Quarter I: Special Products and Factors and Quadratic Equations / Topic: Special Products and Factors
Subtopic: Rules on finding special
products / Time Frame: 20 days
Time Frame: 4 days
Stage 1
Content Standard:
The learner demonstrates understanding of the key concepts on the rules applied to finding special products. / Performance Standard:
The learner formulates real-life problems involving special products and analyzes these using a variety of strategies with utmost accuracy.
Essential Understanding(s):
Patterns in finding special products facilitate the analysis of real- life situations / Essential Question(s):
Why do we need to study the rules in finding special products?
How are patterns used to analyze real-life problems involving special products?
The learner will know:
  • rules on finding special products.
  • types of special products.
  • special products of two binomials.
  • applications of the rules on special products in the analysis of real- life situations.
/ The learner will be able to:
  • explore the product of two binomials.
  • identify special products.
  • find special products of two binomials.
  • apply the concept on rules on special products in the analysis of real- life situations.

Stage 2
Product or Performance Task:
Problems formulated
  • are real life.
  • involve special products.
  • are analyzed through appropriate and accurate representations
/ Evidence at the level of understanding
The learner should be able to demonstrate understanding of special products using the six (6) facets of understanding:
Explanation
Discuss how special products are found using different methods.
Criteria:
Clear
Coherent
Thorough
Interpretation
State the process of finding special products of two integers and relate it to the patterns in getting the product of two binomials.
Criteria:
Creative
Illustrative
Meaningful
Application
Pose situations in real life involving special products and analyze them.
Criteria:
Appropriate
Authentic
Practical
Perspective
Compare and contrast the different ways of finding special products.
Criteria:
Credible
Critical
Realistic
Empathy
Describe the difficulties one can experience without knowing the process of getting special products.
Criteria:
Open
Responsive & Sensitive
Self- Knowledge
Assess how one can give the best representation to a situation involving special products.
Criteria:
Receptive
Reflective
Relevant / Evidence at the level of performance
Performance assessment of problems formulated based on the following suggested criteria:
  • real-life situations
  • situations involve special products
  • situations are analyzed through appropriate representations
Tools: Rubrics for assessment of problems formulated and analyzed.
Stage 3

Learning Activities:

  1. Explore

Exit Card: IQ Card (Students will use half sheet of paper then write the things they learned at front page and things they don’t fully understand about multiplication of Polynomials at the back page.

Pass the Hat (This activity will serve as review for students and will prepare them for the lesson. Student will pick one question from the hat and will answer it.)

  1. A rectangular piece of land has x+y unit length and x-y unit wide. What is the area of the land?
  2. What is the equivalent exponential expression of 3a . 3b . 3c?
  3. If 4x2-3x+5 is multiply by 4, what is the product?
  4. The product of two positive numbers is ______.
  5. Find the product of 3y2 (4a-9b+3c)
  6. Simplify x20 . x18 . x16
  7. The product of a positive and a negative numbers is ______.
  8. What is the exponent in the expression 4x3y?
  9. What is the shorter way of writing the expression 3.3.3.x.x.x.y.y.y.?
  10. ______is an expression which is made up of constants, variables, and other mathematical symbols and operations.
  11. What property states that multiplication can be distributed over addition and subtraction?
  12. ______expressions contain three terms.
  13. What is the product of (4a2b2c) and (-5a3b2c4)
  14. Give an example of binomial.
  15. Add: 8y2 and – 7y2
  16. The simplified form of (5x2)(4x) is ______.
  1. Firm Up

Activity 3.

Directions: Group yourselves into groups with 3 members. Select a leader, a recorder, and a reporter. In your group, investigate, discuss and complete the table below. Then answer the questions and record your group answers.

Expressions / Solutions / Steps Used
1. (4x2) (3x2y) =? / = (4x2) (3x2y)
= 12x4y / Copy the original expression.
Multiply the terms.
2. 3(2x2 + x - 4) =? / = 3(2x2 + x - 4)
= 3(2x2) + 3(x) – 3(4)
=______/ Copy the original expression.
Use the distributive property.
Multiply the terms.
3. (3k+m) (4k-m) =? / = (3k+m) (4k-m)
= ______
= 12k2 – 3km +4km –m2
= ______/ Use the distributive property.
______
Combine similar terms.
4. (x-2) (x+5) =? / = ______
= x(x) + x(5) -2(x) -2(5)
= ______
= x2 +3x -10 / Copy the original expression.
______
Multiply the terms.
5. (a + 3)2 / = (a + 3)(a + 3)
= ______
= a2 + 3a + 3a + 9
= ______/ ______
Use distributive property
Multiply the terms
______
6. (y – 4)(y – 4) / = ______
= ______
= ______
= ______/ Copy the original expression
Use distributive property
Multiply the terms
Combine similar terms
7. (x – 2)(x + 2) / = (x – 2)(x + 2)
= x(x) + x(2) – 2(x) – 2(2)
= x2 + 2x – 2x – 4
= x2 – 4 / ______
______
______
______

Questions:

  1. Explain the distributive property. When do we apply such property?
  2. What pattern was used in multiplying a monomial to a polynomial like the expressions in numbers 1 and 2?
  3. What pattern/method of multiplying binomial to a binomial was utilized in finding the product of the expressions in numbers 3 to 7?
  4. In (3k+m) (4k-m), what are:
  1. the first terms?
  2. the outer terms?
  3. the inner terms?
  4. the last terms?
  1. In (3k+m) (4k-m), what is the product of its:
  1. First terms?
  2. Outer terms?
  3. Inner terms?
  4. Last terms?
  1. State and explain the pattern “FOIL” method of multiplying binomial to a binomial.
  2. Can you apply “FOIL” method in finding the product of the expressions in numbers 3 to 7? If yes, how? Discuss the answer within the group.
  3. Aside from “FOIL” method, can you find other pattern that could be apply in multiplying two binomials in the expressions from number 5 to 7? If yes, solve the expressions from number 5 to 7 using the pattern found.
  1. Deepen

A. What have you learned?

Direction: On the spaces, write what you have learned about finding special products.

  1. Product of the square of the sum of two terms

______

  1. Product of the square of the difference of two terms

______

______

  1. Product of the sum and difference of two terms

______

  1. Product of two binomials

______

B. Answer the following:

  1. A student claimed that (x+y)2 and x2+y2 are equal? Do you agree with this statement? Why or why not?
  2. Provide an example of each of the following:
  3. Product of the square of the sum of two terms using special pattern.
  4. Product of the square of the difference of two terms using special pattern.
  5. Product of the sum and difference of two terms using special pattern.
  6. Product of two binomials using “FOIL” method.
  7. The length of a garden is 4 meters longer than twice the width. Express the area of the enlarged garden in terms of x.
  8. If the length and width of a rectangle are represented by (x – 1) and (3x + 2) respectively, express the area of the rectangle as a trinomial.
  9. Find the trinomial that represents the area of the square if the measure of the side is (7b – 3).
  1. Transfer

Activity 4. Make me an Application Problem

Directions: Write at least three application problems using the skills learned in special product. (Note: Rubric on page 26 of the Teaching Guide will be used).

Rubric (Individual)

5 / 4 / 3 / 2 / 1
Accuracy/
Organization
(50%) / Ideas are very clear, computations are very accurate, and concepts are very well manifested. / Ideas are clear, computations are very accurate, and concepts are well manifested. / Ideas are not so clear, with 1-2 errors in computations, and some concepts are not manifested. / Ideas are not clear, with more than 2 errors in computations. / No attempt to do the activity.
Authenticity(20%) / Problems are very real and originated from true-to-life experience. / 2 problems are not so real or true to life. / 1 problem is not true or real. / Problems are not real. / No attempt to do the activity
Neatness (20%) / No erasures and very neat. / With 1-2 erasures and neat. / With 3-5 erasures and not so neat. / With more than 5 erasures and not neat. / No attempt to do the activity
Creativity(10%) / Interesting, colorful, and creative. / Colorful but not so creative. / Not colorful and not so creative. / Without color application and no creativity. / No attempt to do the activity