• Processing will take place as they do the experiment. Questions, as follows, may be asked:
a. How thick is the sheet if the paper is not yet folded? How do you define thickness using the paper? What does
thickness mean in this experiment?
b. How thick is the paper when you fold the paper once? Twice? Thrice? Four times? etc.
c. Is it possible to determine the thickness if the paper will be folded 10 times?
d. Suppose you will not fold the paper anymore, can you still determine the thickness given the data at hand?

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e. What pattern do you see?

2. differentiate constant from • From the pattern, the teacher will start to develop the basic definitions and concepts of the following:
variable; a. Constant
b. Variable
3. define exponents and algebraic c. Exponents
expression; d. Algebraic Expression

• To facilitate discussion, the following questions may be asked:
a. From the generalized pattern, what value is fixed? What makes it fixed? Why do you consider it fixed?
b. What could be other examples of fixed values?

c. From the pattern, what is changing? What real life examples that you can think of can be considered
changing?
d. What could be other term for changing?
e. What is the difference between constant and changing?

f. From the pattern, how else can we describe n, aside from being a variable?
g. Generally and collectively, how do we describe the pattern?

3. Group Activity
• Students will be grouped and they will be given tasks involving identification of any of the following: constant,
variable, exponent, algebraic expression.

4. Synthesis statements:
• Using the terms constant, variable, exponent, and algebraic expression, show their relationships using a simple
graphic organizer or a concept map. Include definitions and examples.

REFLECTION
4. recognize relevance of the terms, 1. Get the lyric of the song by Jose Mari Chan, entitled “Constant Change.”
like constant and variable, in real 2. Get the chance to listen to the song. Try to understand the meaning of the song as you enjoy listening to its
life situations. melody and music.
3. Answer the following questions:
a. Do you like the song? Why?
b. Are there lines which you can relate very much and you find meaningful to you?
c. Why do you think the song was entitled “Constant Change”?
d. Do you agree that change is something constant?

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ACTION
Draw an image that best describes your idea of “Constant Change.” Then write down your responses to the
questions in the reflection part.

EVALUATION
Output of the group activity

1. Drawing materials
2. Textbooks and references
3. Research materials
4. Lyrics of the song “Constant Change”
5. Cardboard


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Date of coverage: 3 Periods July 15, 2008 Tuesday 1 period
July 16, 2008 Wednesday 2 periods

2.2. Laws of Exponents (Note: Extended to the following week because of review of topics discussed by student teacher.)

July 15, 2008 Objectives
At the end of the period, the
PRELECTION: The Place Value System
• The Place Value System will be presented to the class.
• The following questions may be asked:
a. How do you describe each place value in the system?
b. What does each mean?
c. How else is each described?
• The teacher will present to them the term “exponents” as a way of describing each place value in the system.

1.define exponent, base, and power; 1. Dyad Work: Problem Solving
• Present to the class a problem: Pedro Hardinero is constructing a den for his chicken. The measure of the
length is the same as the measure of the width.
a. If the measure of the width is 5m, what is the measure of the length?
b. What kind of figure represents the actual den?
c. What will be the area to be covered by the den?

• Let the pairs work on the problem.
• Call on some pairs to present their solutions on the board. (Different solutions are highly appreciated.)
• Processing questions:
a. Are the solutions similar or different? Are the answers similar or different?
b. How did you get your solution? What operation was involved?
c. How did you get the area of the den?
• Focus discussion on the area of the figure: A = s 2
• The following questions may be asked that will lead to the definition of exponents.

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a. The formula A = s gives us the area of a square figure. How did you use the formula?
2

b. For some of you, you used A = s x s. Does it give the same answer?
c. What can we say about s 2 and s x s?

• Let’s us try to explore more:
a. The volume of a cubic figure is V = s 3 . If the measure of the side is 10 cm, what is its volume? Express
solution in two ways possible.
b. Find the product:
1. 3 4
2. (−2) 5
3. 10 5

• Then, students will be asked to define the term “exponents” in their own words.
• Formal definition will also be presented to them. Other related terms will be defined, such as base, power,
exponentiation, exponential expression, and the like.
• The teacher will also ask them to observe some patterns in the following:
a. (−2) 3 and (−2) 4
b. (−3) 3 and (−3) 4
• Generalization will follow.

July 16, 2008 Objectives (original)
July 17, 21-23, 2008 Objectives

At the end of the two periods, the PRELECTION:
students should be able to:  Recall the fundamental definition of exponent:

If b is a real number and n is a natural number, then
b n = b ⋅ b ⋅ b ⋅ ... ⋅ b , where b appears as a factor n times.
b n is read “the nth power of b ” or “ b to the nth power”. Thus, the nth power of b is defined as the product of n factors of b .

1. formulate the different laws of
exponents, namely: 1. Classroom Discussion (Induction)

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a. Product Law  Present to them the different sets of mathematical expressions.
b. Power of the Product Law SET A: Find the area of the rectangle below.
c. Power of the Power Law
d. Quotient Law 8 in
e. Power of Quotient Law

4 in

Questions to ask:
a. Find the area of the rectangle using the area formula for rectangles.
b. How else can we express in the formula the factors 8 in and 4 in, aside from A = (8in)(4in) ?
c. What do you observe with the factors written in exponential form?
d. Try to expand both factors. What product do you get?
e. Can we syncopate the factors and yet get the same product?
f. What makes is possible?

PRODUCT LAW: x m ⋅ x n = x m + n
(Additional examples will be presented to them.)

SET B: Find the area of the square figure below.

4 in

Questions to ask:
a. Find the area of the square using the formula A = s 2 . What is the product?
b. Express 4 in exponential form. How would you insert the expression in the formula?
c. How would you then get the same product as in using the formula?
d. What have you noticed with the expression?
e. If similar expressions appear, what will you do?

POWER OF THE POWER LAW: ( x m ) n = x mn
(Additional examples will be given to them.)

SET C: Find the product of 12 2 .
Questions to ask:
a. Expand 12 2 . Find the product.

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b. Suppose we express 12 as two smaller factors raised to 2. Can we still get the same product? Show in more
than one possible way.
c. For instance, 12 2 = (6 ⋅ 2) 2 . How would you manipulate the right side of the equation to find the product the
easier way without resorting to multiplying 6 and 2?
d. For expressions such as (6 ⋅ 2) 2 , what would be a corresponding exponential expression for this?
e. In case you encounter similar expressions such as this, what will you do?

POWER OF THE PRODUCT LAW: ( x ⋅ y ) n = x n y n
 23 
SET D: Suppose we manipulate the expression in SET A and get  2
2  , instead of 2 3 ⋅ 2 2 .

 
Questions to ask:
a. How similar are the two expressions?
b. Expand both the numerator and denominator, then simplify. What do you get?
23 2 ⋅ 2 ⋅ 2
c. In the equation = = 2 , what is the exponent of 2? What manipulations can we make in the original
22 2⋅2
expression to get the same result? Why is that possible and when is that possible?
d. If you encounter similar expressions such as this, what will you do?

x m x m−n
QUOTIENT LAW: n
= = x m − n , m > n . The assumption of which is x n ≠ 0 .
x 1

Extension of the Quotient Law:
23 22
 Suppose we reverse the expression from to 3 , what would be the result? Do we get the same result?
22 2
What relationship can you establish?
xm 1
 State the observation and come up with the rule. n
= n−m , m < n .
x x
 Suppose the exponent in the numerator is lesser than the exponent in the denominator as in the extension
example, and you did not follow the rule, what result do you get?

 Since the sign of the exponent is negative, is there a way to make it positive since any expression with
negative exponents is not simplified?
1 1 xn
x −n = ⇔ = = xn .
xn x −n 1

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SET E: Use the given expression in Set C. This time express two numbers as a quotient of 12, then raise it to 2.
Questions to ask:
2
24  24 
a. Take one instance, then raise to the power of 2. We have   . Then find the product by expressing the
2  2 
factors as quotients.
2
 24 
b. What would be the exponential expression equivalent to   ?
 2 
c. In case you encounter similar expressions such as this, what will you do?
2
 22 
d. Suppose the expression is  3
3  , will the law apply?

 
n p
 x xn  xn  x np
POWER OF THE QUOTIENT LAW:   = n . Similarly,
 y  m
y  = mp .

  y   y

2. apply the laws of exponents to
different exercise items and 2. Dyad Work: Solving Exercises
situations;
 A set of exercises will be presented to them for each dyad to work. Sample items are as follows:
A. Evaluate each exponential expression.
0
 3a −5 b 2 
1. (−9) 2
6. (x )11 5
11. (−5 x y )(−6 x y )
4 7 11 3 −2
14. (4 x ) 17. 
 12a 3 b − 4 

 
3
8 x 20 24 x 3 y 5  30a 14 b 8 
2. − 9 0 −6 4
7. ( x ) 12. 15. 18. 
 10a 17 b −2 

2x 4 32 x 7 y −9  
−2
25a 13b 4  5x 3 
3. 3 ⋅ 3
2 3 4 2
8. (6 x ) 13. 16. 
 y  
− 5a 2 b 3  
4. x 11 ⋅ x 27 9. (−3 x 2 y 5 ) 2
x 30
5. 10. (3x 4 )(2 x 7 )
x10

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 Problem Solving: Approximately 2 × 10 4 people run in New York City Marathon each year. Each runner runs a
distance of 26 miles. Write the total distance covered by all the runners (assuming that each person completes
the marathon) in scientific notation.

3. Individual Work: Writing in Mathematics (Journal Writing to replace Reflection-Action)

 Essay. Answer each of the following.
1. Describe what it means to raise a number to a power. In your description, include a discussion of the
difference between − 5 2 and (−5) 2 .
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2. Explain the power of the power rule for exponents. Use 2 in your explanation.
5
−5
3. Why is (−3 x )(2 x ) not simplified? What must be done to simplify the expression?
2

4. Synthesis:
 In their index cards, the students will be asked to write down important notes about exponents.

Remember!
−n 1 xm
1. x = 5. = x m−n
xn x n

2. x 0 = 1 6. ( xy ) n = x n y n

n
a an
3. x ⋅ x = x
m n m+ n
7.   = n
b b

4. ( x m ) n = x mn

EVALUATION
 Quiz (separate sheet)
 Exercise Output

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1. Exercise worksheets
2. Textbook/References
3. Acetates and other visual aids
4. Power Point Presentations where appropriate taken from Internet sites


21

Date of coverage: 3 Periods August 07, 2008 2 periods
August 08, 2008 1 period


2.3 Evaluating Algebraic Expressions

August 07, 2008 Objectives:

At the end of 2 periods, the learners
should be able to: PRELECTION:
Presentation of the Problem for the Day and the questions. The teacher will clarify important points of the problem.

Mrs. Alvarez wants to keep track of her students’ scores on the latest examinations. She is preparing a program
(in this case a formula) that will give each student’s score on the examination after she enters just the number of items
that a student missed. To do this, an algebraic expression for the test score is needed.

Questions:

1. There are 100 points on the examination. Each item is worth 5 points. What quantity varies from student to student
and could be used to find each student’s score?

2. Define the variable you will use. Write an algebraic expression for the examination score.

3. Using your expression in number 2, complete the table.

22
Student
Number of Items Missed
Examination Score

a. Alvin
2

b. Gio
4
1. describe the process on
evaluating algebraic expressions;
c. Homer
5

d. Madel
3

e. Rose
6

f. Any student
x

4. How could the expression in number 2 help Mrs. Alvarez to compute grades? As a student, could you find a use for
this expression? Explain.


23
1. Small Group Activities
• The class will be grouped into 11 groups of 4 members each.
• Each group will assign a facilitator, a reporter and a secretary.
• The groups will be asked to perform the tasks under the prelection part.
• The groups will be given 15 minutes to accomplish the tasks.

2. Presentation of Solutions and Processing
(Classroom Discussion)
• Each group will be asked to post their output on the board. Outputs will be categorized according to similarity
of final answers, regardless of the different solutions.
• Reporter of each group will present the solution/s.
• Clarificatory questions may be asked as the reporters present.
e. How many different solutions are there? Do they share the same answer despite the differences in
solutions?
f. How different is one solution from the other?
g. Why are other groups having different solutions and answers?
h. Which of the outputs give us the most reasonable solutions and correct answer? Why?
• The teacher will explain the connection of the whole activity to the topic on Real Number System.

3. Synthesis: In Grade School, the manner we look at a problem may be very narrow or myopic, with certain structures
to follow. As you move higher with learning Mathematics, it is very possible that we can look at a problem in many
perspectives and offer different solutions to it, but with the same answer in the end. Just like what this activity has
shown us today.

REFLECTION/ACTION:
Guide Questions:
g. How is it working with group members?
h. Why is it there are members who would point at one person for the solution and answer? (optional)
i. Were the solutions and answers a group’s decision or a decision of selected few?
j. Was there a point in your discussion that you did not agree with each other? Why? How did you resolve it?
k. For those who reported their group’s output, how does it feel to be in front of the whole class? Was it your first
time or you did it already in the past?
l. How does it help you?

EVALUATION:
The presentations of the group will be the evaluation for the day.

24
5. USAid Instructional Materials
6. Manila Paper
7. Crayons
8. Masking tape

Prepared by: Rommel M. Gonzales, MAST

Date of coverage: August 11 – 13, 2008 5 periods

Content Coverage: Chapter 3: Operations on Polynomials
3.1. Addition and Subtraction of Polynomials

25
August 11, 2008 Objectives:

At the end of 2 periods, the learners
should be able to: PRELECTION:
Presentation of the Problem for the Day and the questions. The teacher will clarify important points of the problem.
This will be worked by pairs.
Martin has a rectangular fishpond. In the afternoon, he finds time walking along the dike of his fishpond. The
length is (14 x + 5) meters and the width is (5 x − 2) meters. What is the distance around the pond?
Questions:
1. Draw the rectangular fishpond according to how you imagine it. Indicate the measures of the sides.
2. What does “distance around the pond” mean?

1. add/subtract polynomials 1. Classroom Discussion: Presentation of Solutions and Processing of the Problem Posted in the Prelection Part
vertically and horizontally; • Some pairs will be asked to show their drawing of the fishpond.
1. How did you decide to draw the fishpond that way?
2. How did you interpret “distance around the pond”?
3. How did you find the distance around the pond? Are there different solutions and answers?
4. How did you resolve difficulties?

• The class will be asked of the concept behind their solution.
• Then the facilitator will now check the solutions presented on the board.
• The following questions will be asked:
1. How do you add/subtract polynomials?
2. What rules can you formulate in adding or subtracting polynomials?

• The students will also be presented two ways in adding and subtracting polynomials – horizontal and vertical
methods.

2. Pair Work: Exercises

A. Add the following polynomials.

26
1. (3a 5 − 9a 3 + 4a 2 ) + (−8a 5 + 8a 3 + 2) 6. (4k 3 + k 2 + k ) + (2k 3−4k 2 − 3k )
2. 2c 2 − 4 + 8 − c 2 7. (3 p 2 + 2 p − 5) + (7 p 2 − 4 p 3 + 3 p)
3. 6 + 3 p − ( 2 p + 1) − (2 p + 9) 8. (2a 2 + 3a − 1) + (4a 2 + 5a + 6)
− 6m 3 + 2m 2 + 5m
4. 6m 2 n − 8mn 2 + 3mn 2 − 7 m 2 n 9. 8m 3 + 4m 2 − 6m
− 3m 3 + 2m 2 − 7 m
5. ( y 3 + 3 y 2 + 2) + (4 y 3 − 3 y 2 + 2 y + 1)

1. describe the process on B. Subtract the following polynomials.
evaluating algebraic expressions;
1. 8a − (3a + 4) − (5a − 3) 4. (q 4 − 2q 2 + 10) − (3q 4 + 5q 2 − 5)
2. (3r + 8) − (2r − 5) 5. ( z 5 + 3 z 2 + 2 z ) − ( 4 z 5 + 2 z 2 − 5 z )
3. (2a 2 + 3a − 1) − (4a 2 + 5a + 6) 6. (5t 3 − 3t 2 + 2t ) − ( 4t 3 + 2t 2 + 3t )

3. Synthesis:

• When adding polynomials, simply combine like terms. But more than just the combining of like terms,
learners should not forget the basic rules of adding integers.
• When subtracting two polynomials, add the first polynomial and the negative of the second polynomial. The
basic rule applies: Change the sign of the subtrahend, then proceed to addition.

REFLECTION: When combining terms, only those that are like can be combined. On similar stance, accomplishing a
group task necessitates a common orientation of the goal which the group has to achieve. Otherwise, if there are some
members who do not believe in concerted efforts, then the goal simply cannot be reached.

1. How do you assess your working dynamics in the different group activities?
2. Was it helping or not? Why?

ACTION: Suggest at least two ways on how you think your group dynamics be improved.

27

EVALUATION: Analyze each of the items, then perform the indicated operations.

1. Subtract 4 y 2 − 2 y + 3 from 7 y 2 − 6 y + 5 .
2. Subtract − (−4 x + 2 z 2 + 3m) from [(2 z 2 − 3 x + m) + ( z 2 − 2m)] .
3. (−4m 2 + 3n 2 − 5n) − [(3m 2 − 5n 2 + 2n) + (−3m 2 ) + 4n 2 ]
4. − [2 p − (3 p − 6)] − [(5 p − (8 − 9 p)) + 4 p ]


1. Reference materials
2. Exercise items
3. Textbook

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