Tg New 4th Rating

5 MATHEMATICS TEACHER’S GUIDE

UNIT 4

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Lesson 81: Visualizes Area of a circle Week 1 Objectives:

Visualize the area of a circle Identify the diameter and radius of the circle Illustrates circle with different radii Find enjoyment in doing the activity

Prerequisite Concepts and Skills:  

Visualizing the area of a circle Knowledge about measuring instrument

Materials: chart, ruler, real circle objects, pencil, compass References: XL Excelling in Mathematics 5 Mathematics 5 &6 Lesson Guides

http://www.mathgoodies.com/lessons/vol2/challenge_unit2.html http://www.slideshare.net/GradeSix1/lp-circle Code: M5ME –Iva 72

Instructional Procedure: A. Preliminary Activities 1. Drill Have the pupils identify which of these is a circle

2. Review Have a review on solving problems involving circumference of a circle. Review the formula, give examples, and then give exercises for the pupils to do. 3. Motivation Ask the pupils Is a circle a polygon? Why? and why not? B. Developmental Activities 1. Presentation A. Have the pupils observe the circles below Take a look at each of the circles. Do you find any line segments?

A circle is a plane closed figure. That is not made out of line segments so, it is not a polygon. A circle is named by its center.

2

2. Performing the Activities Group Activity Divide the class into five groups. Distribute the cue card and let them answer the cards. Let them discuss. Use circle cero to complete the following statements:

1. 2. 3. 4.

The distance from point O to point F is __________. The distance from point O to point M is __________. The distance from point O to point G is __________. If point G, O and F lie on one line, the distance from point G to F is _______.

B. Have the pupils observed the circle. Introduce the Radius and Diameter of a circle. Show examples of radius that are connected to the tangent and from a center. Use compass in drawing a circle. 3. Processing the Activities After the presentations of each group, ask: how did you find the activity? Did you able to visualize the area of the circle? What value is developed in performing the activity? Expected Answers:  A little bit confusing  Yes by listening to the teacher explanation  Enjoyment and Cooperation 4. Reinforcing the Concept and Skill Ask the pupils to answer the activity under Get Moving on page ___ LM Math Grade V. Ask them also to answer the activity under Keep Moving on page ____ LM Math Grade V. 5. Summarizing the Lesson Lead the pupils to give the following generalization.     

A circle is a set of all points in a plane that are at fixed distance from a point called center. A radius is a line segment from the center to a point on the circle. A diameter is a line segment which passes through the center of a circle whose endpoints are on the circle. The length of radius is one half the length of a diameter of a circle. A compass is an instrument used to draw circles.

6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page _____ LM Math Grade V. 3

C. Assessment Use a real compass or an improvised one to draw circle with these given radii. 1. 1 cm 2. 1.5 cm 3. 2.5 cm 4. 6 cm 5. 5 cm D. Home Activity Refer to circle O. Explain why line segment OP and OQ do not form a diameter?

Remediation Provide exercises similar to those given in the lesson. If the problem is on the mastery of the area of a circle. Enrichment Use the circle O. to answer the following. a. Name the two diameters 1. 2. b. Name six radii. 1. 2. 3. 4. 5. 6.

Lesson 82: Derives a formula in finding the area of a circle Week 1 Objectives:

Derives a formula in finding the area of a circle Illustrates circle with different orientation Find enjoyment in doing the activity

Prerequisite Concepts and Skills:  

Deriving a formula in finding the area of a circle Knowledge about measuring instrument

Materials: A large, heavy-paper or cardboard circle, about 12" in diameter, scissors, rulers, colored markers or crayons. References:

XL Excelling in Mathematics 5 4

Mathematics 5 &6 Lesson Guides http://www.shastacoe.org/uploaded/Dept/is/scimath/scmp_resources/pdf/march09/DerivingAreaCircle.pdf

Code: M5ME –IVa 73 Instructional Procedure: E. Preliminary Activities 4. Drill Have the pupils cut the circle in any orientation

5. Review Have a review about the parts of the circle. 6. Motivation Ask the pupils If the shape of the circle can be parallelogram

F. Developmental Activities 6. Presentation 1. Discuss with students practical applications for finding the area of a circle. Explain the problems associated with partitioning a circle into unit squares to find its area. Elicit suggestions on how the area might be determined. 2. Pass out the paper circles, scissors, rulers and colored markers or crayons. 3. Have students draw a diameter (it does not need to be exact), and use two different colors to fill in the resulting semicircles. 4. Instruct students to cut the circle in half along the diameter. Then have them cut each of the resulting semicircles in half again. There are now a total of four pieces, two of each color. 5. Ask students to assemble the four pieces, alternating colors, so that they form a shape which resembles a parallelogram

7. Performing the Activities Group Activity. Divide the class into three groups. Distribute the activity card and let them follow the direction written in the activity card. Group A.Have students cut each of the sectors in half, once more, resulting in a total of 8 equal sectors, four of each color.

Ask students to assemble the eight pieces,

alternating colors, so that they form a shape which resembles a parallelogram.

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Group B. Have students cut each of the sectors in half, once more, resulting in a total of 16 equal sectors, eight of each color. Ask students to assemble the sixteen pieces, alternating colors, so that they form a shape which resembles a parallelogram.

Group C. Solicit suggestions as to how to make the shape even more like parallelogram. (This can be achieved by cutting each of the sectors in half over and over again). Note: Do not allow students to create more than 16 sectors since they can become unmanageable.

Explain the following points. 

This is very close to a parallelogram! You can see that the top and bottom are still not perfectly straight … they are definitely a little bumpy. Can you visualize what would happen if we kept going? If we continued to break the circle up into thinner and thinner sectors, eventually, the bumps would become so small that we couldn’t see them, and the top and bottom of the shape would appear perfectly straight.



Now we can use the area formula for a parallelogram to help us find the area of the circle.



(A=b⋅h) The next question is, “How long are the base and height of the parallelogram we made from the circle parts?”



The original circle’s outside perimeter was the distance around, or the circumference of the circle: C=2⋅ π ⋅r

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

Half of this distance around goes on the top of the parallelogram and the other half of the circle goes on the bottom.

This is known as the base of the

parallelogram.



The height of the parallelogram is just the radius of the original circle.



Now let’s substitute the information into the formula for the parallelogram.

8. Processing the Activities After the presentations of each group, ask: how did you find the activity? Did you able to derive a formula in finding the area of the circle? What value is developed in performing the activity? Expected Answers:  A little bit confusing  Yes by listening to the teacher explanation  Enjoyment and Cooperation 9. Reinforcing the Concept and Skill Ask the pupils to answer the activity under Get Moving on page ___ LM Math Grade V. Ask them also to answer the activity under Keep Moving on page ____ LM Math Grade V.

10. Summarizing the Lesson Lead the pupils to give the following generalization.     

Now we can use the area formula for a parallelogram to help us find the area of the circle. The original circle’s outside perimeter was the distance around, or the circumference of the circle Half of this distance around goes on the top of the parallelogram and the other half of the circle goes on the bottom. This is known as the base of the parallelogram. The height of the parallelogram is just the radius of the original circle. Now let’s substitute the information into the formula for the parallelogram.

6. Applying to New and Other Situations 7

Have the pupils do the exercises under Apply your Skills on page _____ LM Math Grade V. G. Assessment Do another guided activity. Let them make their own circle, cut it out into parallelogram and try to find the area of a circle. H. Home Activity Find another polygon that can be derive in finding the area of a triangle.

Lesson 83: Finding the Area of a Given Circle Week 1 Objectives:

Finding the area of a circle Manipulate and measure the diameter and radius of the circle Find enjoyment in doing the activity

Prerequisite Concepts and Skills:  

Mastery in finding the area of a circle Knowledge about measuring instrument

Materials: chart, ruler, real circle objects References: XL Excelling in Mathematics 5 Mathematics 5 & 6 Lesson Guides http://www.mathgoodies.com/lessons/vol2/challenge_unit2.html Code: M5ME –Iva 74

Instructional Procedure: A Preliminary Activities 1 Drill Have a drill on solving multiplication, base and exponents 8x9

7 2

3

12 x 3

4

5

23 x 4

18

3

Review Have a review on solving problems involving circumference of a circle. Review the formula, give examples, and then give exercises for the pupils to do.

3

Motivation Show real circular objects, ask them to give examples of circular things, ask them how circle differ from other objects?

B Developmental Activities 1 Presentation Present this situation to the class. Ask the pupils to read and understand it. Every time it rains, Mrs.Flores saves water in a big clay jar called “Tapayan”. She covers them with a circular galvanized iron with a radius of 5 dm. What is the area of the circular cover? 8

Ask: How will you solve for the problem? 1 Look at the figure of the circle. What is the radius? 2

Explain to the pupils that the ratio of the circumference of a circle to the diameter is the same for all circles. The circumference of any circle is about 3.14 times the diameter. The ratio is represented by the Greek letter

π

spelled pi and pronounced as pie. 3

Let the pupils find the area

A = π r2 = 3.14 x 5 x 5 = 3.14 x 25 Area = 78.50 dm2 2

Performing the Activities Group the pupils into six to eight members per group. Distribute cut outs of circle with dimensions and let the pupils find the area. Call as many pupils to solve for the area of the circle on the board. 8cm

12dm

20 dm

18m

6cm

Answers: (200.96cm2, 452.16dm2, 254.34m2, 314dm2, 113.04cm2) 3

Processing the Activities After the presentations of each group, ask: how did you find the activity? Did you able to find the area of the circle? What value is developed in performing the activity? Expected Answers:  Happy and curious  Yes by solving the area of a circle using the given formula  Cooperation and camaraderie

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Reinforcing the Concept and Skill Ask the pupils to answer the activity under Get Moving on page ___ LM Math

Grade V. Ask them also to answer the activity under Keep Moving on page ____ LM Math Grade V. 5

Summarizing the Lesson

Lead the pupils to give the following generalization. The area of a circle with pi, radius or diameter can be solved by the formula Always remember that radius is half of the diameter. Area of Circle = pi x radius x radius

A = π r2

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6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page _____ LM Math Grade V. C Assessment Ask the pupils to solve the following: Find the area of a given circle

3c

8m

7c

m

m

12m 15cm D Home Activity Remediation Provide exercises similar to those given in the lesson. Enrichment Ask the pupils to solve these problems. 1 2 3

What is the area of a circle with a diameter of 5 meters? If a circle has a diameter of 46centimeter what is the areaof the circle? Granda has an old family recipe for blueberry pancakes. She can make 8 pancakes that are each 18 inches in diameter. What is the area of the pancake? Answer: (78.5 square meters, 72.22 squared centimeter, 254.34 inches)

Lesson 84 : Solving Routine and Non-Routine Problems Involving the Area of a Circle Fourth Quarter Week 2 Objective:

Solves routine and non-routine problems involving the area of a circle Value Focus: Helpfulness and Cooperation

Prerequisite Concepts and Skills: 

Formula for the area of a circle in square meters and centimeters



Measuring the diameter and radius of the circle

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

Problem Solving

Materials: cutouts of circles, chart, flashcards, real objects References: M5M-IVb-75 Growing up with Math 5 pages 299-301 Ateneo Lesson Guide pages 382-386 Instructional Procedure: A. Preliminary Activities 1. Drill Game Ka Na Ba? Mechanics: a. Read the questions with choices b. Ask: “Would you like to go on P 100 or stop?” If he/she goes on, the price goes higher and higher until he/she gets the prize. Example: (Number to be squared should not be more than 15) 1. What is 12

2

A. 100

? B. 120

2

2. What is 15 B. 250

C. 124

D. 144

C. 200

D. 150

? B. 225

2. Review A. Checking of Assignment B. Identify the parts of a circle C. Review the steps in solving word problems. 3. Motivation Name any round objects inside the classroom or any round object that you brought. Show the diameter and the radius. D. Developmental Activities 1. Presentation Present the situation under Explore and Discover on page ___, LM Math Grade 5. Discuss the situation with the class. 2. Performing the Activities Divide the class into four groups and instruct them to bring out the materials that they brought like paper plate, ice cream cup cover or any round object. Let the pupils measure the diameter. Divide the diameter by

11

2 to get the radius. Tell the pupils that the value of π is approximately 3.14 and that the formula in finding the area of a circle is A= π r

2

Solve for the area of the circle. Ask the leader to report their answers. 3. Processing the Activities After the presentation of the groups, ask: 

How did you find the activity?



How did you go about the task?



What did you do with the objects before getting their areas?



How did you solve the area?

4. Reinforcing the Concept and Skill a. Class Activity Say: Let us solve more problems. Ask pupils to do the exercises by pairs under Get Moving on pages _____ of LM Math 5. Check the pupils’ answers. b. Group Activity Divide the class in four groups. Let them choose a leader and a secretary. Give each group an activity card with problems written on it. Then each group will post their work on the board. The leader will explain their answers and solutions. Activity Card 1 Problem 1: A circular basement has a radius of 6 m. If it will cost ₱471 per square meter to pave the basement with bricks, what will the total cost be?

Activity Card 2 Problem 2: Lyn wants to refinish a circular table that is 2.4 meters in diameter. If the refinishing costs ₱255 per square meter, how much will she spend?

Activity Card 3 Problem 3: Carlo has a circular window with an area of approximately 4069.44

cm 2 . Find the radius of the window

Activity Card 4 Problem 4: What is the area of a circular garden whose diameter is 15 meters? 12

5. Summarizing the lesson Lead the pupils generalize the following. Steps in solving problems involving the area of a circle The formula in finding the area of a circle A=π r

2

6. Applying to New and Other Situations a. Group Activity Divide the class in two groups. Give each group an activity card with problems written on it. Let each group post their work on the board. The leader will report to the class the answer and solution of the problem. Activity Card 1 Problem 1: Cellular telephones send messages within a circular area called a cell. Suppose a cell has a radius of about 1000 meters. Find the area of the cell. Activity Card 2 Problem 2: You are making a design for a circular button. Your design fits on a circle with a radius of 3 centimeters. How much area will be covered by your design?

b. Individual Activity For more exercises, ask pupils to do the exercises under Apply Your Skills on page ___, LM Math Grade 5. C. Assessment Solve the following problems. 1. Find the area of circular playground whose radius measures 6 meters. 2. An extension of a house is semicircular in shape with a radius of 4 meters. Can you find its area? 3. A circular fountain has a radius of 12 meters. What is the area of the circular fountain? 4. The diameter of the drum is 70 cm. What is the area covered when the drum stands? 5. Ana’s circular bed cover has a diameter of 2.25 m. How many square meters is it?

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E. Home Activity Remediation Find the area of the circle. Draw and Write the measurement of the radius or diameter. 1. radius- 9.5 cm

2. diameter- 14 cm

A = _________

A = __________

3. radius- 12 cm

4. diameter- 9 cm

A = _________

A = __________

5. radius- 20 cm A=__________ Enrichment: Solve each problem. 1. Every time it rains, Mrs. Lapis saves water in a big clay jar called ‘tapayan’. She covers them with a circular galvanized iron with a radius 14 m. What is the area of the circular cover? 2. Find the area of a circular clock that has a radius of 13 cm. 3. What is the area of a circular pool with the diameter of 15 m?

Lesson 85 : Creating Problems Involving a Circle, with Reasonable Answers Quarter 4 Week 2 Objective: Create problems involving a circle, with reasonable answers. Value Focus: Accuracy and Cooperation Prerequisite Concepts and Skills: 

Multiplication facts



Finding the area of a circle



Steps in Solving Problems

Materials: cutouts of circles, chart, flashcards, real objects, manila paper, ruler/meter stick, pentel pen, show me board References: M5M-IVb-76 14

Growing up with Math 5 pages 299-301 Ateneo Lesson Guide pages 382-386 Instructional Procedure: B. Preliminary Activities 4. Drill Have a drill on the multiplication facts 5. Review Have a review on solving the area of a circle. Let the pupils do the following. 6 cm

1.

2.

10m

6. Motivation Let the pupils find any circular objects inside the classroom. Ask them to record the area of each object. C. Developmental Activities 4. Presentation Let the pupils present their answers. Ask them how they got the area. 5. Performing the Activities Divide the class into four groups. Let each group discuss how will they make a problem based on the given situations. The groups 1 and 2 will discuss situation 1, while groups 3 and 4 will focus on Situation 2. Situation 1: Inside the classroom, find any circular objects, create a problem involving area of a circle. Use a ruler/meter stick as the measuring tool. Situation 2: In the school campus, find any circular objects, create a problem involving area of a circle use a ruler/meter stick as the measuring tool. 6. Processing the Activities After the activities have been done, let the groups post their formulated problems in each of the situations given and let them do the tasks below. 1. Read the problem and ask the class to solve the problem. 2. Illustrate and solve the problem with the solution. 15

4. Reinforcing the Concept and Skill a. Class Activity A. Ask the pupils to do the exercises in the Get Moving and Keep Moving pages_____ and ____, LM Math Grade 5. B. Ask the pupils to work by groups. Check the pupils answers 5. Summarizing the lesson Lead the pupils to give the generalization by asking: How did you create problems involving area of a circle? Steps in Creating Problems 1. Familiarize yourself with the mathematical concepts. Think of the application to everyday life situations. 2. Think of the type of the problem you want to make and the formula to be used. 3. Read and study more on math problems. Study the solutions. 4. Make your own styles/strategies to justify the solutions.

6. Applying to New and Other Situations Let the pupils do Apply Your Skills on pages ___, LM Grade 5. Check the pupils’ work. D. Assessment Let the pupils do the exercises in Keep Moving on page ___, LM Math Grade 5. Check pupils’ work. D. Home Activity Remediation Create problem involving area of a circle using the given data below. 1. circular bed

2. circular plate

3. circular playground

radius- 130 cm

radius- 15 cm

diameter – 30 m

Area=?

Area = ?

Area = ?

4. circular rug radius – 2.5 m Area = ?

5. circular placemat radius – 18 cm Area = ?

Enrichment: Ask the pupils to create problems involving area of a circle.

Lesson 86: Visualizes the Volume of a Cube and Rectangular Prism

16

Fourth Quarter Day 1 Week 3 Objectives

: at the end of the lesson, you will be able to; a. Visualize the Volume of a Cube and Rectangular Prism Value Focus: Patience, Orderliness and Cooperation

Prerequisite Concepts and Skills:  

Multiplication Facts Meaning of volume

Materials: cubes (big and small), rectangular prism, ruler, flash cards, marbles, worksheet, 1 transparent rectangular container

References: Code - M5ME-IVc-77 K to 12 Grade 5 Curriculum TM Math Grade 4 pages 298 - 307 Ateneo Lesson Guide 5 pages 395 - 402 Diwa New High School Mathematics First Year pages 71-72 Ateneo Lesson Guide 6 Chapter IV-Volume page 8-9 Distance Education for Elementary School (Volume of a Cube and Rectangular Prism) pages 2 - 3 Instructional Procedure: A. Preliminary Activities 1. Drill Have a drill on the multiplication facts using the activity sheets. 1) 2) 3) 4) 5)

5x5 9 x 11 10 x 12 4x4 6x8

6) 7 x 7 7) 11 x 11 8) 9 x 12 9) 8 x 5 10) 4 x 12

2. Review Have a review on the meaning of volume. Volume is the amount of space occupied by any quantity. 3. Motivation Show a transparent cube and rectangular prism filled with marbles. Ask pupils to guess the number of marbles inside the cube and rectangular prism. Let a volunteer count the marbles to find out the answer. Elicit from them how they can make a good guess of the total number of marbles. Instill the value of patience and orderliness. Relate this to the concept of volume. B. Developmental Activities 1. Presentation a. Tell the class that the number of small cubes that make up the Rubik’s cube is its volume. b. Activity – Group Work Materials: worksheet, 1 transparent rectangular container, small cubes Procedure: Fill the container with small cubes until its upper portion. Example 17

Guide Questions: 1) What kind of solid figure is the container? 2) How many cubes did you put inside the rectangular container? 3) How can you find the number of cubes in the container without counting them all? a) Count the cubes in one layer. Example 4 x 2 = 8 cubes b) Count the layers. Ex.: 3 layers c) How many cubes in all? 8 x 3 = 24 cubes 4) When we get the total number of cubes that the container has, what have we looked for? (Answer: Volume) 5) What kind of polygon is the base of the container? What are its dimensions? ) How many cubes fit the length? the width? 7) What other dimension does the rectangular container have? How many cubes fit the height? 8) Can you give the volume of the rectangular prism by just using the dimensions (length, width, height)? How? (Note: Teacher must tell the pupils that by multiplying the length x width x height will give the volume thus, Volume = L x W x H)) 2. Performing the Activities Group the pupils into 4 working teams and have them perform the task. Activity 1. They need small cubes, big cubes and rectangular prism.

If each is a

cubic unit, how many cubic units are in the figures?

How many cubic units are there in one row? How many cubic units are there in one layer? How many layers are there? What have you notice in the number of layers and rows of cube and prism? What can you say about the number of layers and rows of a cube? 18

What have you notice in the length, width and height of a cube? What can you say about the number of layers and rows of a prism? What have you notice in the length, width and height of a prism? a. Have pupils count the number of cubes in the figures. b. Define volume as the number of unit cubes in the solid figure. Mention the correct label (cubic units) c. Have them imagine filling up the classroom with such cubes. Then we find the volume of the classroom. Elicit similar application of volume in daily situations. 3. Processing the Activities Ask the groups to present and discuss their answers on the board. Expected answer:  Cube is a solid whose length, width and height are equal.  Rectangular prism whose length, width and height are not equal. 4. Reinforcing the Concepts/Lesson Discuss the presentation under Explore and Discover on page 1 of LM Math Grade 5. Ask pupils to work on exercises under Get Moving on pages 2 and 3 of LM Math Grade 5. Check the pupils’ answers. For mastery, have them answer the exercises under Keep Moving on page 3 and 4 of LM Math Grade 5. Check on the pupils’ answers. 5. Summarizing the Lesson Summarize the lesson by asking: How can we visualize the volume of cube and rectangular prism? Lead the pupils to give the generalization.  

Volume is the amount space a solid figure occupies. We can visualize volume of cube and rectangular prism a. using more units to fill the container (like the used of marbles, pebbles, rice grains, seed, etc) this is what we called non-standard units. Non standard units do not give consistent and accurate measure of the volume of a container.

b. Using standard units, to find the volume o a space figure, count the number of cubic units needed to fill the space. Standard units are consistent and accurate. 6. Applying to New and Other Situations Have the pupils do the exercises under Apply Your Skills on page 3 LM Math C. Assessment Ask the pupils to find the volume of each figure by counting the cubes. 1. 2.

19

(Use anon standard unit of the same material and size) 3.

4. marbles tamarind seeds

4.

Gravels 2. Home Activity Remediation Find the volume.

1.

2.

Lesson 87: Names the Appropriate Unit of Measure Used for Measuring the Volume of a Cube and a Rectangular Prism. Fourth Quarter Day 2 and 3 Week 3 Objectives

: at the end of the lesson, you will be able to; a

Name the unit of measure for measuring the volume of cube and rectangular

b

prism. Write the value of measuring accurately Value Focus: Accuracy

Prerequisite Concepts and Skills:    Materials:

Knows different unit of measures Meaning of volume, cube and rectangular prism Visualize cube and rectangular prism flash cards (mm, cm, dm, m, etc.), real objects, pictures

References: Code - M5ME-IVc-78 K to 12 Grade 5 Curriculum Integrated Mathematics I pages 177 - 178 LM Math Grade 5 pages 1 to 3 Ateneo Lesson Guide Chapter IV Measurement/Volume pages 6 -18

https://en.wikipedia.org/wiki/Volume Instructional Procedure: A Preliminary Activities 1 Drill 20

Drill on Choosing the Appropriate Unit of Measure Game: “Korek Ka Ba Dyan?” Materials: flash cards (mm, cm, dm, m, etc.), real objects, pictures Mechanics: a. Pupils will be grouped into 4. Each group will have flashcards (mm, cm, m, etc.) b. Teacher will ask, “What unit of measure will you use?” Ex.: Teacher will show a pencil. c. Pupils in the group will flash their answer. (Ex. cm) d. Teacher announces the correct answer. Repeat the process. Teacher will show another object or picture. e. Group with the most number of correct answers is the winner. 2

Review What is difference between cube and rectangular prism? What are the dimensions of cube and rectangular prism?

3

Motivation Richard has a rectangular box with sand inside. He wants to know the amount of space the sand occupied. He wants to know also what unit of measure he will use. Elicit the value of accuracy.

B Developmental Activities 1 Presentation A Present a rectangular box with sand inside. Ask the following questions: a. How can we be able to measure the capacity of the box? b. What will you use? What do you think are we looking for? c. What unit of measure will you use? The volume of a solid is the amount of space the solid occupies. Volume is measured in cubic units. One way to find the volume of a rectangular prism is to multiply the 3 dimensions: Volume = length x width x height Ask the pupils to measure the 3 dimensions of some objects inside the room using cm3 and m3. 1 liter = 1 dm3 B Teacher shows a cube (box) filled with blocks 2 cm on each side. Ask a pupil to get one block and describe it. What can you say about the block? What are the dimensions? A cube is a special type of rectangular prism having equal edges. Empty the box then let the pupils fill the box with the number of cubes. The total number of cubes that will fill the box represents the volume of the box. When finding volume, the units of volume are cubic units. What are the units of volume? (cubic millimeters – mm3, cubic centimeters – cm3, cubic decimeter – dm3, cubic meters – m3, etc.) 2

Performing the Activities 21

Group the class into four. Let them perform the give activity. Give the appropriate unit of measure to be used in finding the volume of (Select from the given choices: mm3, cm3, dm3, m3) : a) room _______ b) shoe box _______ c) globe _______ d) refrigerator _______ e) ice cream cone _______ f) baseball _______ 3

Processing the Activities Ask the groups to present and discuss their answers on the board. Expected answer: a) room

m3

b) shoe box

cm3

c) globe

cm3

d) refrigerator dm3 e) ice cream cone

cm3

f) dice mm3 Discuss the presentation on Explore and Discover of page 1 of LM Math Grade 5. Ask pupils to work on exercises A under Get Moving on pages 1 LM Math Grade 5. Check the pupils’ answers. For mastery, have them answer the exercises A under Keep Moving on page 2 of LM Math Grade 5. Check on the pupils’ answers.

4

Summarizing the Lesson Summarize the lesson by asking: What do you call the capacity of things or the total space within a 3-dimensional figure? What unit of measure will you use in measuring volume?  

5

Volume is the amount of space occupied by a space figure. Volume measured in cubic units, such as cubic centimeter (cm3) cubic meter (m3) cubic millimeter (mm3) cubic decimeter (dm3)

Applying to New and Other Situations Give the cubic unit of measure used in the following problems. 1) A piece of soap is 9 cm by 4 cm by 3cm. 2) An aquarium is 0.8 m long, 0.4 m wide, and 0.45 dm deep. 3) An iron bar 2 m long and 0.05 m in diameter. 4) An ice cream cone 2 cm in radius and 6 cm in height.

C Assessment A Write the cubic unit of measure used. 22

1

20 mm

2)

2 dm 8 dm

3) 3 cm

10 cm 2 cm

20 mm

20mm

1 dm B Use cm , m , dm to tell which cubic unit of measure is appropriate to be used. 3

3

3

a) box of chocolate b) tent c) glass d) gymnasium e) math book D Home Activity Remediation Give the cubic unit of measure for finding the volume of the following: a) a box 44 cm by 9 cm by 6 cm b) a room 4m by 5m by 6 m c) a cabinet 1.2 m by 0.9 m by 0.5 m d) a ball with radius 10 cm e) a cylindrical tank 25 dm long and radius 8 dm

Lesson 88: Derives the Formula in Finding the Volume of a Cube and A Rectangular Prism Using Cubic Centimeter and Cubic Meter. Fourth Quarter Day 4 and 5 Week 3 Objectives

: at the end of the lesson, you will be able to; c

Derive a formula for finding the volume of a cube and a rectangular prism

d

using cubic centimeter and meter. Appreciation of application of volume in daily life situations. Value Focus: Appreciate the application of volume in daily life situations

Prerequisite Concepts and Skills:   Materials:

Deriving formula in finding the area Concepts of solid dimensions. flash cards containing questions on finding area of parallelogram (square, rectangle, rhombus, parallelogram)

References: Code - M5ME-IVc-79 K to 12 Grade 5 Curriculum Ateneo Lesson Guide Grade IV Measurement/Volume pages 11 -16 Instructional Procedure: 23

E Preliminary Activities 4 Drill Mental computation/drill on finding the area or missing side of a parallelogram Materials: flash cards containing questions on finding area of parallelogram (square, rectangle, rhombus, parallelogram) Finding the missing side on the given area Mechanics: a. Divide the class into 3 groups. Have members of the group count off. Pupils remember their #s in the team. b. Teacher shows card to pupils for 10 seconds or depending on the level of difficulty of questions. 1

A= ?

3)

A=? 5 cm

4 cm 6 cm 8

cm

2

L=?

4)

Rectangle:

Width 2 cm, Area 10 cm2 L=?

5) Square A = 1 unit2, S = ? c. Teacher calls out a number randomly. The three pupils having that number stand up and call out the answer with correct units. The pupil who gives the correct answer first gets the point for the team. d. Teacher may do drawings first before shifting to pure numerical problems. Teacher may also include finding area of trapezoids making sure that the dimensions can be solved mentally. 5

Review Memory Game Materials: pocket chart, flash cards Mechanics: a. Teacher prepares flash cards with figure and dimensions on a set of cards and the corresponding area of the figure on another set of cards. Teacher then place the shuffled cards into pocket chart slots. At the back of each card, label them with letters. Ex. front back b. Divide class into 3 groups. 24

c. Have a member of group 1 choose 2 letters corresponding to 2 cards. Teacher turns over the cards. If the cards match (figure and its area), then the team gets the point and the cards taken out of the pocket chart. If the cards do not match, then the cards are turned over again in the same place/position in the pocket chart. d. Have a member of group 2 call out another pair of cards. Continue the game until all the cards have been used up. Team with the most number of points wins. e. Teacher may divide set of cards into a) finding area of parallelograms and trapezoid making sure that the dimensions given are manageable by the pupils, or b) finding the missing side/dimension given the area. 6

Motivation Show a transparent plastic container filled with balls. Ask pupils to guess the number of balls inside the container. Let a volunteer count the balls to find out the answer. Elicit from them how they can make a good guess of the total number of balls. Relate this to the concept of volume.

B. Developmental Activities 6

Presentation

Let a pupil fill a rectangular box with cubes. For purposes of having exact measurements and no half-cubes, it is ideal that teacher prepares boxes/ rectangular prisms that have corresponding measurements as the cubes that are going to be used in the activity. Ask the pupils the following questions: a. How many cubes did it take to fill the prism? How many cubic units is the length? The width? The height? b. What similar situations require you to fill up a solid such as the rectangular prism? c. Define these situations as finding the volume of solids. Define volume as the number of cubic units (unit cubes) used to fill up a space. Use correct unit of measure. d. Using this definition, ask the pupils the volume of the rectangular prism. e. Ask: Without actually counting the number of unit cubes in the solid how can you find its volume? What formula can we use to find the number of f.

cubic units in it or the volume of the rectangular prism? Elicit from the pupils that → To find the volume of an object means to find the number of cubic units

it contains or holds g. Lead them to state the formula for the volume of a rectangular prism as V = l x w x h. h. Define volume as the number of unit cubes in the solid figure. Mention the i. j.

correct label (cubic units). Using this definition, ask the pupils the volume of the cube. Ask: Without actually counting the number of unit cubes, how can you find the volume of the cube? What formula can we use to find the number of

cubic units in it? k. Try to elicit from the pupils that to find the volume of a cube, the length of its side is multiplied by itself three times. 25

l.

Lead them to state the formula for the volume of a cube as V=SxSxS

or

V = S³

m. Let pupils apply the rule by actually measuring and finding the volume of some rectangular prisms and cube inside the room. n. Present situations like how much water does it take to fill the aquarium, how far does it take to run around the park, etc. and distinguish perimeter/ circumference from area and volume. Elicit similar applications of volume in daily life situations. 7

Performing the Activities Group the pupils into 4 working teams and have them perform the task. Find the Volume write the Given, Formula and Answer 1

12 cm

3)

9 cm 9 cm 9 cm

10 cm 6 cm 2

3m 7m

4) s = 6 m V = ___________

25 cm

8

Processing the Activities Ask the groups to present and discuss their answers on the board. Expected answer: 1 Given:L = 6 cm W = 10 cm H = 12 cm Answer : V = 23 100 cm3 2 Given:L = 25 cm W = 3 cm H = 7 cm Answer : V = 525 cm3 3 3 Given:S = 9 cm Answer : V = 729 m 4 Given:S = 6 m Answer : V = 324 m3

9

Reinforcing the Concepts/Lesson Discuss the presentation under Explore and Discover on page 1 of LM Math Grade 5. Have the pupils do the activity under Get Moving on pages 1 of LM Math Grade 5. Check the pupils’ answers. For mastery, have them answer the exercises A and B under Keep Moving on page 2 and 3 of LM Math Grade 5. Check on the pupils’ answers.

10 Summarizing the Lesson Summarize the lesson by asking: How can you find the volume of a cube and a rectangular prism?  

The formula in finding the Volume of a cube is; Volume = side x side x side or V = S x S x S or V = S3 In rectangular prism we need L = Length, W = Width and H = Height,



the formula in finding the Volume of a rectangular prism is; Volume = Length x Width x Height V = L x W x H Volume is measured in cubic units, such as cubic centimeters ( cm3), 26 cubic meters (m3), and millimeters (mm3)

11 Applying to New and Other Situations Find the volume of the following figures. 1

2)

F

3)

4)

Assessment Find the volume of these solid figures 1

2

3)

4)

G Home Activity Remediation Draw the figure with their measurements and find their volume. 1 L=9m W=4m H=3m 2 L = 10 m W=7m H = 15 m 3 L = 14 m W = 10 m H=9m 4 S = 12 cm 5 S = 7 cm Enrichment Draw the figure with their measurements and find their volume. 1 L=2m W=3m H=4m 2 L = 11 m W=2m H=5m 3 S = 10 cm 4 S = 8 cm

Lesson 89: Converting cu.cm to cu.m and vice versa; cu.cm to L and vice versa Week 4 Objective: Converts cu.cm to cu.m and vice versa; cu.cm to L and vice versa

Value Focus: Cooperation 27

Prerequisite Concepts and Skills: 

Mastery of the basic conversion units

Materials: flash cards, pocket chart, problem written on the chart. References:Curriculum Guide in Math 5 M5ME-IVd-80 Ateneo Lesson Guide Grade 5 p.392 Instructional Procedures: I.

Preliminary Activities 7. Drill: Conversation Mother bought a dressed chicken weighing 1.3 kg. How many grams is it? 8. Review Give the equivalent: Conversion of linear measure. 6cm= ____ mm 5m= _____cm ____dm= 4m ____cm= 9dm ____dm= 3m 9. Motivation Which cubic unit of measure will you use to measure the following: a.cabinet d.thumbtacks box b.gravel and sand truck e.rectangular water tank

J. Developmental Activities 11. Presentation Present each problem to the class. A truck delivers sand weighing 54000 dm3 or L, what is the weight of the sand in cubic metre (m3)? In cubic centimetre (cm3) ? a. What is asked in the problem? What are given? b. What must we know to be able to change 54000 dm3 to cubic centimetres and to cubic metre? c. Which is larger a cubic decimetre or a cubic centimetre? d. How many cubic centimetres are there in cubic decimetres or L ? To change cubic decimetre to cubic centimetre we multiply by 1000. Since: 1dm=10cm Therefore: 1dmx1dmx1dm= 10cm x 10cm x 10cm Thus, 1dm3 = 1000cm3 54000 dm3 = ____ cm3 54,000x1,000 = 54,000,000 cm3 How will you compare cubic decimetres to cubic metres? Since a cubic metre is larger thana cubic decimetre, we divide by 1000. Using conversion 1m3= 1000dm3 54000dm3 = 54m3 1000 12. Performing the Activities Group the pupils into three working teams and have them perform the task. Problem 1. Change to dm3 54 cm3= _____ 64cm3= _____

28

523cm3= ______

Problem 2. Change to cm3 0.023m3=_____

3.48 m3= ______

2.53 dm3 = _____ Problem 3. Change to m3 2400 cm3 = _______

1240cm3 =________

320 dm3= ________ 3. Processing the Activities How do we change and convert a smaller unit to a higher unit?  when converting from larger unit to a smaller unit, use multiplication  when converting from a smaller to a larger unit, use division 4. Reinforcing the Concept and Skill Discuss the presentation. On page ___ of LM Math Grade V, Have the pupils solve the following exercises. Supply the missing number. 1. 6700 dm3= ____m3 2. 28 dm3= _____cm3 3. 11500 cm3 =_____ m3 4. 4 m3 =______cm3 5. 8m3 =______dm3 5. Summarizing the Lesson  In converting from a larger unit to a smaller unit, use multiplication  In converting from a smaller to a larger unit, use division 6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page LM Math Grade V. Encourage some pupils to show and discuss the answers. K. Assessment Change to smaller units. 1. 15 cm3= _____mm3 2. 61 dm3= _____cm3 3. 64 cm3 = _____dm3 4. 25 cm3= _____mm3 5. 87 dm3= _____cm3 L. Home Activity Remediation Change these units to larger or smaller units: 1.7cm3= ______mm3 2. 5000 dm3= _____m3 3. 5m3 = _____cm3 4. 20000 cm3 = ____m3 5. 17m3= ____dm3

29

Lesson 90: Finding the volume of a given cube and rectangular prism using cu.cm and cu.m Week 4 Objective: Finds the volume of a given cube and rectangular prism using cu.cm and cu.m

Value Focus: Cooperation Prerequisite Concepts and Skills:  

Mastery of the basic conversion units Area of polygons

Materials: flash cards, model cubes and rectangular prisms set, problem written on the chart. References: Curriculum Guide in Math 5 M5ME-IVd-81 Ateneo Lesson Guide Grade 5 p.395 Instructional Procedures: E Preliminary Activities 4 Drill Mental computation /drill on finding the area or missing side of a parallelogram 5

Review

Find the area of the following figures. Write the answer on your notebook.

1. 3cm 2. 5m

3. 6cm

6cm 6

Motivation Show a transparent plastic container filled with balls. Ask pupils to guess the number of balls inside the container. Let a volunteer count the balls to find out the answer. Elicit from them how they can make a good guess of the total

number of balls. Relate this to the concept of volume. F Developmental Activities 6 Presentation Using concrete objects a Let a pupil fill a rectangular box with cubes. b Ask the pupils the following questions:  How many cubes did it take to fill the prism?  How many cubic units is the length/ the width? the height? c Define these situations as finding the volume of solids. Define volume as the d

number of cubic units used to fill up a space. Use correct unit of measure. Using this definition, ask the pupils the volume of rectangular prism. 30

e 7

Let them state the formula for the volume of a rectangular prism as V=lxwxh.

Performing the Activities Solve for the volume of these rectangular prisms, given their measurements. 1 l=9m 3. s=12cm w=4m h=3m 2

l= 10cm w=7cm h=15cm

7

l=14 m w=10m h=9m

5. s=6m

3. Processing the Activities What is volume? What is the formula in finding the volume of a cube? Rectangular prism? 4. Reinforcing the Concept and Skill Discuss the presentation. On page ___ of LM Math Grade V, Have the pupils solve the following exercises. Find the volume of the following figures. 1. 8cm

4cm

2.

10c m 15cm

12cm

25cm

3

30m

31 12m

8m

5. Summarizing the Lesson  Volume of a rectangular prism= L X W X H  Volume of a cube=S X S X S or S3

6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page LM Math Grade V. Encourage some pupils to show and discuss the answers. G Assessment Find the volume of these solid figures.. 1

3m 6m

3m

2.

10cm

5cm 15cm

3.

8cm 4

5m 5. 10m

7m 15m

32

H Home Activity Remediation Draw the figure with their measurements and find their volume. 1

l=4m w=1m h=3m

2

s=14cm

3

3=20cm

4

l=8cm w=3cm h=10cm

5

s=12cm

Lesson 91: Estimating and Using appropriate units of measure for volume Week 4 Objective: Estimate and use appropriate units of measure for volume

Value Focus: Sharing Prerequisite Concepts and Skills:  

Mastery of the basic conversion units Volume of prisms

Materials: flash cards, model cubes and rectangular prisms set, aquarium. References:

Curriculum Guide in Math 5 M5ME-IVd-82 Ateneo Lesson Guide Grade 5 p.399

Instructional Procedures: I

Preliminary Activities 8

Drill

Mental computation Magic Square –Give the next five perfect square. 9

Review

Find the volume of these prisms. Write the answer on your notebook.

33

1 l=9m

2. s=12cm

3.l=15m

w=5m

w=10m

h=4m

h=6m

10 Motivation Show a rectangular prism to each group and guess which has the greatest or least volume. J Developmental Activities 8

Presentation Using concrete object (present an aquarium) An aquarium is 35 cm. long, 25 cm wide and 33 cm high is to be filled with water. How many cubic centimetre of water will be needed? 1.What is asked in the problem? 2.What data are given? 3. Is the unit of measure appropriate with the data given?

9

Performing the Activities a Group the pupils. Give rectangular prism to each group. b Have each pupil first guess which prism has the greatest and which prism c

has the least volume. Give the unit of measure to be used. Have the students estimate the volume of the rectangular prisms.

3. Processing the Activities What is volume? How do we estimate volume of a prism? 4. Reinforcing the Concept and Skill Discuss the presentation. On page ___ of LM Math Grade V, Have the pupils solve the following exercises. Write the best unit of measure to find the volume of the following: (mm3, cm3, dm3, m3) 1 water in a rectangular pool 2 an ice before it melts 3 a dice 4 a blackboard eraser 5 oil in a rectangular box

5. Summarizing the Lesson  How do we use appropriate unit of measure for volume?  How do we estimate volume? 6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page LM Math Grade V. Encourage some pupils to show and discuss the answers. 34

K Assessment 1 Marilou’s sewing box is 3 dm long, 2.5 dm wide and 4.3 dm high. What is its volume? 2 Find the volume of a closet which is 2.5 m long, 5m and 2m high L

Home Activity Remediation Draw the figure with their measurements and find their volume. 6 l=9m w=4m h=6m 7

s=18cm

8

3=30cm

9

l=12cm w=5cm h=8cm

10 s=14cm

Lesson 92: Solving Routine and Non-routine Problems Involving Volume of a Cube and Rectangular Prism in Real-Life Situations Using Appropriate Strategies and Tools Week 5 Objective: Solves routine and non-routine problems involving volume of a cube and rectangular prism in real-life situations using appropriate strategies and tools Value Focus: Accuracy and Prerequisite Concepts / Skills:   

Multiplication Facts Finding the Volume of a Cube Rectangular prism Using the Steps in Solving Problem

Materials: meter stick, ruler, manila paper and marker pen References: Mathematics for a better life 5, pages 264-265 Guide in Elementary Mathematics Grade VI pages 403 and 405 Curriculum Guide 5, Instructional Procedure: A Preliminary Activities 1 Drill Have a drill on the multiplication of fractions and whole numbers using the activity sheet. Example: 35

1 ×6 × 8 3

40 × 6

1 ×7 × 9 3

1 ×21 × 4 3

51× 7

2 Review Have a review on estimating and using appropriate units of measure for volume. 3 Motivation Group the pupils into four. Give each group a set of steps in solving problems. Let them arrange the steps in correct order. (This can be done in the form of game) Example: What operation is needed to solve the problem? What are the given facts? What is the correct number sentence? What is being asked? B Developmental Activities 1 Presentation Present these problems. A A swimming pool is 12 m long, 9 m wide, and 1.85 m deep. How much water can it hold? Ask: What is the shape of the swimming pool? Call a pupil to draw the figure of the swimming pool and put the dimensions. How will you solve the problem? B. A wooden cube has a volume of

500 cm

3

. How many

3

4 cm

cubes can

you cut from it? Ask: What is the shape of the wooden cube? What is its volume? What is asked in the problem? Solve. 2

Performing the Activities Let pupils solve the problem by pairs. Problem A Solution: Use the 4-step plan in solving the problem. Understand - Know what is asked.

- The amount of water the swimming pool can hold. - 12 m long, 9 m wide, 1.85 m deep

- Know the given facts. Plan - Determine the operation or

- Multiplication

V =l × w× h

formula to use. Solve - Show how the solution is done.

- V =l × w× h =

12 m×9 m ×1.85 m 3

= 199.8 m Check and Look Back

- Use inverse operation. 36

-

Verify if the answer is correct.

199.8 ÷ 1.85 = 108 108 ÷ 9 = 12 The answer is correct.

Problem B. Solution:

500 cm3 ÷ 4 cm3

Answer: 125 pieces 3

Processing Activities Call some pupils to show their solutions and answers on the board. Ask: How did you solve the problem? Expected answers: For Problem 1:  We used the 4-step plan in solving the problem.  We used the appropriate formula.

V =l × w× h

For Problem 2: 3

4 cm

Since the volume of the wooden box is given, we divided it by 4

.

Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page

, LM Math

Grade 5. Let the pupils do the activity under Get Moving on page

, LM Math

Grade 5. Check the pupils’ work. For more practice, let them solve the problem under Keep Moving on page

,

LM Math Grade 5. 5

6

Summarizing the lesson Ask the following questions: How do you solve problems involving a cube or a rectangular prism? What are the steps in solving word problems?

The four-step method to solve the problem. 1 Understand - Know what is asked. - Identify the relevant facts. 2 Plan - Choose the operation or formula to use. 3 Solve - Perform the strategy. 4 Check - Verify if the answer is correct. - State the complete answer. Applying to New and Other Situations 1 Let the pupils solve these problems. a How much space in a room will a cabinet occupy if it is 1.9 m long, 0.61 m wide, and 2.74 m high? b

A box is 3.5 dm long and 6 dm high. Its volume is

210 dm

Let the pupils do items under Apply your Skills on page 5. 37

3

. How wide is it? , LM Math Grade

A Evaluation Let the pupils solve the following problems: 1 A flower box is 4.3 m long, 0.6 wide, and 0.53 m high. How many cubic meters of soil 2

will fill the box? A rectangular container is 0.4 m long, 0.3 m wide and 1 m high. What is its volume in

3

cubic centimeters? A water tank is 0.8 m long, 0.6 m wide and 1 m high. If the tank is half full, how many cubic centimeters of water does it hold?

B Home Activity Analyze then solve the problems. 1 A box of milk is 9 cm long, 8 cm wide and 18 cm high. Find its volume? 2 Each book of a set of encyclopedia measures 2.85 dm by 2.15 dm by 0.4 dm. The encyclopedia has 19 books. What is the total volume of all 19 books? 3

The toy hat of Alex is in the shape of a cone. Its base area is

72 cm2

and its

height is 21 cm. What is its volume? Enrichment Let the pupils solve the following problems. 1

A rectangular block of wood is 25 cm long, 20 cm wide and 15 cm thick. What is its volume? 3

2

The volume of cube is 729 cm

3

A school garden is 20 cm long and 3 m wide. How many cubic meters of soil will

. What is the length of its side?

Lesson 93 : Creating Problems (with reasonable answers) Involving Volume of a Cube and Rectangular Prism in Real-Life Situations Week 5 Objective: Creates problems (with reasonable answers) involving volume of a cube and rectangular prism in real-life situations Value Focus: Accuracy, cooperation, Prerequisite Concepts / Skills:  

Finding the Volume of a Rectangular prism Using the Steps in Solving Problem

Materials: real object References: Mathematics for a better life 5, pages 264-265 Guide in Elementary Mathematics Grade VI pages 403 and 405 Curriculum Guide 5, Instructional Procedure: C Preliminary Activities 38

4 Drill Have a drill on the finding the volume of cubes and rectangular prism. Example:

15 cm

15 cm

5 cm

15 cm 10 cm

15 cm

5 Review Have a review on solving problems on volume. Ask: What are the steps in solving word problems? Let the pupils solve this problem. Leo has a box measuring 15 cm long, 20 cm wide and 10 cm high. Find its volume? 6 Motivation Group the pupils into four and let them read the problem and ask them to draw the solid figure described in the problem. A rectangular garden is 25 cm long, 15 cm wide and 10 cm thick. What its volume? Ask: Can you create a problem on volume similar to the one given? Say: This time you will create problems involving the volume of a cube and a rectangular prism. D Developmental Activities 6 Presentation Each group will present the solid figure formed. Ask: What is asked in the problem? What are the given data? What process is needed to solve the problem? What is the number sentence? What is the correct answer? 7

Performing the Activities Group Work Activity Divide the class into four groups. Let each group discuss how they will make a problem based on the given situations. The first two groups will discuss situation 1 and the remaining two groups will focus on situation 2. Situation 1: Ana has a front yard measuring 15 m long and 8 m wide. She wants to elevate it by

1 meter . 2

Situation 2: Lito’s business is to deliver water to schools. Her water tank measures 4 meters long, 2 meters wide, and 2 meters high. Every morning, he delivers a tank full of water to each of the schools

39

Guide and assist the pupils when doing the activity. Ask each group to show its work and to explain its output. 8

Processing Activities After the activities are done, let the groups post their created problems from the given situations and let them follow the task below. 1 Read the problem and ask the class to solve the problem. 2 Illustrate and solve the problem with its solution. Ask: How did you create problems? Expected answer:

9

1

We familiarized ourselves with the mathematical concepts and their application to

2 3

real-life situations. We thought of the type of problems we want to create. We read and studied some problems that we have solved and their solutions.

Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page

, LM Math

Grade 5. Let the pupils do the activity under Get Moving on page

, LM Math

Grade 5. Check the pupils’ work. For more practice, let them solve the problem under Keep Moving on page

,

LM Math Grade 5. 10 Summarizing the lesson Ask the following questions: What did you do to be able to create problems involving the volume of cube and a rectangular prism? What are the steps in creating problems?

Steps in creating problems.

7

1

Familiarize yourself in the concepts. Think of an explanation to everyday

2

life real situations. Think of the type of problem you want to create and the formula to be

3 4

used. Relate the problem to real life situations. Study the solution in solving the problems. Make your own styles/strategies to justify the solutions.

Applying to New and Other Situations Let pupils do the activity under Apply Your Skills on page

, LM Math Grade 5.

Check the pupils’ work. C Evaluation Let the pupils make problems involving the volume of a rectangular prism with corresponding answers based on the given situations. 1 In constructing a new building, a hole 4 m deep, 10 m wide, and 115 m long was 2 3

dug in the ground. A room is 15 m high, 4 m wide and 10 m long. A bar of gold is 25 dm long, 3 dm wide, and 2 dm high.

D Home Activity 40

Let the pupils create problems involving volume, then provide solutions. 1 2

Ana’s sewing box is 7 dm long, 4 dm wide and 3 dm high. An antique wooden chest is in the form of a cube. Its edge is 20 cm.

Enrichment Let the pupils create problems for the following situations: 1 2

A small gift box measures 8 cm long, 7 cm wide and 2 cm high. A rectangular water tank is 5 meter high, 2 m wide and 3 m long. It contains water 2 meter high.

3

The volume of a rectangular prism is

75 cm 3 , its height is 6 cm, and its length is 4

cm. Lesson 94 : Reading and measuring temperature using thermometer (alcohol and/ or Digital) in degree Celsius. FOURTH QUARTER- Week 6 Objective: Reads and measure temperature using thermometer (alcohol and/ or Digital) in degree Celsius.

Value Focus: Accuracy Prerequisite Concepts and Skills 

Parts of a thermometer



Reading thermometer



Measures temperature

Materials: picture, thermometer, activity sheets, improvised thermometer, a glass of hot water and cold water References: K to 12 Curriculum for Grade 5, M5ME-IVf-85 Lesson Guide in Math V p.405 Mathematics For a Better Life 5 p. 266- 267 Instructional Procedure:: A Preliminary Activities 1

Drill Rearrange the jumbled words to form science terms a

EPATMERETRU

b

RURMCYE

c. THEREMOMRTEE d. CSALE

41

2

Review Give the equivalent. Conversion of linear measure.

5m= ___d m 6cm= ------mm

3

Motivation Mother wants to find out if her son has a fever. What is the best thing mother can use to find the body temperature of her sick son?

B Developmental Activities 1

Presentation Present a model of an improvised thermometer. It has a movable red ribbon

which resembles the mercury in an actual thermometer. Ask: What does the red ribbon represents? Give each group an improvised thermometer, announce the temperature readings, The pupils will reflect it in their thermometer model. Check if the temperature reading each group is showing is correct. 2

Performing the Activities Group Activity Divide the class into four groups. Distribute activity sheets in each group. Provide group 1 with digital thermometer, Group 2 with set of pictures showing temperature readings and Group 3 using pictorials, Group 4 with alcohol thermometer. Group 1 - Using digital thermometer Group 2 - Using pictures of temperature readings Group 3 - Using pictorials Group 4 – Using alcohol thermometer

42

Let them discuss how they read and measure the temperature Group 1- Measure and read the pupils body temperature by putting the digital thermometer under their armpits. Record and compare the results with the other pupils. Group 2 - Read and record each thermometer reading Group 3 - Give pictures and write if it is HOT or COLD -

Picture of Baguio city

-

Picture of a dessert

-

Picture of a glass of cold glass of water

-

Picture of cup of coffee

Group 4 - Give 2 glasses of water, one has cold water and the other has hot water, using alcohol thermometer measure the temperature of each glasses. Read and record. 3

Processing the Activities Ask: How did you find the activity? How were you able to read and measure the temperature? Discuss. Emphasize that ◦C is read as “degree Celsius” it is used to express temperature. Discuss the difference between an alcohol and a digital thermometer.

4

Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page _____ of LM Math Grade 5. Then, ask the pupils to do the activity under Get Moving on page____ of Math Grade 5. For more practice, ask them to do the activity under Keep Moving on page _______ of LM Math Grade 5.

5

Summarizing the Lesson Ask the following questions: What is a temperature? How can we measure temperature? What are the parts of a thermometer? What is the metric unit for measuring temperature? 

Temperature is the measure of hotness or coldness of an object.



We can measure temperature by using thermometer.



The parts of a thermometer are: mercury, glass tube, glass bulb, and scale.



The commonly used unit to measure temperature is degree Celsius ( ◦C ).

43

6

Applying to New and Other Situations Let the pupils do items 1 and 2 under Apply Your Skills on page ______, LM Math Grade 5.

C Assessment Ask the pupils to find the temperature of the following. 1

A kettle of water was made to boil for 5 minutes more than after it reached its boiling point. What is the temperature of the water?

2

What is the room temperature if the red liquid (mercury) rose to 30◦ above the freezing point?

Lesson 95: Estimate the Temperature (e.g. inside the classroom) FOURTH QUARTER- Week 6 Lesson 95: Estimate the Temperature (e.g. inside the classroom) Value Focus : Taking care of one’s health Prerequisite Concepts and Skills: 

Estimating temperature

Materials : activity sheets, thermometer References : K to 12 Grade 5 Curriculum, M5ME- IVf-86 Lesson Guide in Math 5 p.409 Instructional Procedure: A Preliminary Activities 1

Drill Estimate each sum.

2

38

83

98

78

87

+ 76

+67

+34

+43

+ 65

45

34

27

29

32

Review Match the parts of the thermometer with their function. Column A

Column B

1. Mercury

A. holds the tube that contains the liquid

2. Glass tube

B. rises and fall when there is a change

3. Glass bulb

in temperature

4. Scale

C. tells how far the liquid goes up and down D. holds the liquid

44

3

Motivation How do you know if you have a fever? One has a fever if one’s body temperature is above the normal body temperature. The normal body temperature is 37◦C? What will you do if one of the members of your family has a fever?

B Developmental Activities 1

Presentation Present the situation to the class. Mother wants to find out if her son Rommel has fever. She got her thermometer and found out that the mercury level in the thermometer is at 38.5◦C, If the normal body temperature is 37.5◦C, how much higher is her son’s temperature than the normal body temperature? Ask: What did Mother wants to find out? What did she do? What kind of mother is she? Is your mother as kind as Rommel’s mother? Why is it important to know one’s temperature? Ask:

What are the given facts? What is asked in the problem? What operation are you going to use? Do we need the exact/ actual answer in the problem? What word/s suggests that we need only to estimate?

2

Performing the Activities Say: Estimating is an educated guess. There are times when an estimate is needed and not the actual one. Say: Let us solve and analyze the solution to the problem. 38.5◦C

39◦C

- 37.5◦C

-38◦C 1◦C estimated difference

So, 1◦C is much higher is her son’s temperature than the normal body temperature.

3

Processing the Activities Ask:

How is estimation done in the solution we have in the problem? What was done first to the numbers? 45

Then, what was cancelled in the rounded numbers? Then what was done next? Say :

Now, let us compare the actual answer to the estimated one.

Ask:

Are the difference the same or different? How near or far is the estimated answer to the actual one? What will you do if the estimated answer is too large or small compared to the actual one?

Say:

There are times that the estimated answer is too long or small if we round both the numbers to the highest place value. One way to make our estimated answer reasonable or close to the exact answer is by using compatible numbers.

4

Reinforcing the Concept and Skill Let the pupils study Explore and Discover on page ________of the LM Math Grade 4. Emphasize the estimating of temperature. Ask the pupils to do the exercises under Get Moving on page _______ of LM Math Grade 5. Give more activities. Group the class into two. The first group do set A and group 2 will do set B. SET A 1

Look at the chart of temperature readings in a day. 6:00 a.m.- 24.5 ◦C 8:00 a.m. - 28◦C 10.00 a.m. - 30.4◦C 12:00 a.m. - 31◦C

a

At what time was it coolest?

b

Did the temperature go up or down during the morning?

c

What is the estimate temperature on 6:00 a.m.?

d

What was the estimate temperature on 10:00 a.m?

e

What was the estimated difference in temperature at 6:00 and 8:00?

SET B 1

Choose the correct estimate of the temperature of each. a

Hot coffee

30◦C

85◦C

b

Strawberry shake

5◦C

50◦C

c

Distilled water

20◦C

75◦C

d

High fever

40◦C

-15◦C

e

Air conditioned room

10◦C

90◦C

Ask : Which is the best estimated answer? Ask pupils to work on exercises under Keep Moving on page _______ of LM Math Grade 5. Check the pupil’s answer. 46

5

Summarizing the Lesson Lead the pupils to generalize as follows. To estimate temperature, round the number to the highest place value and use compatible numbers for the number to be estimated. This will make your estimated temperature reasonable.

6

Applying to New and Other Situations Do the activity by pairs. 1

At the start of the marathon the thermometer registered a temperature of 36.7◦C. after the marathon, the temperature dropped by 3.5◦C. What was the estimated temperature after the marathon?

2

What is the estimated temperature if a 30.◦C temperature rises 5.5◦C? For more exercises, ask pupils to do the exercises under Apply Your Skills on page _____, LM Math Grade

C Assessment Estimate the temperature. Give the estimated sum or difference. 1

3.5 ◦C higher than normal body temperature

2

10.5◦C below 0◦C

3

Halfway between 78.6◦C and 80.2◦C

4

The sum of 32.4◦C and 33.8◦C

5

The difference between 98.2◦C and 72.8◦C

D Home Activity Remediation Estimate the temperature by rounding method. 1

36.2◦C

2

43.7◦C

3

19.25◦C

4

29.2◦C

5

18.6◦C

Enrichment Find the estimated sum or difference using rounding method then compare with the exact answer. 1

Equation 45.2◦C + 35.5◦C

Rounding off

47

Estimated sum/ difference

2 3 4 5

100.2◦C- 98.6◦C 73.5◦C- 65.2◦C 35.3◦C +23.4◦C 17.5 ◦C - 10.3◦C

Lesson 96: Solves routine and non- routine problems involving temperature in real-life situations. Fourth Quarter-Week 6 Objective: Solves routine and non- routine problems involving temperature in real-life situations. Value Focus: Awareness, alertness Prerequisite Concepts and skills : 

Steps in solving word problems



Concept of four basic operations

Materials: improvised thermometer, digital or liquid thermometer, activity sheets/cards References: K to 12 Grade 5 Curriculum Guide, M5ME- IVf-87 Lesson Guide Grade 5 page409 Mathematics For A Better Life 5 p.268- 269 Instructional Procedure: A Preliminary Activities 1

Drill Using improvised thermometer, show the following temperature readings. a

32.5◦C

18.6◦C

39◦C

b

57.3◦C

20◦C

59.2◦C

c 2

Review Give the temperature when the liquid or digital thermometer is:

3

1

at the freezing point of water

2

10◦C below the normal body temperature

3

25◦C above the boiling point of water

4

between 30◦C to 40◦C

5

at the boiling point of water

Motivation Show 2 glasses of water, one has cold water and the other has hot water. Let the pupils get the actual temperature of the 2 glasses of water. Record the results. Ask: Which of 2 has a higher temperature? lower temperature? How much higher is the temperature of one glass than the other? Valuing: Getting the actual temperature of one’s body is important. 48

Why should we read the thermometer with accuracy? B Developmental Activities 1

Presentation Present a problem opener. Problem A The weather report in one newspaper predicted the lowest temperature for the day to be 24◦C and the highest at 32◦C. What was the difference in the predicted temperatures for that day? Problem B Marina has a fever. At 12 noon, her temperature increased by 1.8◦C from her temperature at 7 A.M. Then her temperature went down by 1,3◦C at 5 P.M. At 11 P.M., her temperature rose again by 1.1 ◦C. If her temperature at 11 P.M. was 39.7◦C, what was her temperature at 7 A.M.? Ask: How are you going to solve each problem?

2

Performing the Activity Group the pupils into four learning teams. Ask the groups to work together in Solve for the answer to each problem. Give the learning teams enough time to do the task. Solution to Problem B : Using the 4- Step Plan Understand : Know what is asked : What was Marina’s temperature at 7 A.M.? Know the given facts : At 12 noon, her temperature increased by 1.8◦C from her temperature at 7. A.M .Then it went down by 1.3◦C at 5 P.M. The temperature at 11 P.M. was 39.7◦C. Plan: Determine the operation to be used: Addition and subtraction Write the number sentence: 39.7◦C - (1.8◦C-1.3◦C+1.1◦C) = N Solve: Show your solution (Illustrate the problem by using a diagram) 39.7◦C - (1.8◦C-1.3◦C+1.1◦C) =38.1◦C Marina’s temperature at 7 A.M. Check and Look back:

38.1◦C + 1.8◦C = 39.9◦C 39.9◦C - 1.3◦C = 38.6◦C 38.6◦C + 1.1◦C= 39.7◦C

3

Processing the Activities After all groups have presented their output, ask these questions. 

How did you find the activity?



How were you able to find the answer to the problem?



In how many ways were you able to arrive at the answer? 49

Discuss with the pupils the ways on how they were able to solve for the answer to The problems. ( Use the 4- step plan and illustrating a diagram) Ask: Are there was by which you can solve the given problems? The first problem is an example of a routine problem. Routine problem solving concerns solving problems that are useful for daily living ( in the present or future). The second problem is an example of a non routine problem. Non routine problem solving is mostly concerned with developing pupil’s mathematical reasoning power and fostering the understanding that mathematics is a creative endeavor. This kind of problem helps the teacher to motivate and challenge their pupils.

Some strategies used in this kinds of problem are Guess and Check,

Drawing

Diagram, Using patterns, Working Backwards.

4

Reinforcing the Concept and Skill. A Discuss the presentation under Explore and Discover on page ______ of LM Math 5. Then ask the learners to think of ways on how to solve the following problems. 1

At 1:00 pm, the air temperature was 31.9◦C. By 5:30 pm, it was recorded to be 20.6◦C. Is there a change in temperature? By how much?

2

Enzo’s temperature lowered by 1.75◦c after he was given a sponge bath. Before the bath, his body temperature was 40.25◦C.What is his body temperature now?

5

Summarizing the Lesson Lead the pupils to give the generalization by asking How do you solve routine and non- routine word problem solving involving temperature in real life situation? To solve routine problems involving temperature in real life situations, follow these steps: Understand 

know what is asked



Know the given facts



If any, determine the hidden questions

Plan 

Determine the operation to be used



Write the number sentence

Solve 50



Use the operation to solve

Check and Look Back 

Write the correct answer

Non routine problems can be solved without using a standard procedure. They can be solved by drawing a picture, using a number line, acting out, making a table, and others.

6

Applying to New and Other Situations Ask the pupils to do items 1 and 2 under Apply Your Skills on page _____ LM, Math Grade 5

C

Assessment Solve the following problems:

1

The recorded temperatures for 5 days were 21◦C, 27◦C, 29.2◦C,29.8◦C and 30◦C.What was the average temperature?

2

A freezer is set at 0◦C. Corina reset it to 8.5◦C. Did the temperature in the freezer rise Or drop? By how many degree?

D Home Activity Remediation Solve the following problems; show the solution in your notebook. 1

From the normal body temperature, Joseph’s temperature rose by 2,5◦c due to high fever. What is Joseph’s body temperature?

2

The temperature reading is 42◦C. It changed to 53.5◦C.by how much temperature was increased?

Enrichment Solve the problem. Upon reaching the top of the mountain, a group of mountain climbers boiled water. They observed that the water started to boil at a temperature 6.5◦C lower than the boiling point of water at sea level. What is the boiling point of water at the top of the mountain?

51

Lesson 100: Interpreting Data Presented in Different Kinds of Line Graphs (Single to Double-Line Graph) Week 8 Objective: Interpretsdata presented in different kinds of line graphs (single to double-line graph)

Value Focus: Cooperation Prerequisite Concepts and Skills:  

Interpreting data in a bar graph. Mastery on skip counting by 2s, 5s, 10s and so on.

Materials: graph, grid board References: K to 12 Grade 5 Curriculum Guide, M5SP-IVh-3.5 Lesson Guide in Elementary Mathematics V pp.501-507 Instructional Procedure: M Preliminary Activities 11 Drill Drill on skip counting by 2s, 5s, 10s, etc. 12 Review Conduct a review on interpreting data presented in a bar graph. Gemma’s First Quarter Grade on the Major Subjects 89 87 85 83 81 79 77 75 English

Math

Science

Filipino

HEKASI

a b c d

In what subject did Gemma have the highest grade? In what subject did she have the lowest grade? In what subjects did she get the same average grade? What is the difference between the highest and lowest grade she got on the first

e

quarter? What was her average score on the five subjects? 13 Motivation How many of you are observant with the day’s temperature? Why does a weatherman inform us about temperature readings?

52

Why do you think there is a need to check the day’s temperature from time to time? N Developmental Activities 10 Presentation Present a line graph with complete parts and let the pupil interpret the data.

Temperature Readings Taken in a Day 40 38

Temp36 erat 34 ure (⁰C) 32 30 28 26 24 22 20

Tim 8:00 a.m. 10:00 a.m. 12:00 a.m. 2:00 p.m. 4:00 p.m. 6:00 p.m. 7:00 a.m. 9:00 a.m. 11:00 a.m.e 1:00 p.m. 3:00 p.m. 5:00 p.m. Ask: 1 What are the parts of a line graph? 2 Looking at the data, can you interpret what is presented by the graph? How? 3 How does a line graph help in data presentation? 4 Is it important to have an accurate data? Why? 11 Performing the Activities Group the pupils into five. Give activity sheets involving line graph to each group for interpretation. Ask each group to work together in interpreting the data on the graph. Once finished, the assign member will post their work on the board and discuss their answer. A

53

Mrs. Alba’s Monthly Sales

45,000

40,000

Sale s in35,000 Peso 30,000 25,000

20,000

15,000

Jan

Feb

Mar

Apr

May

Jun

2014

2015

Month s

B. Gregorio Elementary School Enrolment from S.Y. 2010-2015 2,100 2,000 1,900 1,800 1,700 1,600

Nu 1,500 mb er 1,400 of 2010 Enr oll ees C.

2011

2012

2013 Year

Shiela’sWeight for 6 Months

54

40 39 38 37 36

Wei ght (Kg)

35 34 33 32

Jun

Jul

Aug

Sept

Oct

Month s

Nov

D.

Carla's Height for 6 Months 86 84 82

Heig ht (cm)

80 78 76 74

Jan

Feb

Mar

Apr

E.

55

May

Jun

Grade V- Narra's Attendance for Five Days 50 49 48 Number 47 of Pupils 46 45 44 43

Mon

Tue

Wed Day

Thur

Fri

s

3. Processing the Activities Each group will present their interpretation of the graph. Then ask: a How did you find the activity? b How were you able to interpret the graph? Discuss with the pupils how to use the data to interpret the graph. 4. Reinforcing the Concept and Skill A Discuss the presentation under Explore and Discover on pages ___of LM Math Grade V. B Have the pupilswork on items under Get Moving and the items under Keep Moving on pages ____, LM Math Grade 5. Check the pupil’s answers. 5. Summarizing the Lesson Lead the pupils to give the generalization of the lesson by asking: What are the parts of a line graph? Why is it useful? How do we interpret data presented on a line graph?   

A line graph has a title, information on the x-axis (horizontal axis) and information on the y- axis (vertical axis). Changes in the data presented are easily seen on a line graph. To read and interpret the data presented in a line graph, we usually compare the data in terms of size and amount.

6. Applying to New and Other Situations Have the pupils do the items under the activity on Apply Your Skills on page ____, LM Math Grade 5 C Assessment Study the line graph, and then answer the question below.

56

Ramon's Weekly Mango Harvest 70 Quanti 65 ty 60 Harve 55 sted 50 45 40 35

1 a b c d e

Wee

2

3k

4

5

6

What is the title of the graph? How many mangoes were harvested for the first two weeks? In what week was there the greatest amount of harvest? What is the least amount of mango harvested? What is the total amount of harvest for six weeks?

D Home Activity Remediation Study this graph carefully, and then answer the questions that follow.

Kiana's Monthly Deposit Amount 1,600 1,400 1,200 in Peso 1,000 800 600 400 200 0

Deposit

Sept 1 2 3 4 5

Oct

Nov

Mont h

What is the graph about? How much was her initial deposit? In which month was her bank deposit greatest? What was her average deposit?? What was her total deposit for six months?

Enrichment Use the graph to answer the following.

57

Dec

Jan

Feb

Average Daily Sales at Aling Eva's Store 900 800 700 600 Pesos

500 400 300 200 100 Mon

Tues

Wed

Thurs

Fri

Sat

Sun

Day s 1 2 3 4 5

What is the title of the graph? How much was the sale on Wednesday? On what day was the highest sale? What is the stores average sale for the week? How much was the total sale?

Lesson 101: Solving Routine and Non-routine Problems Using Data Presented in a Line Graph Week 8 Objective: Solves routine and non-routine problems using data presented in a line graph.

Value Focus: Perseverance Prerequisite Concepts and Skills: Interpreting data in a line graph Materials: graph, grid board References: K to 12 Grade 5 Curriculum Guide, M5SP-IVh-4.5 Mathematics Teachers Guide IV pp. 346 Instructional Procedure: O Preliminary Activities 14 Drill Conduct a drill on reading and interpreting a graph.

58

Mark's Score in Math Summative Test 5

4

Score

3

2

1 Mon

Tues

Wed

Thurs

Days 1 2 3 4 5 15

What is the graph about? On what day did he get the lowest score in Math? On what days were his scores the same? When did he get a perfect score? What was his average score for the week? Review Conduct review onthe parts of a line graph. Have them construct a line graph using the following data: Results in an Experiment Weeks

Height of Plant

1 2 3 4 5 6

1 cm 2 cm 2.5 cm 3.5 cm 4 cm 6 cm

16 Motivation Is it important to keep track of your performance in school? What do you do in order to maintain good performance track? P Developmental Activities 12 Presentation Present a line graph to the class.

59

Fri

Ella’s Grade in Math

86 85 84 83 Grade 82 81 80 1st Quarter

2nd Quarter Quarter

3rd Quarter

4th Quarter

Ask: In what quarter did Ella get the lowest grade? What about the highest grade? Why do you think Ella got the lowest grade during the 2nd Quarter? What will you do in order to get good grades? 13 Performing the Activities Divide the class into groups. Give them enough time to solve problems using the data presented in a line graph. After few minutes, they are required to present their output. 45000

Mr. Sanchez’s Monthly Sales

40000 35000 30000 25000 Sales

in

20000

Pesos 15000 10000 Jan

Feb

Mar

Apr

Use the data in the line graph to answer the following questions. 1

2

What was the sale for the first three consecutive months? a What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer? How much more was his sale in March than in February? a What is asked? b What facts are needed to solve the problem? 60

May

Jun

3

4

5

c What operation will you use? d What is the number sentence? e What is the complete answer? What was the difference between the highest and lowest sale? a. What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer? What was his total sale from January to June? a What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer? What was his average sale for six months? a What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer?

3. Processing the Activities Allow each group to present their output. Ask: How did you find the activity? How did you solve the problem? Expected Answer: Using the four-step plan in solving the problem  Understand  Plan  Solve  Check and Look Back Discuss how to solve routine and non-routine problems. 17 Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on pages ___of LM Math Grade V. Have the pupils work on items under Get Moving and the items under Keep Moving on pages ____, LM Math Grade 5. Check the pupil’s answers. 5. Summarizing the Lesson Lead the pupils in generalizing the following: Routine problems are problems that follow standard procedure in solving word problems: Understand:   

What does the problem ask for? What are the given data? What is the word clue?

 

What operation is/are to be used? What is the mathematical sentence?

Plan

61

Solve 

Show how the solution is done using the operation.

 

Check if the answer is correct. State the final answer.

Check

Nonroutine problems are problems that can be solved even without following the steps or procedure. 6. Applying to New and Other Situations Let the pupils do the problems under Apply your Skills on page ___, LM Math5. Q Assessment Use the data in the line graph to answer the following questions.

50

Ramon’s Electric Consumption

45 40

Number

35

Of

30

Kilowatts 25 20 15 Jan

1

2

Feb

Mar

Mont hs

Apr

May

Jun

What is the total electric consumption from January to June? a What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer? If the cost of electricity per kilowatt is Php. 14.00, how much would Ramon pay for the month of May? a What is asked? b What facts are needed to solve the problem? c What operation will you use? d What is the number sentence? e What is the complete answer?

R Home Activity Remediation 1 What is the total number of immigrants starting 2010 up to 2015? 2 What is the average number of immigrants for the last three years? Immigrants Admitted in One Country

62

Numb er of Immi grant s

Year

75000 70000 65000 60000 55000 50000 45000 40000 2010

2011

2012

2013

2014

2015

Enrichment 1

About how many immigrants are there during the fifth year than during the second

2

year? Would the number of immigrants increase for 2016 or decrease? Why do you say so?

Lesson 102: Drawing Inferences Based on Data Presented in a Line Graph

63

Fourth Quarter Week 8 Objective: Draws inferences based on data presented on a line graph.

Value Focus: Perseverance in studies Prerequisite Concepts and Skills:Interpreting data in a line graph Materials: graph, grid board References: K to 12 Grade 5 Curriculum Guide, M5SP-IVh-5.5 Mathematics Teachers Guide IV pp. 346 Instructional Procedure: S Preliminary Activities 18 Drill Each group will use the grid board to plot several points on the graph. At the signal “Go”, they will start plotting. The first group to finish will win the game. Let the first group describe the figure they form based on the points they plotted on the graph. (1, 20) (3, 40) (4, 60) (5, 120) (7, 120) (7, 60) (4, 60) 160 140 120 100

y-axis 80 60 40 20 0 1

2

3

4

5

6

7

8

9

10

x-axis

19 Review Which of the following line graphs below best describe the height of a child? Defend your answer.

64

3

T

Motivation Is it important to get good grades in school? What will you do in order to attain it?

Developmental Activities 1 Presentation Ana’s Grade in Math

86 85 84

Gra de

83 82 81 80 1st Quarter

a b c 2

2nd Quarter

Quarte r 3rd Quarter

4th Quarter

At what quarter did Ana get the highest grade in Math? What is the lowest grade she got? Why do you think Ana got low grade on the second quarter? Performing the Activities Give each group activity sheets involving line graph for interpretation. Ask the group to work together in interpreting the data and make inferences out of it. After they have finished, the leader of each group will display the output on the board and discuss their answers.

Paulo’s Weight

65

44 43 42 41

Weight in

40

Kg

39 38 37 Jan

Feb

Mar

Apr

May

Month 3

Processing the Activities Each group will discuss their work. After all the groups have presented their answers to the task given, ask: How did you find the activity? How did you make inferences based on the data observed on the line graph? Discuss with the pupils how to make inferences based on the data.

4

Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page __, LM Math Grade 5.

5

Summarizing the Lesson Guide the pupils to give the following generalization. To draw inferences it is important to:  observe the parts of the graph  understand the relationship being illustrated on the graph  make prediction based on the describe situation presented by the data on the graph 6. Applying to New and Other Situations Ask the pupils to work on items under Apply your Skills on page ___, LM Math Grade 5 U Assessment Study the line graph them answer the question below. Baskets made During Practice

66

78 76 74

Number 72

of

Marco

Shoots

Series 3

70 68 66 64 1

2

3

4

5

Session a b c

How many baskets did each one make during the third session? Who made more baskets on the fourth session? What is their average number of baskets during the five-day session of

d e

practice? How many baskets did each one make all throughout the session? Who is more successful in making a basket?

V Home Activity Remediation Study the graph and answer the questions below. Angelo and Angela’s Journey in Going to School 300 200 100

Dis tan ce in (m)

0

1 2 3

What is the distance covered by each at 60 seconds? 80 seconds? What is the difference in the distance they covered at 100 seconds? What is Angelo’s speed at 40 seconds? Angela’s speed?

4 5

Enrichment How do you compare the speed of the two? What makes it possible that the other one reach school faster the other? Explain.

Time (sec) Lesson 103 : DESCRIBING EXPERIMENTAL PROBABILITY

67

Fourth Quarter Week 9 Objective: Describes experimental probability Value Focus: Love of Nature Prerequisite Concepts and Skills 

Telling whether an event is sure to happen, likely to happen or impossible to happen

Materials: Coins, die spinner, playing cards References: K-12 Grade 5 Curriculum M5SP-IVi-14, SRA Real Math pp. 336 - 339 Instructional Procedure: A Preliminary Activities 1

Drill Tell whether the following is sure to happen, likely to happen or impossible to happen.

2

a

The baby cooks for the family.

b

The lost cellular phone was found.

c

The teacher teaches the pupils.

d

The man collapses during the rally.

e

The cat drives the car.

Review Conduct a review on drawing inferences based on data presented in a line graph.

Wa ges of an Em plo yee

MONTHLY WAGE OF AN EMPLOYEE 12 000 10 000 8 000 6 000 4 000 2 000 0 Jan

Feb

Mar

Ap r

May

Jun

Jul

What does the line graph tell about the wage of the employee in seven months? 3

Motivation Have the class listen to the song Kapaligiran. Discuss the message of the song relating to prediction. Which line in the song tells something that will likely happen? Will unlikely happen ? Is it impossible to happen? or certain to happen?

B Developmental Activities 1

Presentation

68

Present to the class a number cube. Ask: If you roll a 0-5 number cube, what is the probability that you will roll 7? If you roll a 0-5 number cube, what is the probability that you will roll a number less than 7? If you roll a 0-5 number cube, what is the probability that you will roll an even number? If you roll a 0-5 number cube, what is the probability that you will roll an odd number? 2

Performing the activities Pair-Share Activity For each of the following spinners, give the probability that the pointer will stop on A.

B A A

3

B A

A A B B A

B A A

Processing the activities Ask the pair to put their output on the board. Ask: How did you find the activity? How did you perform the simple probability experiment? How did you express the outcomes of your probability experiments? Say: A probability tells us how likely something is to happen. We use fractions to describe probability. For example, if you flip a coin it has an equal chance to land on either of its two faces. The probability that the coin will land heads up is 1 result out of two possible outcome, or ½ . Since it is likely that the coin will land tails up, that probability is also ½. Even though we might imagine the coin landing on its edge, this event is so unlikely that we don’t usually consider it. We expect a coin to land heads up half of the time and tails up the other half. Nothing else is likely to happen. If something cannot possibly happen, the probability is 0. If something is certain to happen, the probability is 1.

4

Reinforcing the Concept and Skill a Discuss the presentation on top of page ___ LM Math Grade 5. Then give the following activity. Which spinner gives a ¼ probability of landing on red?

69

b

Have the pupils do the items under Get Moving, page ___ of LM math Grade 5. Check the pupils’ answers and provide corrective measures if needed. To further reinforce the skill, ask the pupils to answer items under Keep Moving, page ____ of LM Math Grade 5.

5

Summarizing the Lesson A probability tells us how likely something is to happen. If something cannot possibly happen, the probability is 0. If something is certain to happen, the probability is 1.

6

Applying to New and Other Situations Describe three instances where the probability of those events happening are 0 .

Describe three instances where the probability of those event happening is 1. C Assessment Answer the following questions. Jimmy and Naomi are rolling a regular 0-5 number cube. Jimmy wins if 0 is rolled. Naomi wins if 1,2,3,4 or 5 is rolled. 1 Who do you think will win more often? 2 What fraction of the time do you think Jimmy will win? 3 What is Naomi’s probability of winning? 4 If they roll the cube 6 times, how many times would you expect Jimmy to win? 5

What is 1/6 of 6? Should you be surprised if Jimmy did not win exactly 1 time out of 6 tries?

D Home Activity Remediation Write 0 for impossible to happen, ½ for equally likely to happen and 1 for certain to happen. _____1. From a class of 30 boys and 30 girls, what is the probability that a girl is chosen as a leader? _____ 2. Without looking, what is the probability that a green pen is drawn from a box of green pen? _____ 3. What is the probability that a tomato is drawn from a box of apples and oranges. ______ 4. From tossing a coin, what is the probability that the head shows up? ______ 5. What is the probability that an odd number of dots show up if a die is rolled?

Lesson 104 :PERFORMING AN EXPERIMENTAL PROBABILITY AND RECORDS RESULT BY LISTING Week 9 Objectives: Performs an experimental probability and records result by listing Value Focus : Acknowledgement on the contributions of some European Mathematician Prerequisite Concepts and Skills Describing experimental probability Materials: Calendar , marbles, strips of cartolina, box 70

Reference: K-12 Grade 5 curriculum M5SP-IVi- 15, Integrative Mathematics 6 pp.443 – 447 Instructional Procedure A Preliminary Activities 1 Drill a Spin the spinner b Put a mark in the tally column for each color where the spinner stops. Do this experiment for 10 times c Add the tally marks for each column and write the number in the frequency column. color

tally

frequency

Blue Yellow Green

2

Review If you roll a die, what is the probability that you will roll 2? 1? 8? Even numbers? Odd numbers?

3

Motivation Show the pictures of the Great European Mathematician like Gerolamo Cardano, Pierre de Fermat, Blaise Pascal and Christian Huygens. Say: Did you know that they began to analyse simple games of chance involving cards and dice?

B Developmental Activities 1 Presentation Show a calendar to the class. Say: Consider the days of the week. If you choose a day at random, the probability that it is a Monday is 1 out of 7 of 1/7. The probability that you choose begins with the letter T is 2 out of 7 or 2/7. The probability that the day you choose has less than 15 letters is 7 out of 7 or 1. The probability of an impossible event, such as choosing a day with only 3 letters is 0 out of 7 or 0. 2

Performing the Activity Group the class into four. Ask the class to perform the task assigned to them. Require them to write the results of the simple experiments on manila paper using the table. PICK A COLOR

Materials: a box, 6 marbles, ( 3 green, 2 blue, 1 red) Groups : four Procedure: a

Put the marbles in the box. Without looking, draw one marble from the box and record the color in the table below. color

tally

Green Blue red

71

number

b

Put the marble back in the box. Do more 19 trials. Replace the marble each time

c

after recording the color. How many times out of 20 did you draw a blue marble? The probability can be approximated by the fraction P( event) = number of times an event occurred Number of times the experiment was performed Such a fraction is called the experimental probability of an event. Give your experimental probability for each event. P(green) = ______ 20

P(blue) = ______ 20

P (red) = ______ 20

The greater the probability of an event, the more likely it will occur. The smaller the probability of an event, the less likely the probabilities. 3. Processing the Activities Instruct the group to post their outputs on the board. Ask; How did you find the activity? How did you perform the probability experiment? How did you express the outcomes of your probability experiment? What did you notice in the results of your probability experiment? Lead the discussion on using the formula in expressing outcomes of probability experiments 4.Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page _____LM Math 5, Then let the pupils do the activities under Get Moving and Keep Moving on pages _____ LM Math Grade 5 4

Summarizing the Lesson Lead the pupils in generalizing the following: Ask: How do you record prediction? By doing probability experiment, we can determine the number of times an event occur. We use a table and record the outcome of probability experiment. The probability can be approximated by the fraction P( event) = number of times an event occurred Number of times the experiment was performed

5

Applying to new and other Situations Lorraine puts cards with letters of her name into a box. What is the probability that the card she pulls out is _____

a L? ______ b O? ______ c R? ______ d A? ______ e I? ______ f N? ______ g E? ______ C Assessment Express the outcomes of your prediction. Write your answer in your notebook. 72

1 2 3 4

What is the chance that you will get a perfect score in you Math quiz? What is the probability that a newly born puppy is a girl? Toss a die, what is the probability that you will get 4 on top? What is the probability that Claire chooses a rose from a flower shop selling

5

sunflower, tulips, and dahlia? Toss a coin. What is the probability that neither the head not the tail shows up?

D Home Activity Remediation What is the probability that this spinner will land on ___? a. b. c. d. d

Lesson 105 :ANALYZING DATA OBTAINED FROM CHANCE USING EXPERIMENTS INVOLVING LETTER CARDS (A TO Z) AND NUMBER CARDS ( 0 – 20) Week 9 Objectives: Analyzing data obtained from chance using experiments involving letter cards (a to z) and number cards ( 0 – 20) Value Focus :

Have faith in life

Prerequisite Concepts and Skills  

Telling the number of favourable outcomes/chances Writing the ratio of favourable outcomes/ chances to the total number of outcomes/chances

Materials: letter cards (A to Z), number cards ( 0-20 ) Reference: K-12 Grade 5 curriculum M5SP-IVi- 16, Elementary Mathematics VI p. 330 - 333 Instructional Procedure E Preliminary Activities 1 Opening Song – “ Pagdatingng Panahon” sung by Aiza Seguerra 1 Drill Game ka na ba? Materials: 4 rolled papers numbered ( 1 to 4 ) 8 hidden questions on situations to be predicted Mechanics: a Form 4 teams having equal number of members. The leader of the team draws and gets 2 questions to be predicted by the team in terms of: 73

b c

2

 Likely to happen  Impossible to happen  Unlike to happen  Certainty to happen  Equally likely to happen Output of each team will be presented on the board. The class, together with the teacher, processes the responses of teams.

Review : Writing Ratio Find my Partner Materials: 25 cards – with ratio expressed in fraction 25 cards – with ratio expressed in colon equal to the former sets of cards Mechanics: a b

Form 4 teams. Have the cards distributed to the class. The first team will stand and look for the partner of the ratio. The next team

c

follows. The team with the highest number of partner wins

3

Motivation How many sides does a coin have? If you are to toss a coin, what is the chance that your coin will land head?

4

Developmental Activities 3 Presentation PICKING A CARD

J

B

F

D

E

A

G

H

I

C

a

Have each member of the team pick a letter without looking . Let them find the

b c

probability of picking letter G. Ask them to find the number of possible outcomes. Let them answer on the prediction card. Encourage them to determine the probability

d e

of picking G. Lead them to come up with G is 1out of 10 or 1/10 Ask them to symbolize the probability as P(G) = 1/10 Let us use the number line to show the probability of an event. LIKELY

UNLIKELY

impossible 0

1/10 We can see on the number line that50% if probability is less than ½ , an event is 1/2

certain 1

unlikely to happen. If the probability is more than ½ the event is likely to happen. A probability of 1 means the event will certainly happen and a probability of 0 means the event is impossible to happen. 4

Performing the Activity Alphabet cards of the same size and shape were put in a bag. 3 cards have letter M, 4 cards have letter A, 2 cards have letter T, and 1 card has letter H. 1. What is the total number of possible outcomes? ______________ 2. What is the probability of picking a: a. card with letter M ________ b. card with letter A ________ 74

c. card with letter T d. card with letter H e. card with a vowel f. card with a consonant g. card with M or T h. card with letter J i. card with T of H j. card with letter A or T

________ ________ ________ ________ ________ ________ ________ ________

3. Processing the Activities Instruct the group to post their outputs on the board. Ask; How did you find the activity? How did you perform the probability experiment? How did you express the outcomes of your probability experiment? What did you notice in the results of your probability experiment? Lead the discussion on using the formula in expressing outcomes of probability experiments. 4.Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page _____LM Math 5, Then let the pupils do the activities under Get Moving and Keep Moving on pages _____ LM Math Grade 5 5

Summarizing the Lesson Lead the pupils in generalizing the following: Ask: How do you tell the number of favourable outcomes/chances? A favourable outcome is the result we want to happen in an event.

6

Applying to new and other Situations There are 4 different letters to match with 6 different numbers. If you look for the probability of getting 1 letter and 1 number combination, what will be your total number f possible outcomes? C Assessment Study the cards with letters.

I

L

O

V

E

M

A

T

H

One card is drawn from a well-shuffled 9 letter cards. What is the probability of drawing a card having the following letter/s? a b c d e

L,O,V,E M, A, T I V, E Y

D Home Activity Remediation There are 4 strawberries – flavoured candies and 5 cherry-flavoured candies in a jar. If Kristine picks first and Randy picks next, what is the probability of picking a strawberryflavoured candy? What is the probability of picking cherry- flavoured candy? 75

Lesson 106: Solving Routine and Non-routine Problems Involving Experimental Probability Week 10 Objective: Solves routine and non-routine problems involving experimental probability

Value Focus: Awareness Prerequisite Concepts and Skills: 

Solving routine and non- routine on simple probability

Materials:coin, spinner, dice, References: M5SP-IVj-17, LM IV p. 266-268 & TG IV p. 352-354 Lesson Guide in Mathematics VI p.349-353,Simplifying Mathematical Challenges 6 p.454-457, XL Excelling in Mathematics 6 p.116-120, Math for Today’s Generation 5 p.344-347 Instructional Procedure: W Preliminary Activities 20 Drill Have a drill on: Conduct a game on recording and expressing outcomes of experimental probability 21 Review Conduct a review on how to solve routine and non- routine problems. Ask the learners to say something about the 4- step plans in solving problems. Ask them to give some strategies in solving problems. 3

Motivation

M

T

A

H

Ask the class of the probability of picking letter A without looking. Return the card if it is not letters A, do this 10 times. X Developmental Activities 14 Presentation Present the situation to the class. A bag contains 12 apples and 4 oranges. What is the probability of pulling apples?

Ask the pupils to read, and let them solve the problem by groups. 15 Performing the Activities 76

Group the pupils and have them perform the task. Understand 

Know what is asked: The probability of pulling apples



Know the given fact: There are 16 fruits in the bag

Plan:

There are 16 fruits inside the bag. Twelve are apples. 

Use the formula, and then substitute.



P(E) = number of times the event occurs Total number of Trials

Solve: 

The probability of pulling an apple is:

12 16

=

3 4

or 0.75 = 75%

Check and Look Back: 

Since the bag contains 16 fruits and 12 are apples, the probability of

pulling an apple is =

3 4

or 0.75 = 75%

3. Processing the Activities  

Let the groups present their outputs. Encourage the children to share to the class how they felt doing the activity. How did you solve the problem? Expected answers:  We used the 4- step plan in solving the problem: Plan, Solve, check and look back.

4.Reinforcing the Concept and Skill Discuss the presentation under Explore and Discover on page ___ of LM Math Grade V Ask the pupils to solve the problems under Get Moving on page ____ LM Math Grade V. Check their Answer. For mastery, have them solve the problems under Keep Moving on Page _______ of LM Math Grade V. Check the pupil’s answer. 5. Summarizing the Lesson Lead the pupils to generalize that : 

To solve problems, use the 4-step plan: Plan, Solve, Check and Look Back.

6. Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page ___LM Math Grade V. Encourage some pupils to show and discuss the answers.

Y Assessment

77

1

A die is thrown 100 times out of which 4 appears 30 times. Find the experimental

2

probability of getting the number 4? A Box contains 15 red balls,

12

blue

balls

and

13

green

marbles. Find the experimental probability of not getting a green ball?

Z

Home Activity Remediation Give the answer to the question. A bag contains 3 red lollipops, 3 green lollipops and 3 orange lollipop. What is the

probability of picking a green lollipop? Enrichment 1.If a coin tossed 15 times, head appears 3 times. Find the experimental probability of getting a head?

Lesson 107: Creating Routine and Non- Routine Problems Involving Experimental Probability Week 10 Objective: creates routine and non- routine problems involving experimental probability

Value Focus: Awareness Prerequisite Concepts and Skills: 

Solving routine and non- routine problems involving experimental probability

Materials: spinner, coins, manila papers, pens References: M5SP-IVj-18, LM IV p. 269-270 & TG IV p. 355-356 Lesson Guide in Mathematics VI p.349-353, XL Excelling in Mathematics 6 p.116-120 Math for Today’s Generation 5 p.344-347 Instructional Procedure: A Preliminary Activities 1 Drill Record your prediction on simple probability. Write 0= impossible to happen ½= equally likely to happen 1= certain to happen 1) When one writes, he is writing a love song. 2) When one reads his notes, he can pass the test tomorrow. 3) Once a teacher always a teacher. 4) Covering the book makes the owner orderly. 5) A first honor in Grade I will graduate valedictorian in Grade VI. 2

Review Have a review on solving experimental probability 78

A bag has 1 blue, 3 green, 2 red, and 2 yellow marbles. Find the probability of drawing: a

1 blue marble

b

3 green marbles

c

2 red marbles

d

2 yellow marbles

e

2 black marbles

3

Motivation Show a picture of a stormy weather. Ask the pupils, what would likely to happen?

B Developmental Activities 1 Presentation Present to the class this information. Have the class create a problem on experimental probability. In a bag, there are 15 M & Ms chocolate 4 red, 5 yellow, 3 blue and 3 brown.

2 Performing the Activities Group the pupils and have them perform the task. Sample Answer based on the situation above: 1. What is the probability of picking blue M & Ms? . 3   

Processing the Activities How did you create a problem? We familiarized the concept and its application to real-life situation. We thought of the problem we created. We studied some problems and their solutions.

4 Reinforcing the Concept and Skill Discuss the presentation under explore and discover on page ___ of LM Math Grade V, Have the pupils perform the exercises under Get Moving on page ____ LM Math Grade V. Check their Answer. For mastery, have them solve the problems under Keep Moving on Page _______ of LM Math Grade V. Check the pupil’s answer. 5

Summarizing the Lesson

Lead the pupils to generalize that: In creating a problem, we do the following. 

Familiarized ourselves with the concept and its application to real-life situations.



Think of the types of problems we want to create.



Read some problems and study their solutions. 6 Applying to New and Other Situations Have the pupils do the exercises under Apply your Skills on page ___LM Math Grade V. Encourage some pupils to show and discuss the answers. 79

C Assessment Create a problem on experimental probability for the following information. Anna conducted a survey of the students on her classes to observe the distribution of notebooks. The table shows the results of her survey. Notebooks Number

Blue 12

Green 14

Red 8

Pink 16

D Home Activity Remediation Create a problem for the information below. 1 There is a bowl containing blue, black, red and green marbles. There are 2 blue, 6 black, 4 red and 3 green marbles. Enrichment Create a problem for the information below. 1 I record 40 different vehicles that pass my house. The result are shown in the table below. Vehicles Frequency

Jeep 15

Tricycle 18

80

Motorcycle 4

car 3