TEACHERS’ SYMPOSIUMIN-DEPTH UNDERSTANDING OF KPUP

MATHEMATICS

June 13, 2014

Mr. Marjune M. Nepaya

KNOWLEDGE QUESTIONS

QUESTION NO.1

LEARNING COMPETENCY

Illustrates quadratic equations.

KNOWLEDGE QUESTION

Which of the following is NOT a quadratic equation?A. B. C. D.

The correct answer is B. The equation is linear. 

QUESTION NO.2

Illustrates situations that involve the following variations:

(a) direct; (b) inverse;(c) joint; (d) combined.

LEARNING COMPETENCY

KNOWLEDGE QUESTION

2 4 5 91 2 2.5 4.5

What type of variation is illustrated by the table?

A. Direct C. Direct SquareB. Inverse D. Joint

The correct answer is A. From the given table,

QUESTION NO.3

Identifies trapezoids and kites.

LEARNING COMPETENCY

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.

PROCESS QUESTIONS

QUESTION NO.1

LEARNING COMPETENCY

applies the theorems to show that given triangles are similar

PROCESS QUESTION

Given Find the perimeter of .

6

B

A

8

4C

D

FE

4

The answer is 9.

SOLUTIONS

1.  

2. Use the idea that the corresponding sides of similar triangles are proportional to find and , then add all the measures of the sides of DEF to find the perimeter of the triangle.

QUESTION NO.2

LEARNING COMPETENCY

Solves problems involving quadratic functions.

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. C. B. D. Since if gives 5,000 . The answer is D.

QUESTION NO.3

LEARNING COMPETENCY

Uses trigonometric ratios to solve real-life problems involving right triangles.

PROCESS QUESTION

The angle of elevation at the top of a building is . 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 mThe answer is A.

UNDERSTANDING QUESTIONS

QUESTION NO.1

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.

ESSENTIAL QUESTION

How can various real-life situations involving maximum and minimum values can be solved and analyzed?

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:

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 week2. 160 casings for the second week3. 185 for the third week4. 210 for the fourth week

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

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.

SITUATION C

The number of items sold per week are as follows:1. 135 casings for the first week2. 130 casings for the second week3. 117 casings for the third week4. 85 casings for the fourth weekPrice per week 150 165 180 195

Revenue for selling cellphone casing

3 375 5 200 6 435 5 950

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?

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?

QUESTION NO.2

ESSENTIAL UNDERSTANDING

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

ESSENTIAL QUESTION

What is the best way to solve problems involving similar triangles?

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, stickGiven:Length of the stick = 3 mLength of the stick’s shadow = 1.5 mLength of the building’s shadow = 8 m

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, selfGiven:Height from the ground to your eyes = 150 cmDistance of your feet from the middle of the mirror = 100 cmDistance from the middle of the mirror to a point directly under the traffic signal = 450 cm

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 stickGiven:Look for any post which can be measured with the use of a meter stick.Consider the illustration below.

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?

PRODUCT/ PERFORMANCE

QUESTIONS

QUESTION NO.1

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.

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.

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?

SCORING RUBRIC

Criteria4

Excellence3

Proficient

2Progressin

g

1Beginning

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 Computations

Computations are accurate and supported with correct and clear interpretation.

Computations are accurate and supported with correct interpretation

Computations are correct but interpretation is incorrect.

Most of the computations and interpretations are erroneous.

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

SCAFFOLD FOR TRANSFER

DIRECTED PROMPTOPEN PROMPTGUIDED TRANSFERINDEPENDENT TRANSFER (PERFORMANCE TASK)

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?

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?

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.

QUESTION NO.2

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.

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.

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?

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?

SCORING RUBRIC

Criteria4

Excellence3

Proficient

2Progressin

g

1Beginning

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

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

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.

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?

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.

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.

THANK YOU FOR LISTENING!