1. Detailed lesson Plan in Mathematics (Grade 7)
Prepared by: Abbygale Jade P. Delos Reyes
I. Objectives.
At the end of the lesson, 75% of the students will be able to:
1. Define polynomial and the rules involving operations on polynomials.
2. Multiply polynomials such as;
a) monomial by monomial,
b) monomial by polynomial with more than one term,
c) binomial by binomial,
d) polynomials with more than one term to polynomial with three or more terms
3. Solve problems involving polynomials.
II. Subject Matter:Multiplying Polynomials
A. Reference: Vistro-Yu, C.P., et al. (2013) Mathematics – Grade 7 (Teacher’s Guide)
Department of Education
B. Material: Visual Aid tiles.
C. Values: Patience and Critical Thinking
III. Procedure:
Teacher’s Activity Student’s Activity
A. Daily Activities
1. Prayer
“Everybody please stand, class let us pray…”
2. Greetings
“Good morning class…”
(One student will lead the prayer)
“Good morning Ma’am!”
B. Review
“All right class, who can tell everyone what
was our lesson yesterday all about?”
“Very good!”
“What are the things we need to remember in
adding and subtracting polynomials?”
“Ma’am, our topic yesterday was all about
Adding and Subtracting Polynomials.”
Ma’am, we must remember to combine like
terms the variable and the power of each
variable must be exactly the same.”
2. “That’s right!
Seems that you already understand our lesson
yesterday. Are all of you now ready for our
new topic today?”
“Yes Ma’am!”
C. Lesson Proper
“Our lesson for today is all about Multiplication
of Polynomials
Familiarize yourself with the following tiles:
Stands for (+x)
Stands for (-x)
Stands for (+x2
)
Stands for (-x2
)
Stands for (+1)
Stands for (-1)
Examples:
X2
-x
+1
Stands for x2
-x+1
(Students listen Attentively)
3. Stands for
x2
-4x+2
Monomial by Monomial
To multiply monomial by simply multiply the
numerical coefficients then multiply the literal
coefficients by applying the basic laws of
exponent.
Examples:
1) (x3
)(x5
) = x8
2) (3x2
)(-5x) = -15x3
3) (-8x2
y3
)(-9xy8
) = 72x3
y11
Monomial by polynomial
To multiply monomial by a polynomial, simply
apply the distributive property and follow the
rule in multiplying monomial by a monomial.
Examples:
1) 3x (x2
– 5x + 7) = 3x3
– 15x2
+ 21x
2) -5x2
y3
(2x2
y – 3x + 4y5
) = -10x4
y4
+ 15x3
y3
–
20x2
y8
Binomial by Binomial
To multiply binomial by another binomial,
x
x X2
4. simply distribute the first term of the first
binomial to each term of the other binomial
then distribute the second term to each term of
the other binomial and simplify the results by
combining similar terms. This procedure is
also known as the F-O-I-L method or Smile
method. Another way is the vertical way of
multiplying which is the conventional one.
Examples:
1. (x + 3)(x + 5) = x2
+ 8x + 15
2. (x - 5)(x + 5) = x2
+ 5x – 5x – 25 = x2
– 25
3. (x + 6)2
= (x + 6)(x + 6) = x2
+ 6x + 6x + 36 =
x2
+ 12x + 36
4. (2x + 3y)(3x – 2y) = 6x2
– 4xy + 9xy – 6y2
=
6x2
+ 5xy – 6y2
5. (3a – 5b)(4a + 7) = 12a2
+ 21a – 20ab –
35b
There are no similar terms so it is already in
simplest form.
Polynomial with more than one term to
polynomial with three or more terms.
To multiply a polynomial with more than one
term by a polynomial with three or more terms,
simply distribute the first term of the first
polynomial to each term of the other
polynomial. Repeat the procedure up to the
last term and simplify the results by combining
similar terms.
Examples:
1) (x + 3)(x2
– 2x + 3) = x(x2
– 2x + 3) – 3(x2
–
2x + 3)
= x3
– 2x2
+ 3x – 3x2
+ 6x – 9
= x3
– 5x2
+ 9x – 9
2) (x2
+ 3x – 4)(4x3
+ 5x – 1) = x2
(4x3
+ 5x – 1)
+ 3x(4x3
+ 5x – 1) - 4(4x3
+ 5x
– 1)
5. = 4x5
+ 5x3
– x2
+ 12x4
+ 15x2
– 3x – 16x3
–
20x
+ 4
= 4x5
+ 12x4
– 11x3
+ 14x2
– 23x + 4
3) (2x – 3)(3x + 2)(x2
– 2x – 1) = (6x2
– 5x –
6)(x2
– 2x – 1)
= 6x4
– 17x3
– 22x2
+ 17x + 6
*Do the distribution one by one.
Activities:
Now, find the following products and use the
tiles.
1.) (3x)(x) 2.) (-x)(1+x) 3. (3-x)(x+2)
Discuss with you seatmate about your
answers.
Analysis:
How did you solve the problem class?
Did you discuss your answer with your
seatmates?
Abstraction:
What are the steps in multiplying polynomials?
Application in Problem Solving
Read each problem carefully and then solve it
1) What is the area of the square whose side
measures (2x – 5) cm?
(Hint: Area of the square = s2
)
2) Find the volume of the rectangular prism
whose length, width and height
are (x + 3) meter, (x – 3) meter and (2x + 5)
meter. (Hint: Volume of rectangular prism = l x
w x h)
3) If I bought (3x + 5) pencils which cost (5x –
1) pesos each, how much will I pay for it?
(Students perform the activity)
“We just follow the steps Ma’am.”
“Yes Ma’am and we do have the same
answers”
“We could use the FOIL method and using
vertical way of multiplying numbers.”
(Students answer the problem)
6. D. Generalization
“Now class what are the things that you have
learned and should remember in multiplying
polynomials?”
“Yes Class, how about the others? What have
you learned?”
“Thank you for your answers class.”
“Ma’am I learned that in multiplying
polynomials you must first multiply each term
in one polynomial by each term in the other
polynomial
add those answers together, and simplify if
needed “
“Just like her Ma’am you need to distribute
each term of the first polynomial to every term
of the second polynomial. Remember that
when you multiply two terms together you
must multiply the coefficient (numbers) and
add the exponents”.
“Ma’am I also remember that the product of a
positive multiplied by a positive will be positive.
The product of a negative multiplied by a
negative will be positive.
The product of a positive multiplied by a
negative will be negative.”
IV. Assessment
A. Define polynomials and its rules.
B. Exercises:
Simplify each of the following by combining like terms
1) 6x + 7x
2) 3x – 8x
3) 3x – 4x – 6x + 2x
4) x2
+ 3x – 8x + 3x2
5) x2
– 5x + 3x – 15
Give the product of each of the following.
1. (12x2
y3
z)(-13ax3
z4
) 6. (3x + 4y) (5x – 6y)
2. 2x2
(3x2
– 5x – 6) 7. (2X4
) (3X8
)
3. (x – 2)(x2
– x + 5) 8. (x4
+ 9X + 2) (x7
- 10)
4. (2x2
+ 3x + 4) (x2
– 2x + 1) 9. (9x) (6x7
)
5. (3x – 4) (-5x2
– 2x) 10. (x2
– 3x – 15) (2x2
)
7. C. Problem Solving.
Read each Problem carefully then solve it.
1. If Ana bought (2x2
– 3xy) pieces of Cheese cake that cost (3x) each, how much did she pay?
2. What is the area of the square whose side measures (2x6
- 24) cm?
3. Find the area of a rectangle who’s length measures (4ab – b2
) and height (a4
+ 2ab + 25).
Evaluation:
Section Remarks
Grade 7 - Archimedes
Grade 7 - Babbage
V. Assignment
Advance reading of your next topic which is Division of polynomials on your textbook pg. 141 –
145.
