Learning resource in teaching Mathematics 9

1. MATHEMATICS
9

2. - get yourself always ready and attentive
CLASS RULES
G
O - open your mind to aspire positivity and
new learnings
A- avoid going around during discussion
L- live to the word RESPECT to your Teacher &
Classmate

3. GOAL!

4. FILL IN THE GAP
ACTIVITY 1

5. ACTIVITY 1:
Directions:
1. The class will be divided into (3) three groups.
2. Every member of the group will have a voluntary grabbing of
opportunity to evaluate each expression in order to fill in the gap.
3. After filling in, the first group to finish within 3 minutes will garner 5
points followed by 4 points, then 3 points and last will have 2 points.
4. Then later on, the teacher will present the correct answer.
5. Each group will send 1 representative in order to check correctly each
answer and will be scored through point system.

6. 8-7 (correct answer) = 10 points
6-5(correct answer) = 9 points
4-3 (correct answer) = 8 points
2-1 (correct answer) = 7 points

8. ARRANGE ME
PROPERLY
ACTIVITY 2

9. Directions:
1. The class will form 3 groups then identify a leader, secretary, material manager
and time keeper in order to have an organize collaboration.
2. Then, the teacher will hand the materials need and GIVE an envelope carries
laws of radical as well as expression to evaluated.
3. After that, the group will arrange the expression base on the correct answer
guided by the laws of exponent.
4. First to finished within 3 minutes corresponds 5 points, followed by 4 points and 3
points.
5. When every group is settled in front, the leader and output handler will proceed
in front of the board to check whether they arrange the expressions properly.
5 point each correct arrangement of the expression
2 points if correct process wrong answer

10. Laws of radical
1. 𝒏
𝒂 ⋅
𝒏
𝒃 =
𝒏
𝒂𝒃 2.
𝒏
𝒂
𝒏
𝒂
=
𝒏 𝒂
𝒃
2.
𝒏 𝒎
𝒂 = 𝒎𝒏
𝒂
Expressions :1. 𝟗𝒙𝟐 = 𝟗 ⋅ 𝒙𝟐= 3x
2.
𝟒𝟓𝒙𝟐
𝟓𝒙
= 𝟗𝒙= 3 𝒙
3.
𝟑
𝟔𝟒 =
𝟑
𝟖 =
𝟑
𝟐𝟑 = 2

11. Find the product of the given expression.
1. 2x(3y) = 6xy
2. x (x + 3) = 𝑥2
+ 3𝑥
3. 2x (𝑥 + 4) = 2𝑥2
+ 8𝑥
4. (2𝑥2 + 𝑥) (3𝑥2 − 7𝑥) =
6𝑥4 − 14𝑥3 + 3𝑥3 − 2𝑥2= 6𝑥4 − 11𝑥3 − 2𝑥2

12. SIMPLIFYING
EXPRESSIONS
USING LAWS
OF RADICALS

13. a.) Identify perfect numbers at a certain power;
b.) Simplify radicals using the law of radicals; and
c.) Demonstrate the ability to work well in simplifying
radical expression during individual or group activity.
LEARNING OBJECTIVES
At the end of the lesson, the student can:

15. a)Removing Perfect nth Powers
𝒏
𝒂𝒃 = 𝒏
𝒂 ⋅
𝒏
𝒃
𝟏𝟐𝟓𝒏 = 𝟐𝟓 ⋅ 𝟓𝒏 = 𝟓𝟐 ⋅ 𝟓𝒏
= 5 𝟓𝒏

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𝟔𝟒𝒎𝟑𝒏𝟑
= 𝟖𝟐 ⋅ 𝒎𝟐⋅ 𝒎 𝒏𝟐 ⋅ 𝒏
= 8mn 𝒎𝒏

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b. Reducing the index to the lowest possible order
𝒎 𝒏
𝒂 = 𝒎𝒏
𝒂 =
𝒎 𝒏
𝒂
Examples:
1.14
27𝑒21𝑓14 =
2 7
27𝑒21𝑓14 =
2
2𝑒3𝑓2

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𝟐𝟎
𝟑𝟐𝒎𝟏𝟓𝒏𝟓
=
𝟒 𝟓
𝟑𝟓(𝒎𝟑)𝟏𝟓𝒏𝟓
=
𝟒
𝟐𝒎𝟑𝒏

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𝒐𝒓
𝟐𝟎
𝟑𝟐𝒎𝟏𝟓𝒏𝟓
= (𝟐𝟓
𝒎𝟏𝟓
𝒏𝟓
)
𝟏
𝟐𝟎
= 𝟐
𝟓
𝟐𝟎𝒎
𝟏𝟓
𝟐𝟎𝒏
𝟓
𝟐𝟎 = 𝟐
𝟏
𝟒𝒎
𝟑
𝟒𝒏
𝟏
𝟒
= (𝟐𝒎𝟑
𝒏)
𝟏
𝟒 =
𝟒
𝟐𝒎𝟑𝒏

20. c. Rationalizing the denominator of the radicand
𝒏 𝒂
𝒃
=
𝒏
𝒂
𝒏
𝒂
1.
𝟖𝟎𝒙𝟓
𝟓𝒙𝟑
=
𝟖𝟎𝒙𝟓
𝟓𝒙𝟑 = 𝟏𝟔𝒙𝟐 = 𝟒𝒙

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𝟑
𝟏𝟑𝟓𝒙𝟓
𝟑
𝟓𝒙𝟐
=
𝟑 𝟏𝟓𝟑𝒙𝟓
𝟓𝒙𝟐
=
𝟑
𝟐𝟕𝒙𝟐 = 3x

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ACTIVITY 3
PICK ME, IN
EXPRESSWAY

23. Mechanics:
1. The class will be divided into 3 then the teacher will provide materials of the
activity.
2. After that, the group should have a leader, secretary, material manager and time
keeper.
3. Then, the team leader pick as fast as they can to choose radical expression in
order to simplify using laws of exponents and discuss to the group the process of
solving.
4. First group to finish will receive 5 points, followed by 4 and 3 points.
5. When all groups finished the task after 5 minutes, the leader will choose to pick a
popsicle stick that number 1-10 in order to identify who among the members to
explain their answer which will be rated by the other group guided with the rubrics.

24. RUBRICS
Criteria Percentage
Accuracy of the solution 20%
Delivery (clear and
audible
15%
Presentation (Neatness
and Readable
10%
Collaboration and
Discipline
Total
5%
50%

25. 1.
𝟒
𝟏𝟔𝒙𝟏𝟐𝒚𝟐𝟏 = 𝟐𝒙𝟑𝒚𝟓𝟒
𝒚
2.
𝟖
𝟏𝟎𝟎𝒈𝟖 =
𝟒 𝟐
𝟏𝟎𝟐𝒈𝟒 =
𝟒
𝟏𝟎𝒈𝟐
3.
𝟓𝒙𝟕
𝟔𝟎𝒙𝟒 =
𝟓⋅ 𝒙𝟔⋅𝒙
𝟒⋅𝟏𝟓𝒙𝟒
=
𝟓⋅𝒙 ⋅ 𝒙𝟔
𝟒⋅𝒙𝟒 ⋅ 𝟏𝟓
=
𝒙𝟑 𝟓⋅𝒙
𝟐𝒙𝟐 𝟏𝟓

26. CREDITS: This presentation template was created by Slidesgo, and includes icons by
Flaticon, infographics & images by Freepik and content by Swetha Tandri
ASSESSMENT
Instructions: Simplify the following expressions using laws of
exponents. 5 points Each.
𝟏. 361 =
2.
12
16𝑐16 =
3. 𝟑.
4𝑎5
𝑏6 =

27. CREDITS: This presentation template was created by Slidesgo, and includes icons by
Flaticon, infographics & images by Freepik and content by Swetha Tandri
ASSESSMENT
Instructions: Simplify the following expressions using laws of exponents.
𝟏. 361 = 92 = 19
2.
12
16𝑐16 =
3 4
24𝑐4 =
3
2𝑐4
𝟑.
4𝑎5
𝑏6 =
4𝑎5
𝑏6
=
4𝑎4⋅𝑎
𝑏6
=
2𝑎2 𝑏6
𝑏3

28. Assignment
A.Simplify radical expressions using laws of radical.
1. 45𝑝2
2.
3
2𝑑2
3. 10
4
32
4. 36𝑥2𝑦3𝑧
5. 5𝑥4𝑦2 4
25
𝑥20𝑦30

29. END OF PRESENTATION