3. Component 2 : Lesson Purpose/ Intention
This lesson is about factorizing. This is an
important process that helps you understand more
about algebraic expressions which will eventually
assist in solving equations.
Factorizing enables you to rewrite polynomials in a
simpler and more usable form in which to do other
things.
4. Component 3 : Lesson Language Practice
Key words/ terms are:
PRODUCT
is the result of two or more numbers when
multiplied together.
5. Component 3 : Lesson Language Practice
FACTORS
are numbers or terms that divide exactly into
another number or expression.
6. Component 3 : Lesson Language Practice
SQUARE
is a number that is multiplied by itself.
7. Component 3 : Lesson Language Practice
EXPAND
involves multiplying every term inside the bracket
by the term on the outside and then collecting like
terms with the aim of removing the set of brackets.
8. Component 3 : Lesson Language Practice
FACTORIZING
is finding what can be multiplied to get a given
expression.
9. Component 4 : Lesson Activity
The square of a number equals 16
times that number. What is the
number?
Component 4A
10. Component 4 : Lesson Activity
Component 4B
i) Write an equation to show the information in the problem.
ii) Simplify the expression.
iii) Solve the problem.
11. Component 4 : Lesson Activity
Component 4B
i) Write an equation to show the information in the problem.
Let x be the number
x2 = 16x or x2 – 16x = 0
The square of a number equals 16 times that
number. What is the number?
12. Component 4 : Lesson Activity
Component 4B
ii) Simplify the expression.
x2 – 16x = 0
x (x – 16) = 0
The square of a number equals 16 times that
number. What is the number?
13. Component 4 : Lesson Activity
Component 4B
iii) Solve the problem.
x2 – 16x = 0
x (x – 16) = 0
x = 0 x – 16 = 0
x = 16
The square of a number equals 16 times
that number. What is the number?
14. Component 4 : Lesson Activity
The sum of the ages of a mother and
daughter is 39. The mother is 3 years
younger than the square of the daughter’s
age. How old is the mother and the
daughter?
Component 4C
15. Component 4 : Lesson Activity
Component 4C
Q1. Write expressions to show the information in the problem.
Q2. Form a trinomial using your expressions from Q1.
Q3. Factorize to solve the problem.
Q4. Why is one of the solutions not usable?
Q5. What are the ages of the mother and daughter?
16. Component 4 : Lesson Activity
Component 4C
Q1. Write expressions to show the information in the problem.
Let x be the daughter’s age and y be the
mother’s age.
x + y = 39
y = x2 – 3
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
17. Component 4 : Lesson Activity
Component 4C
x + y = 39
y = x2 – 3
x + x2 – 3 = 39
x2 + x – 3 = 39
18. Component 4 : Lesson Activity
Component 4C
Q2. Form a trinomial using your expressions from Q1.
x2 + x – 3 = 39 when simplified is
x2 + x – 42 = 0
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
19. Component 4 : Lesson Activity
Component 4C
Q3. Factorize to solve the problem.
Factors of x2 + x – 42 are
(x + 7) and (x – 6).
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
20. Component 4 : Lesson Activity
Component 4C
Q3. Factorize to solve the problem.
(x + 7) (x – 6) = 0 when solved is
x = -7 x = 6
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
21. Component 4 : Lesson Activity
Component 4C
Q4. Why is one of the solutions not usable?
-7 cannot be an answer as you can’t
have a negative age
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
22. Component 4 : Lesson Activity
Component 4C
Q5. What are the ages of the mother and daughter?
Solve for y when x = 6
y = x2 – 3
y = 62 – 3
y = 33
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
23. Component 4 : Lesson Activity
Component 4C
Q5. What are the ages of the mother and daughter?
The daughter is 6 and the
mother is 33.
The sum of the ages of a mother and daughter is 39. The mother is 3 years younger
than the square of the daughter’s age. How old is the mother and the daughter?
24. Component 5 : Lesson Conclusion
• What were the key mathematical concepts
addressed in this lesson?
• Is your level of understanding of the
material in this lesson is high, moderate, or
low?
25. Component 5 : Lesson Conclusion
• Has the lesson helped you to gain further
insight into aspects of the material
covered?
• Describe any issue to your progress and
achievement in relation to the topic area?
26. Component 5 : Lesson Conclusion
• What would best assist your progress and
achievement in this topic area?
