Lesson Guide. Elementary Mathematics Grade 4

Transcription

1 Lesson Guide In Elementary Mathematics Grade 4 Chapter IV Measurement Comprehension of Perimeter DEPARTMENT OF EDUCATION BUREAU OF ELEMENTARY EDUCATION in coordination with ATENEO DE MANILA UNIVERSITY 2010 Reformatted for distribution via DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011

2 Lesson Guides in Elementary Mathematics Grade 4 Copyright 2003 All rights reserved. No part of these lesson guides shall be reproduced in any form without a written permission from the Bureau of Elementary Education, Department of Education. The Mathematics Writing Committee GRADE 4 Region 3 Evelyn H. Magpayo Pampanga Myrna Vicente Nueva Ecija Ester Ramones Tarlac Virgie Costales - Zambales Region 4 A (CALABARZON) Flordeliza D. Yamo Laguna Araceli C. Montoya San Pablo City Estelita Q. del Rosario Cavite City National Capital Region (NCR) Remylinda T. Soriano Manila Maria Brucal Makati Lina Seña Taguig/Pateros Analee Pacaña Pasig/San Juan Bureau of Elementary Education (BEE) Rogelio O. Dones Leony M. Achacoso Zosima C. Ventura Ateneo de Manila University Eva Marie Guevarra Support Staff Ferdinand S. Bergado Ma. Cristina C. Capellan Emilene Judith S. Sison Julius Peter M. Samulde Roy L. Concepcion Marcelino C. Bataller Myrna D. Latoza Eric S. de Guia Illustrator Consultants Fr. Bienvenido F. Nebres, SJ President, Ateneo de Manila University Carmela C. Oracion Ateneo de Manila University Pacita E. Hosaka Ateneo de Manila University PROJECT MANAGEMENT Yolanda S. Quijano Director IV Angelita M. Esdicul Director III Simeona T. Ebol Chief, Curriculum Development Division Irene C. de Robles OIC, Asst. Chief, Curriculum Development Division Virginia T. Fernandez Project Coordinator EXECUTIVE COMMITTEE Jesli A. Lapus Secretary, Department of Education Jesus G. Galvan OIC, Undersecretary for Finance and Administration Vilma L. Labrador Undersecretary for Programs and Projects Teresita G. Inciong Assistant Secretary for Programs and Projects Printed By: ISBN x

3 TABLE OF CONTENTS Introduction... iv Matrix... v IV. MEASUREMENT A. Comprehension of Perimeter Perimeter of a Triangle... 1 Perimeter of a Polygon... 4 Solving Problems on Perimeter... 8 iii

4 I N T R O D U C T I O N The Lesson Guides in Elementary Mathematics were developed by the Department of Education through the Bureau of Elementary Education in coordination with the Ateneo de Manila University. These resource materials have been purposely prepared to help improve the mathematics instruction in the elementary grades. These provide integration of values and life skills using different teaching strategies for an interactive teaching/learning process. Multiple intelligences techniques like games, puzzles, songs, etc. are also integrated in each lesson; hence, learning Mathematics becomes fun and enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are incorporated in the lessons. The skills are consistent with the Basic Education Curriculum (BEC)/Philippine Elementary Learning Competencies (PELC). These should be used by the teachers as a guide in their day-to-day teaching plans. iv

5 MATRIX IN ELEMENTARY MATHEMATICS Grade IV COMPETENCIES VALUES INTEGRATED STRATEGIES USED IV. MEASUREMENT A. Comprehension of Perimeter MULTIPLE INTELLIGENCES TECHNIQUES 1. Find the perimeter of polygons 1.1 triangle 1.2 quadrilateral 1.3 pentagon, etc. 2. Derive a formula for finding the perimeter of polygon 3. Application of Perimeter 3.1 Solve word problems involving perimeter measures Conservation of trees Accuracy Accuracy Accuracy Cooperation and accuracy Concept development Write equation Using estimation Develop formula Concept development Write equation Develop formula Concept development Write equation Polya s strategy Hands-on activities, Manipulative, Reading, Writing, Completing tables, Illustration, Diagram, Cooperative groups, Nature Drawing, Reading, Diagram, Hands-on activities, Cooperative groups, Manipulative Diagram, Geometry, Illustrating, Independent study v

6 Perimeter of a Triangle I. Learning Objectives Cognitive: Psychomotor: Affective: 1. Find the perimeter of a triangle 2. Derive a formula for the perimeter of a triangle Measure the perimeter of a triangle Tell the importance of tree conservation II. Learning Content Skills: Reference: Materials: Value: 1. Finding the perimeter of a triangle 2. Deriving a formula for the perimeter of a triangle BEC-PELC IV.A.1 Grade School Mathematics 4 Mastering Mathematics 4 TM pp Mastering Math 4 TX pp modules or illustrations of triangles, ruler Conservation of trees III. Learning Experience A. Presentation 1. Drill Drill on adding numbers mentally Example: Review Review on identifying the different kinds of triangle. Show models of triangle. (scalene, right, equilateral) - What kind of triangle is this? (right triangle) - Why? Because it has a right angle. (Do the same with the other kinds of triangle.) 3. Motivation Let s determine the sum of the sides of each triangle in centimetres. (Write the answers of each group on the board.) Let s see who got the correct answers. 1

7 B. Developmental Activities 1. Presentation a. Provide each group with the same size of triangles. b. Ask the pupils to do actual measurements of the sides of the triangles and take the sum of the sides. c. Compare the results of their measurements and computations. d. Tell the class that what they have measured is the perimeter of a triangle. e. So, can you think of a formula for finding the perimeter of a triangle? (P = S1 + S2 + S3) Don Mario has a triangular piece of land that is planted with coconut trees. He wants to enclose it with a fence. How long will his fence be if the sides measure 24 metres, 18 metres and 20 metres? What is the perimeter of his land? Illustrate his piece of land. 2. Fixing Skills a. Find the perimeter of each triangle. Triangle S 1 S 2 S 3 Perimeter 1 5 cm 4 cm 3 cm cm 2 12 m 21 m 15 m m 3 10 dm 8 dm 12 dm dm b. Give the pupils a set of 3 triangles. Use a ruler to measure the sides. Find the perimeter in centimeters. Use the formula in finding the perimeter of a triangle. 1) 2) 3) Valuing: Do you know what a coconut tree is? Is this tree important? Why? Why is this tree referred to as a tree of life? What do you think we should do to this tree? Why? c. Find the perimeter of the following. Use the formula you have learned. 1) A triangle whose sides measure 12 cm, 15 cm and 10 cm 2) A triangle whose sides measure 20 cm, 18cm and 13 cm 3) A triangle whose sides measure 25 cm, 28 cm and 22 cm 3. Generalization What is a perimeter? (A perimeter is the sum of the length of the sides of a polygon. A perimeter is the distance around a polygon) How do you find the perimeter of a triangle? (By adding all its sides) What is the formula for finding the perimeter of a triangle? P = S 1 + S 2 + S 3 where S 1, S 2, and S 3 are the lengths of the sides of the triangle. 2

8 C. Application 1. a. Distribute cutouts of triangles of different sizes. b. Measure all the sides. c. Find the perimeter. Triangle A : Side 1 cm Side 2 cm Side 3 cm Perimeter cm Triangle B : Side 1 cm Side 2 cm Side 3 cm Perimeter cm Triangle C : Side 1 cm Side 2 cm Side 3 cm Perimeter cm 2. An equilateral triangle has a perimeter of 48 centimetres. What is the length of one side? 3. A triangle has a perimeter of 56 dm. The lengths of two sides are 24 dm and 18 dm. How long is the third side? IV. Evaluation A. Fill in the blanks below. 1. Perimeter = 18 dm + 12 dm + 10 dm P = dm 2. Perimeter = 10 m + 10 m + 12 m P = cm 3. Perimeter = 15 cm + 15 cm + 15 cm P = m 4. Perimeter = 8 m + 5 m + 11 m P = cm 5. Perimeter = 12 cm + 12 cm + 12 cm P = cm B. Complete the table below. Triangle S 1 S 2 S 3 Perimeter 1 14 m 15 m 16 m 2 10 cm 12 cm 14 cm 3 18 cm 5 cm 15 cm 4 12 cm 10 cm 15 cm 5 15 mm 20 mm 20 mm 3

9 C. Find the perimeter of each triangle below. Show how you found the perimeter using the formula V. Assignment Bring to class 5 cutouts of triangles with the measurements of sides. Let their partners find the perimeter of each triangle. Perimeter of a Polygon I. Learning Objectives Cognitive: Psychomotor: Affective: 1. Derive a formula for the perimeter of a polygon 2. Find the perimeter of a polygon Measure the perimeter of a polygon Show accuracy in measuring II. Learning Content Skills: Reference: Materials: Value: 1. Deriving a formula for the perimeter of a polygon 2. Finding the perimeter of a polygon BEC-PELC IV.A.1.2 textbook, real objects, diagrams, illustration, cut outs of polygons, meter stick, tape measure Accuracy III. Learning Experience A. Preparatory Activities 1. Drill Identifying polygons by means of a guessing game Example: I am a polygon with four equal sides. Who am I? 2. Review Ask what unit of measure is appropriate for objects such as these: distance between buildings 4

10 sides of a handkerchief safety pin 3. Motivation Show a plain handkerchief. Do you carry your handkerchiefs everyday? Why? What are the uses of a handkerchief? B. Developmental Activities 1. Presentation a. Show a piece of lace and a square handkerchief. If I m going to sew lace around my handkerchief would this lace be enough? Get the children s opinion. What are we going to do to be sure that the length of the lace is enough? Let the pupils measure the sides and compute for the distance around. Ask what they measured and why. Tell them to describe what they measured leading them to use the phrase distance around. Introduce the term perimeter for this distance. Have the pupils illustrate the object (handkerchief) on the board with the corresponding measures and ask one pupil to write the number sentence for this. ( ) or (4 x 25) The formula in finding the perimeter of a square is P=S + S + S + S or P = 4 x S b. Show a picture frame hanging in the classroom. What is the shape of the picture frame? (rectangle) Measure the sides of the frame. What can you say about the lengths? the widths? To find the perimeter, just add the sides. The formula in finding the perimeter of a rectangle is P=L + W + L + W or P = (2 x L) +(2 x W) or P = 2 x (L + W) c. Show some polygons to be measured and have them compute the perimeter. Example: P = P = = 32 cm = 50 cm How do you measure the perimeter of the other polygons? 5

11 2. Fixing Skills a. Find the perimeter of each figure. b. Group the pupils into 4 groups and have them find the perimeter of the following: 1) their classroom(sides of the room) 2) a table top 3) a pupil s desk top 4) chalk board In each case, they will have to decide on the appropriate unit of measurement. What do you mean by the word appropriate? What is the other term for appropriate? Why do we have to be accurate in measuring things? 3. Generalization Perimeter is the distance around an object or figure. The perimeter of a polygon is the sum of the lengths of its sides. C. Application 1. Have the pupils draw a rectangle. Ask them to measure the perimeter and record it. 2. Let the pupils draw the diagonal of the rectangle. Instruct them to cut the rectangle along its diagonal and arrange the parts to form a triangle. 3. Let them measure the perimeter of the triangle and record it. Discuss why the perimeter is now bigger. (Longer sides are on the outside.) 6

12 4. Let the pupils rearrange the two triangles to form a parallelogram. Have them measure its perimeter and compare this with the first two perimeters. 5. A quadrilateral has a perimeter of 47 dm. The length of the 3 sides are 11 dm, 14 dm, and 7 dm. What is the length of the fourth side? IV. Evaluation A. Give the perimeter of each figure. 1) 2) 3) 10 cm 8.5 cm 15 cm 7 cm 12.5 cm 4) 5) B. Find the perimeter. Use the formula. S = 5 cm Formula Perimeter L = 20 cm W = 10 cm S = 4 cm 15 cm 12 cm 7

13 V. Assignment Make cutouts of polygons. Write the measurement of each side. Solve for the perimeter. Solving Problems on Perimeter I. Learning Objectives Cognitive: Psychomotor: Affective: Solve word problems involving perimeter measure Solve word problems with accuracy Participate actively in group work II. Learning Content Skill: References: Materials: Values: Solving word problems involving perimeter measure BEC-PELC IV.A Mastering Mathematics 4 TX p ; TM p picture chart, pocket chart, flash cards Cooperation and accuracy III. Learning Experience A. Preparatory Activities 1. Drill What formula do we use to find the perimeter of a: - rectangle - triangle - pentagon - square - rhombus - octagon Find your answers in the pocket chart. 2. Review 3. Motivation What must be remembered in solving word problems? What are these steps? Who comes to school by just walking? How far do you walk from your home to the school? Do you know how to find it? 8

14 B. Developmental Activities 1. Presentation Vince walked from his house to the school, then to the market, and then back home. How far did he walk? house school market a. What distances are given in the problem? b. What is asked in the problem? c. What is the word clue? d. What process is needed to solve the problem? e. What is the number sentence? f. What is the answer to the problem? Another example: A rectangular lot has a length of 20 m and a width of 18m. What is it perimeter? What is asked? What are given? What is the process to be need? What is the mathematical sentence? What is the answer? 2. Fixing Skills We will have our groupings now. What will you do while working? Each group will solve a problem. Follow the steps in problem solving. Post the manila paper on the board for checking. a. First Group Sonny walked around a small basketball court. The rectangular court is 8 metres long and 4 metres wide. What is the perimeter of the rectangular court? b. Second Group Jay enclosed his vegetable garden with a fence. The five sides of the garden measure 10, 12, 12, 14 and 8 metres respectively. How long is the fence? c. Third Group An equilateral triangle has a perimeter equal to the perimeter of a rectangle whose length is 12 m and whose width is 8.7 m. Find the measurements of the sides of the equilateral triangle. 9

15 d. Fourth Group A perimeter of a square is 48 cm. What is the length of one side? 3. Generalization How do we solve word problems? How do we get the perimeter of a polygon? C. Application To solve word problems, we follow the steps in solving word probles and then apply the formula to find the perimeter of a particular plane figure. Solve this word problem by yourself. For your project in EPP, you make a square frame that measures 45 centimetres on one side. What is the perimeter of the frame? IV. Evaluation Solve the word problems. Follow the steps in problem solving. 1. Jocelyn s rectangular flower garden has a length of 10 metres and a width of 6 metres. Find the perimeter of the garden. 2. One side of a square playground of San Isidro Central School measures 120 metres. How many metres of chicken wire are needed to enclose the playground? 3. There are 15 regular hexagonal poster frames in Willy s gallery. Each side of the frame is 22 cm long. How much wood had been used for the frames? 4. A rectangular tablecloth is 225 cm long and 95 cm wide. How long is the lace needed to put as an edging for the tablecloth? 5. A softball diamond is 20 metres long on each side. How many metres does a player run if he makes a homerun? V. Assignment A. Solve the following: 1. Rex bought an octagonal mirror with each side measuring 25 cm. What is the perimeter of the mirror? 2. Jelleni jogs around a triangular park which measures 425 metres, 350 metres and 435 metres. How far will she jog if she goes around the park twice? B. Make 2 word problems involving any of the polygons learned. 10