NLC

1. Problems with
Polynomials

2. .
Lesson Component 1 (Lesson Short Review)
Time: 5 minutes
Key Idea: Solve problems involving factors and polynomials.
Q2.Factorize 24𝑎 − 16𝑎2
Q1.Expand 3(2𝑥 + 5)
Q3.Expand and collect like terms to simplify
3𝑥( 2𝑥 + 7) + 6𝑥( 8 − 5𝑥)
Q4.Factorize 𝑥2 + 7𝑥 + 6
Q5.Factorize (3𝑏 − 5)2

3. .
Lesson Component 1 (Answers)
Time: 5 minutes
Key Idea: Solve problems involving factors and polynomials.
Q2.Factorize 24𝑎 − 16𝑎2 = 8𝑎 (3 − 2𝑎)
Q1.Expand 3(2𝑥 + 5) = 6𝑥 + 15
Q3.Expand and collect like terms to simplify
3𝑥( 2𝑥 + 7) + 6𝑥( 8 − 5𝑥) = 69𝑥 − 24𝒙𝟐
Q4.Factorize 𝑥2 + 7𝑥 + 6 = (𝑥 + 1)(𝑥 + 6)
Q5.Factorize (3𝑏 − 5)2 = 𝟗𝒃𝟐 − 30𝑏 + 25

4. .Lesson Component 2
(Lesson Purpose/Intention)
Time: 3 minutes
Goal:
The lesson is about the manipulations of polynomials to solve problems.
Polynomials are often called the ‘language’ of mathematics and algebra.
They are used in nearly every type of mathematics to show numbers and
expressions because of different mathematical operations. The
manipulation of polynomials allows us to simplify mathematical expressions
to make them more useable to solve problems.

5. .
Lesson Component 3 (Lesson Language Practice)
Time: 5 minutes
Key words/terms are:
Expression – Numbers, symbols and operation grouped together.
Simplest form – An expression is in simplest form when it cannot be
simplified further.
Represent – To show or stand in place of.
Perimeter – The total length of a boundary or the distance around the
outside of a shape.
Area –The space enclosed by the boundary of a plane figure.

6. .
Lesson Component 4 (Lesson Activity)
Time: 25 minutes
Component 4A
Joe is planting a garden full of flowers for the summer. He wants
to plant carnations, roses, lilies, and violets. He must have a field
that is broken up into different sections for each type of flower to
be planted as each flower has its own growing needs. He is
unsure how big a plot of land he will be able to use. The plan of
the field is shown below.

7. .
Lesson Component 4 (Lesson Activity)

8. .
Component 4B
Q1. Write an expression to represent the north
side of the garden in its simplest form.
Q2. Write an expression to represent the perimeter
of the garden in its simplest form.
Q3. Why would this expression be useful for Joe?
Q4. Write a polynomial expression for the area of
the carnations plot?
Read the above and answer the four questions below.

9. .
Component 4B (Answers)
Q1. 𝑥 + 3 + 2𝑥 − 4
simplified to 3𝑥 − 1
Q2. 2𝑥 + 4 + 𝑥 + 2 + 𝑥 + 3 + 2𝑥 − 4 + 𝑥 + 1 + 2𝑥 + 5
+ 𝑥 + 3 + 2𝑥 − 4
Simplified to 12𝑥 + 10
Q3. If he wanted to enlarge the size of the garden,
he could still determine the measurements by
changing the value of 𝑥
Q4. (𝑥 + 2)(𝑥 + 3)
= 𝒙𝟐 + 5𝑥 + 6

10. .
Component 4C
Q1. Write an expression to show the perimeter of
the violets in its simplest form.
Q2. Write an expression for the area of the whole
garden in its simplest form
Q3. Write a different expression for the area of the
whole garden.

11. .
Component 4C
Q1. 𝑥 + 3 + 2𝑥 + 4 + 𝑥 + 3 + 2𝑥 + 4
= 6𝑥 + 14
Q2. (2𝑥 + 4 + 𝑥 + 2) × (𝑥 + 3 + 2𝑥 − 4)
= 9𝒙𝟐 + 15𝑥 − 6
Q3. (2𝑥 + 5 + 𝑥 + 1) × (𝑥 + 3 + 2𝑥 − 4)
= 9𝒙𝟐 + 15𝑥 − 6

12. .
Lesson Component 5 (Lesson Conclusion – Reflection/Metacognition on
Student Goals)
Time: 5 minutes
o What were the key mathematical concepts addressed in this
lesson?
o Your level of understanding of the material in this lesson is high,
moderate, or low?
o Has the lesson helped you to gain further insight into aspects of the
material covered?
o Describe any issue to your progress and achievement in relation to
the topic area?
o What would best assist your progress and achievement in this topic
area?