New Grading System for K to 12

1. TEACHERS’ SYMPOSIUM
IN-DEPTH UNDERSTANDING OF
KPUP
MATHEMATICS
June 13, 2014
Mr. Marjune M. Nepaya

2. KNOWLEDGE
QUESTIONS

3. QUESTION NO.1

4. LEARNING COMPETENCY
Illustrates quadratic
equations.

5. KNOWLEDGE QUESTION
Which of the following is NOT a
quadratic equation?
A. 2𝑥2
= 3
B. 2𝑥 + 5 = 7
C. 4 𝑥2
− 5 = 7𝑥
D.
𝑥2
2
= 4 5
The correct answer is B. The equation is linear.

6. QUESTION NO.2

7. Illustrates situations that
involve the following
variations:
(a) direct; (b) inverse;
(c) joint; (d) combined.
LEARNING COMPETENCY

8. KNOWLEDGE QUESTION
𝑥 2 4 5 9
𝑦 1 2 2.5 4.5
What type of variation is
illustrated by the table?
A. Direct C. Direct Square
B. InverseD. Joint
The correct answer is A. From the given table,
y varies directly as x.

9. QUESTION NO.3

10. Identifies trapezoids and
kites.
LEARNING COMPETENCY

11. KNOWLEDGE QUESTION
When comparing a trapezoid and a kite, one
similarity is:
A. They both have congruent diagonals.
B. They both have at least one set of parallel
sides.
C. They both have four congruent sides.
D. They both have four sides.
The correct answer is D. Trapezoid and kites are
quadrilaterals so they both have four sides.

12. PROCESS
QUESTIONS

13. QUESTION NO.1

14. LEARNING COMPETENCY
 applies the theorems to show
that given triangles are similar

15. PROCESS QUESTION
Given ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹. Find the perimeter of ∆𝐷𝐸𝐹.
6
B
A
8
4
C
D
FE
4
The answer is 9.

16. SOLUTIONS
1.
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐴𝐵𝐶
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐷𝐸𝐹
=
𝐴𝐵
𝐷𝐸
18
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐷𝐸𝐹
=
8
4
8 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐷𝐸𝐹 = 72
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐷𝐸𝐹 = 𝟗
2. Use the idea that the corresponding sides of similar
triangles are proportional to find 𝐷𝐹 and 𝐸𝐹, then add
all the measures of the sides of ∆DEF to find the
perimeter of the triangle.

17. QUESTION NO.2

18. LEARNING COMPETENCY
 Solves problems involving
quadratic functions.

19. PROCESS QUESTION
The Brgy. Captain of Barangay Punta is
planning to fence their playground with an
existing wall on one side. As an engineer
of the Barangay, you are tasked to
compute the maximum area that can be
fenced using the available 200 feet fencing
material. What should the maximum area
be?
A. 2000 𝑓𝑡2
C. 3500 𝑓𝑡2
B. 3000 𝑓𝑡2
D. 5000 𝑓𝑡2
Since if 𝑙 = 50, 𝑡ℎ𝑒 𝐴 = −2𝑙2 + 200𝑙
gives 5,000 𝑓𝑡2. The answer is D.

20. QUESTION NO.3

21. LEARNING COMPETENCY
 Uses trigonometric ratios to
solve real-life problems
involving right triangles.

22. PROCESS QUESTION
The angle of elevation at the top of a
building is 50°. If the observer is 90
m from the base of the building, how
high is the building?
A. 107.26 m C. 100.32 m
B. 68.94 m D. 57.85 m
The answer is A.

23. UNDERSTANDING
QUESTIONS

24. QUESTION NO.1

25. ESSENTIAL UNDERSTANDING
Students will understand that
the determination of the
maximum and minimum values
in certain real life problems
depends on the correct use and
solutions of quadratic functions.

26. ESSENTIAL QUESTION
 How can various real-life
situations involving maximum
and minimum values can be
solved and analyzed?

27. SITUATION A
Renee sells cellphone casing at Php 150 each which
she bought originally for Php 125 only. Below is a
table of Renee’s sales for one month.
Number of casings sold per week at
Php 150 each
140 145 160 148
Revenue for selling cellphone
casing
3 500 3 625 4 000 3 700
Note: 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑆𝑎𝑙𝑒𝑠 − 𝐶𝑎𝑝𝑖𝑡𝑎𝑙

28. SITUATION B
Jocille sells cellphone casing at Php 150 each which
she bought originally for Php 125 only. She thought of
maximizing the number of casings sold by decreasing
the price every week by 5 pesos for one month. The
number of casing sold per week as follows:
1. 140 casings for first week
2. 160 casings for the second week
3. 185 for the third week
4. 210 for the fourth week

29. SITUATION B
Below is the table of Jocille’s sales for one month.
Price per week 150 145 140 135
Revenue for selling cellphone
casing
3 500 3 200 2 775 2 100

30. SITUATION C
Jade owns an accessory store in the City. Her most
saleable item is the cellphone casing. The store sells
an average of 140 pieces per week where each item
is sold at Php 150 which she originally bought for Php
125. She plans to raise the price to maximize the
sales by Php 15 per week starting on the second
week of the month. After the second week’s increase,
she observed that fewer casings were not sold.

31. SITUATION C
The number of items sold per week are as follows:
1. 135 casings for the first week
2. 130 casings for the second week
3. 117 casings for the third week
4. 85 casings for the fourth week
Price per week 150 165 180 195
Revenue for selling cellphone
casing
3 375 5 200 6 435 5 950

32. PROCESS QUESTIONS
 What is the maximum revenue for the one
month? At what price?
 What is the total revenue for one month?
 Using the table of values, draw a scatter plot
of each of the girls’ sales for the whole
month.
 What trend can you see? Is it quadratic or
linear?
 What quantity is represented in the y-axis?
 What is represented in the x-axis?

33. PROCESS QUESTIONS
 Write an equation to model the data in each
situations.
 Give a reasonable domain and range of your
model.
 Can each of the girls continue on increasing the
price per week? What will happen if they keep
on increasing the price? Why?
 What determines a maximum profit?
 How does one ensure a maximum profit?
 How can various real-life situations involving
maximum and minimum values can be solved
and analyzed?

34. QUESTION NO.2

35. ESSENTIAL UNDERSTANDING
Students will understand that
problems involving triangle
similarity can be solved
through appropriate and
accurate representations.

36. ESSENTIAL QUESTION
What is the best way to solve
problems involving similar
triangles?

37. SITUATION A: USE YOUR SHADOW
Suppose you want to use the shadow method to
measure the height of a building. You make the
following measurements.
Materials: measuring device, stick
Given:
Length of the stick = 3 m
Length of the stick’s shadow = 1.5 m
Length of the building’s shadow = 8 m

38. SITUATION B: MIRROR YOURSELF
Suppose you want to find the height of a traffic light
for a very important purpose but your measuring
devices are limited. You only have the following.
Materials: mirror, self
Given:
Height from the ground to your eyes = 150 cm
Distance of your feet from the middle of the mirror =
100 cm
Distance from the middle of the mirror to a point
directly under the traffic signal = 450 cm

39. SITUATION C: MEASURE MEASURE
Suppose you want to use the shadow method to
measure the height of a building with the use of a
shorter post. You make the following measurements.
Materials: meter stick
Given:
Look for any post which can be measured with the
use of a meter stick.
Consider the illustration below.

40. PROCESS QUESTIONS
What concept would you use to solve
each of the given problem? Justify
your answer.
Why is it important to know how to
measure things indirectly?
What are the advantages of
estimation?
What is the best way to solve
problems involving similar triangles?

41. PRODUCT/
PERFORMANCE
QUESTIONS

42. QUESTION NO.1

43. TRANSFER GOAL
Students on their own will be
able to investigate and solve
real life problems involving the
determination of maximum and
minimum values thereby using
math as a tool for making
decisions and
recommendations.

44. PRODUCT/ PERFORMANCE
ASEAN 2015 brings life to a country’s
tourism. You are an ARGF travel and tour
agent. You are tasked to make promo
packages for the different Asian tourists.
You are to present a written report of your
proposal to your manager. The proposal
should demonstrate practicality, accuracy,
authenticity and application of concepts
on quadratic functions.

45. PROCESS QUESTIONS:
What are the important factors did you
consider which contributed to the
success of this task?
To what extent is your knowledge, skills
and understanding of quadratic
functions have helped you perform the
task?
How can various real-life situations
involving maximum and minimum
values be solved and analyzed?

46. SCORING RUBRIC
Criteria
4
Excellence
3
Proficient
2
Progressing
1
Beginning
Authenticity of
Data
The data used
are authentic
and updated.
Data are taken
from reliable
resources.
The data
used are
authentic.
Data are
taken from
reliable
resources.
Some of
the data
used are
not
authentic.
Data are
not useful
and
relevant.
Accuracy of
the
Computatio
ns
Computations
are accurate
and supported
with correct
and clear
interpretation.
Computations
are accurate
and supported
with correct
interpretation
Computatio
ns are
correct but
interpretati
on is
incorrect.
Most of the
computations
and
interpretations
are
erroneous.

47. Practicality
of Proposal
The amount
of the price
increase is
realistic and
yield
maximum
profit.
The amount
of the price
increase is
realistic and
yields
profit.
The
amount of
the price
increase is
realistic but
yields
minimal
profit.
The amount
of the price
increase is
unrealistic
and does not
yield profit.
Application
of the
Concepts of
Quadratic
Equations
The quadratic
equation
created is
correct with
additional
model to
support it.
The
quadratic
equation
created is
correct.
The quadratic
equation
created does
not use the
defined
variables.
The quadratic
equation
used is
incorrect.
SCORING RUBRIC

48. SCAFFOLD FOR TRANSFER
DIRECTED PROMPT
OPEN PROMPT
GUIDED TRANSFER
INDEPENDENT TRANSFER
(PERFORMANCE TASK)

49. DIRECTED PROMPT
The students will be ask to look at pictures and
identify real life experience that they can associate
with the given pictures. After which, answer the
process questions that follow:
 Name real life situations that are represented by
each pictures.
 What is common among pictures?
 How does each picture show the use of quadratic
equations?
 Can you name other real life experiences that use
the concepts of quadratic equations like the one
shown in the pictures?

50. OPEN PROMPT
The students will now extend their learning by
interviewing any person in any field where quadratic
equations can be used. They will be asking the
interviewee questions that pertain to the importance
of parabolic paths in the given field.
They may use the following questions in the
interview:
1. Name some math skills that you utilize in your
work. Why are these skills very important?
2. How do you use quadratic equations in doing your
work?
3. Why do you use parabolic paths in doing your
work?

51. GUIDED TRANSFER
Apple Company has releases its new i-phone in the
market with a suggested retail price of Php 35, 500.
Many consumers are waiting for this model because
of its unique and more advanced features. You are
working as a marketing manager of the i-store, one of
its dealer stores. As the marketing manager , it is your
responsibility to maximize the sales and profit for four
months, making sound recommendations regarding
the pricing of the product. It has been observed in the
3rd week of the first month that for every Php 300
increase in the suggested retail price, 3 fewer
customers will not buy the product. The proposal
must be accurate in computations, and represented
using a model.

52. QUESTION NO.2

53. TRANSFER GOAL
The students on their own
will be able to investigate
and solve real problems
involving scaling of objects
thereby using math as a
tool in making decisions
and recommendations.

54. PRODUCT/ PERFORMANCE
The Sto. Nino Church is one of the historical and
biggest churches in Leyte where many devotees
praise the holy child Jesus, Sto. Nino. Last
November 08, 2013 typhoon Yolanda hit Leyte and
devastated the church. Since you are one of the
best architects in the province, you were asked by
the archbishop John F. Du, of the archdiocese of
Palo to make a blue print for the new design of the
church. The blue print must be neat and complete,
the measurements must be accurate and realistic
and there should be appropriateness of the
concept used.

55. PROCESS QUESTIONS
What is the situation all about?
Do you think you can accomplish
the task within the given time?
What attitudes should you
possessed to accomplish the task?
What figure will you use to create
the design of the blue print?

56. PROCESS QUESTIONS
Does the concepts of the triangle
similarity necessary in creating the
design/blueprint?
How did the concept of similarity of
triangles help you in creating your
design/blue print?
What theorem in triangle similarity did
you apply in the scaling of the
measurements of the objects in the
blueprint?
How can we solved problems involving
scaling of objects?

57. SCORING RUBRIC
Criteria
4
Excellence
3
Proficient
2
Progressing
1
Beginning
Completeness
of the output
The blueprint
contains all the
parts and the
labels/legends
are more
specified
The blueprint
contains all the
parts and the
labels/legends
are specified
The blueprint
contains all
the parts and
the labels/
legends are
not clearly
specified
The blueprint
lacks some
parts and the
labels/ legends
are not clearly
specified
Neatness of
the output
There are no
erasures, the
figures are clear,
and the
cleanliness of the
whole output is
properly
observed
There are no
erasures, the
figures are
not so clear,
and the
whole output
is clean
There are no
erasures, the
figures are
not so clear
and the
whole output
is not so
clean
There are some
erasures, the
figures are not
clear and the
whole output is
not clean

58. SCORING RUBRIC
Accuracy of
measurements
The accuracy of
measurement is
well-presented
realistically and
appropriately
The
measurement
is accurate,
realistic and
appropriate
The
measurement
is accurate,
realistic but
inappropriate
The
measurement
is inaccurate,
unrealistic and
inappropriate
Relevance to the
concept being
applied
The concept
of triangle
similarity is
shown
beyond its
application
The
concepts of
triangle
similarity is
correctly
applied in
making the
output
The
concepts on
triangle
similarity are
not correctly
applied
The concepts
on triangle
similarity are
not applied

59. DIRECTED PROMPT
The students will be ask to look at pictures and
identify real life experience that they can associate
with the given pictures. After which, answer the
process questions that follow:
 Name real life situations that are represented by
each pictures.
 What is common among pictures?
 How does each picture show the use of triangle
similarity?
 Name real life experiences that use the concepts
of triangle similarity like the one shown in the
pictures.

60. OPEN PROMPT
The students will be given options
of works that involves triangle
similarity (surveyor, architects-
designer, engineer-planner).
Among the three options which do
you think would you like to
become? And why?

61. GUIDED TRANSFER
You are a newly hired designer of a company
who develops condominiums and housing
projects. The company is presently preparing
for a bidding to develop a condominium with a
floor area of 70 square meters. You are
tasked by your superior to make a two
dimensional design of all the faces of a
condominium. It is important for you to show
similar triangles to make your design
appealing. You need also to solicit ideas from
others to improve your work.

62. GUIDED TRANSFER
You may post your work to any social
networking sites to solicit comments
for improvement or you present your
work to the higher officers of the
company for approval.

63. THANK YOU FOR LISTENING!