MATH 5

STUDY AND LEARN The Bakers’ Bakery is famous for its chocolate muffins which its bakers bakeeach morning. They use 13.52 kilograms of flour everyday. How many days will283.92 kilograms of flour last?Let’s analyze the problem: What is asked in the problem? number of days 283.92 kg of flour will last What are the given facts? 13.52 kg, 283.92 kg What operation is to be used? division What mathematical sentence is appropriate? 283.92  13.52 = n How do we divide a decimal by another decimal?Steps in dividing decimals by decimals:1. Multiply the divisor by 100 to make it a whole number. 13.52 → 1352 x 100 1352.002. Multiply the dividend 100 to make it a whole number. 283.92 → 28392 x 100 2839.003. Divide. 211352 28392 - 2708 1352 - 1352 04. Check by multiplication. 2

Another procedure in dividing decimals by decimals1. Move the decimal point in the divisor to the right to make it a whole number. 13.52 → 13522. Move the decimal point in the dividend to the right according to the number of places the decimal point in the divisor has been moved. 283.92 → 283923. Divide the decimals as you would divide whole numbers. 21 A caret (^) shows where the1352. 28392. decimal point has been moved. 2704 01352 - 1352 04. Check by multiplication.TRY THESEA.Place a caret in the divisor and dividend to show where the decimal point is moved.1) 4.71 15.072 3) 0.06 41.282) 0.6 215.40 4) 0.02 0.72 3

B. Copy, divide and 3) .03 9.09 check. 4) .15 1.351) 1.8 1.17182) 0.025 0.975 WRAP UPIn dividing decimals by decimals:Step 1: Multiply the divisor by the power of ten that makes it a whole number. Or, simply move the decimal point to the right to make it a whole number.Step 2: Multiply the dividend by the same power of ten or simply move the decimal point to the right depending on the number of decimal places the decimal point in the divisor has been moved.Step 3: Divide the decimals as you would divide whole numbers. 4

ON YOUR OWNCopy then divide. Write your solutions and answers in your notebook.1. 0.04 27.242. 0.03 12.843. 0.27 0.544. 0.08 50.565. 0.19 12.35 5

DIVISION OF DECIMGARLASDEBVY WHOLE NUMBERSDIVISION OF DECIMALS BY WHOLE BUMBERS Objective: Divide decimals by whole numbersREVIEWA. Copy and multiply.1) 4.761 2) 0.81 3) 5.134 x 3.21 x 0.96 x 0.25B. Solve these problems. 1. It rained 1.75 centimeters in one hour. How much rain fell in 0.6 of that hour? 2. Allan worked 6.5 hours in a day. If he earns 50.00 an hour, how much will Allan earn? 3. Each sheet of paper is 0.0025 cm thick. How thick is a stack of 50 sheets? 4. A piece of metal is 0.5 cm thick. How thick is a piece of wood twice as thick? STUDY AND LEARNExample 1: Tony drove his car for 8 hours. It traveled a distance of 653.6 kilometers. How far did it travel in 1 hour? Let’s analyze the problem.  What is asked in the problem?  What are the given facts?  What operation should be used?  What is the number sentence? 1

Let’s solve the problem.  Divide decimals as you divide whole 81.7 numbers. 8 653.6  Put the decimal point in the quotient -64 . directly above the decimal point of the 13 -8 . dividend. 56  Check by multiplying the quotient and - 56 0 the divisor.Checking:  quotient 81.7  divisor x8  dividend 653.6Let’s have another example.Example 2:A case of 12 bottles of juice contains a total of 16.32 liters. How much does eachbottle hold? 1.36 Check:12 16.32 1.36 -12 . x 12 43 272 -36 . 136 . 72 16.32 -72 0TRY THESECopy, solve and check.1) 8 0.52 4) 14 37.242) 9 121.23 5) 26 135.23) 4 14.668 2

WRAP UPIn dividing decimals by whole numbers:Step 1: Divide as you would divide whole numbers.Step 2: Put the decimal point in the quotient directly above the decimal point of the dividend.Step 3: Check by multiplication. ON YOUR OWNDivide and check. Write your solutions and answers in your notebook.2) 9 11.115 3) 23 143.751) 6 140.4 4) 5 38.85 5) 19 501.6 3

WORD PROBLEMS INVOLGRVAINDEGVDIVISION OF DECIMALSWORD PROBLEMS INVOLVING DIVISION OF DECIMALS Objective: Solve word problems involving division of decimals REVIEWSolve and check. 3) 0.45 3.42 4) 0.15 20.251) 0.25 42.5 5) 0.25 1.15 2) 0.85 42.5 STUDY AND LEARN A tailor makes shirts, each requiring 1.15 meters of cloth. He has 148.35 metersof cloth available. How many shirts can he make?What information can we get from the problem?What are the steps to follow in solving word problem?Step 1. Read and understand the problem. What are you asked to find? What facts are given?Step 2. Plan. What plan can you make? First, study the problem. Identify the relationships that can help you decide which operation to use. 1

Step 3. Solve. How can you solve the problem?Step 4. Check if your answer is reasonable.Let us now solve the problem following the steps mentioned above.Step 1 What are you asked to find? The number of shirts the tailor can make. What facts are given? 1.15 meters, 148.35 metersStep 2 You are asked to find how many skirts can be made from the available cloth. So you divide.Step 3 Find the quotientSolution: 129115. 148.35. 115 333 - 230 1035 -1035 0Step 4 Review the answer. 129 x 1.15 645 129 129 . 148.35 2

TRY THESEAnalyze and solve the problem.1. Rina is setting up the equipment for her science class. She has 0.336 liters of water and she is going to pour equal amounts into 8 beakers. How much water will each beaker contain? a. What are the facts? b. The number sentence is ____. c. The answer is ____.2. The 342 pieces of freight on a cargo ship weigh 598.5 kilos. What is the average weight of each piece of freight? a. The equation is ___. b. What is asked in the problem? c. The answer is ____.3. Nick is cutting a board to make book ends. How many pieces of 0.65-foot long pieces can he cut from a 6-foot long board? a. What number sentence can be used to find how many pieces of board can be cut? b. What is the answer?4. Doris runs a total distance of 7.5 kilometers on 3 different days. What is the average distance covered by Doris? a. What facts are given? b. What are you asked to find? c. How can you solve the problem? d. What is the answer? WRAP UP What are the steps in solving word problems? Step 1: Understand the problem. Step 2: Plan. Step 3: Solve. Step 4: Check your final answer. 3

ON YOUR OWNAnswer the following problems. Write your solutions and answers in your notebook.1. The maximum weight capacity of a container is 20.4 kilograms. Larry put objects weighing 1.2 kilograms. How many objects of such weight can the container hold? a. What is asked in the problem? b. What are the given facts? c. Solve. Show your solution. d. Check your answer.2. How many 1.15-meters wire can be cut from a 13.8-meter wire? a. What number sentence can be used to solve the problem? b. What information is needed to solve the problem? c. Show your solution. d. Check your answer.3. Ben is filling a pail that can hold 4.5 quarts. He is using a dipper that holds 0.75 of a quart. How many times will Ben fill the dipper? a. What is asked in the problem? b. The number sentence is ____. c. Solve. Show your solution. d. Check your answer. 4

PERCENT, FRGARCATDIEOVN AND RATIO PERCENT, FRACTION AND RATIO Objective: Give the relationship among fractions, ratios and percent REVIEWTwinkle, twinkle little star. Where can I find you? To find it, you have to drawstraight lines to connect equivalent fractions and decimals or ratios. Then color thestar and make a wish. 1

STUDY AND LEARNLet’s analyze this example.Example 1: A sheep sleeps 25% of the time in a day. A lion sleeps 83% of the time in a day. A percent has been defined as a ratio in which the second term is 100.  Let us change the percent in the statement above into a fraction with a denominator of 100. 25 1a) 25% = = 100 4 25% in ratio form is 25:100 or 1:4 83b) 83% = 100 83% in ratio form is 83:100.Let’s try another example.Example 2: An elephant sleeps 12.5% of the time in a day. Write 12.5 percent as a fraction with a denominator of 100.12.5 1 → 12.5 12.5 1 or ÷=100 8 100 12.5 8 12.5% is 12.5:100 or 1:8 in ratio form. 2

Answer these questions:1. Why did we use 100 as denominator? ( We used 100 because percent means “by the hundred.” )1 25 252. How did we get from ? ( We changed to its simplest form. )4 100 1003. What did we use as second term in ratio form? ( 100 ) TRY THESE Fraction RatioComplete the table below. Percent 73% 21% 10% 89% 5%WRAP UPStep 1: Write the percent as a fraction with a denominator of 100. Express in lowest terms.Step 2: Write the percent as ratio. Use the numerator as the first term and 100 as the second term. Express in simplest form. 3

ON YOUR OWNA. Write each percent as fraction. Write your answers in your notebook.1) 51% 2) 30% 3) 43%B. Write as ratio. Write your answers in your notebook.1) 35% 2) 26% 3) 73.5% 4

PERCENTGARNADDEDVECIMALS PERCENT AND DECIMALS Objective: Give the relationship between percent and decimals REVIEW Come and Go Fishing! Summertime is the best time for going outdoor activities, like fishing. Let’stry if you can catch the five fishes in the pond. You’ll have the fishes if you couldgive the correct answer. Just change the number in percent to fraction and ratio. 75% 1

STUDY AND LEARN We have learned that different parts of a whole can be expressed usingfractions or decimals. Another way of naming parts of a whole is through percent. Apercent is a fraction whose denominator is 100. Percent is another way of sayinghundredth or in a hundred.Look at the grids below. Count the shaded part in each.Each of the four letters above is set on a triangle divided into 100 equal squares. 52Letter M has 52 shaded parts or . This can be expressed as 52%. 100 50Letter A has 50 shaded parts out of 100 or or 50%. 100 36The shaded parts in the Letter T can be represented by the fraction or 36%. 100 52Letter H has 52 shaded parts or or 52%. 100Let us change each percent to decimal through the following process:a. Remove percent sign from 54%, 50% and 36%.54, 50 and 36b. Put a decimal point after the last digit.54. 50. 36.c. Move the decimal point two places to the left..54. . 50. .36.d. 54% is now 54% 50% is 0.50 36% is 0.36 2

52% is 0.52Let’s try other examples.13.5% 5% and 8.78%So:13.5%  0.1355%  0.05 (We add zero after the decimal point to complete the8.78%  0.0878 decimal places.) TRY THESEDo what is asked.1. During the two-day show of Teatro Balangaw, the committee was able to record 3 248 people who watched the show. Of this, 87% are females. How do you write 87% as decimal?2. Write the following as decimals.a) 3% b) 11.5% c) 1% d) 7.15% WRAP UP To change percent to decimals; drop the percent sign, then move the decimal point two places to the left. Put a zero as a place holder, if needed. 3

ON YOUR OWNPlay this game and win prizes. However, when you missed a problem be ready withthe consequences. Just change percent to a decimal. Do this as fast as you can. 85% 4

CGIRRACDELEV CIRCLEObjective: Visualize circles Identify the parts of a circleREVIEWMatch the figures with their name. a. 1. pentagon2. octagon b.3. decagon c.4. hexagon d.5. nonagon e. 1

STUDY AND LEARNGet a clean sheet of paper, a ruler and a pencil. Do this activity.1. Mark point A on your paper.A2. Using your ruler, from Point A, mark another point 30 cm away from it. 30 cm A3. Continue marking other points with the same measure apart from Point A until you are able to finish a figure like the one below:  What figure looks like the one above? (Yes, it looks like a circle.) What can you say about the distance from the center point to the other points? They are the same. What is the common measurement? 30 cm Suppose we make one point less than 30 or more, can we form a circle? No. We cannot form a circle.Let us verify your discovery by using another circle. R Q  P O 2

Using your ruler measure the distance from Point O to Point P.The distance is ___ cm. How about Point Q? Point R?Suppose we put more points along the edge, will you arrive at the same measurement?Now, look at the figure below.Figure A Figure B BC  BA A A segment from the center to any point on the circle is called radius.Which figure shows radius? Correct! Figure A. Line segment AB is the radius.A segment passing through the center that connects two points on the circle is thediameter. What is the diameter of the given circle above? Line segment CB is thediameter. 3

TRY THESELook at the circle below. Answer the questions that follow. H GA F X B EC D1. The plural of radius is radii. Name other radii of circle X other than XA .2. How many radii does the circle have?3. Name two diameters of circle X other than FB .4. How many diameters does the circle have?5. Is the length of the radius of a circle always half the length of any diameter of that circle? Why? WRAP UP A circle is a set of points on a plane that are of the same distance or equidistant from a given point, called the center. You name a circle by its center. A radius is a segment that has one endpoint at the center of the circle and the other endpoint on the circle. A diameter is a line segment that passes through the center of a circle and has both endpoints on the circle. 4

ON YOUR OWNName each of the following for Circle O. Write your answers in your notebook.1. three radii S2. a diameter  T O R3. If the diameter of Circle O is 6 cm, what is the radius? 5

CGIRRACDELEV CIRCLEObjective: Visualize circles Identify the parts of a circleREVIEWMatch the figures with their name. a. 1. pentagon2. octagon b.3. decagon c.4. hexagon d.5. nonagon e. 1

STUDY AND LEARNGet a clean sheet of paper, a ruler and a pencil. Do this activity.1. Mark point A on your paper.A2. Using your ruler, from Point A, mark another point 30 cm away from it. 30 cm A3. Continue marking other points with the same measure apart from Point A until you are able to finish a figure like the one below:  What figure looks like the one above? (Yes, it looks like a circle.) What can you say about the distance from the center point to the other points? They are the same. What is the common measurement? 30 cm Suppose we make one point less than 30 or more, can we form a circle? No. We cannot form a circle.Let us verify your discovery by using another circle. R Q  P O 2

Using your ruler measure the distance from Point O to Point P.The distance is ___ cm. How about Point Q? Point R?Suppose we put more points along the edge, will you arrive at the same measurement?Now, look at the figure below.Figure A Figure B BC  BA A A segment from the center to any point on the circle is called radius. Which figure shows radius? Correct! Figure A. Line segment AB is the radius. A segment passing through the center that connects two points on the circle is the diameter. What is the diameter of the given circle above? Line segment CB is the diameter. TRY THESELook at the circle below. Answer the questions that follow. H GA F X B E C D 3

1. The plural of radius is radii. Name other radii of circle X other than XA .2. How many radii does the circle have?3. Name two diameters of circle X other than FB .4. How many diameters does the circle have?5. Is the length of the radius of a circle always half the length of any diameter of that circle? Why? WRAP UP A circle is a set of points on a plane that are of the same distance or equidistant from a given point, called the center. You name a circle by its center. A radius is a segment that has one endpoint at the center of the circle and the other endpoint on the circle. A diameter is a line segment that passes through the center of a circle and has both endpoints on the circle. ON YOUR OWNName each of the following for Circle O. Write your answers in your notebook.1. three radii S2. a diameter  T O R3. If the diameter of Circle O is 6 cm, what is the radius? 4

CIRCUMFERGERNACDEE VOF A CIRCLE CIRCUMFERENCE OF A CIRCLEObjective: Derive the formula for the circumference of a circle Find the circumference of a circle in cm/mREVIEWRecall from previous lessons perimeter refers to the distance around a polygon. Youwere also taught how to find the perimeters of certain polygons. Get a piece of paperand calculate the perimeter of each polygon below. 70 cm1) 2) 33 cm 28 cm3) 24 cm 24 cm 4) 29 cm28 cm 28 cm 30 cm 27 cm26 cm 26 cm 27 cm 27 cm 22 cm 30 cm 27 cm 29 cm 29 cm 29 cm5) What is the perimeter of a regular pentagon whose sides measure 15 cm? 1

STUDY AND LEARNDo this simple activity with anybody in your home.Procedure:1. Get a five-peso coin, one-peso coin, and a twenty-five centavo coin or a tansan.2. Measure their diameters in cm using a ruler. Record them under Diameter. Coin Diameter (D) Circumference Ratio of C:D Quotient of C/D (C)510.253. Take the one peso coin. Mark point A on the edge of the coin.4. Tape a meter stick or tape measure on top of a table.5. Put point A of the coin on 0cm on your meter stick or tape measure.6. Roll your coin along the meter stick or tape measure until point A touches the ruler again. (Make sure that it rolls and does not slide).7. Get the distance covered by the rolling of the coin on the meter stick or tape measure. Record this under “Circumference.”8. Repeat the same procedures using the other coins.cm meter stick or tape measure 1.00 10 20 30 40 50 60 1.00 A   0 cm 70 AHere is the expected result of your activity. Don’t worry if your answer is not exactlythe same as the expected results. What do you think is the explanation behind thedifference?Coin Diameter (D) Circumference Ratio of C:D Quotient of C/D (C) 5 26 mm 81.64 : 26 3.14 1 23 mm 81.64 mm 72.22 : 23 3.14 0.25 19 mm 72.22 mm 59.66 : 19 3.14 59.66 mmThe distance covered by the rolling coin is the length around the circle. We callthis the circumference of the circle. 2

The quotient of the circumference to the diameter is found in the last column of thetable.The quotient of the circumference to the diameter of a circle is the same for anycircle and is equivalent to the value of  which is approximately 3.14.  is spelled pi and read as “pie.” 22 This number is approximately 3.1416 or 7 .Since  = C → circumference d → diameterand d = 2r then C = d or C = 2r where d is the diameter and r is the radius.Let us use this formula in calculating the circumference of the circles A & B below. 15 cm 2) 8 cm1)   A BC = d (since the diameter is given in the first circle) = 3.14 x 15cm = 47.10 cmC = 2r (since the radius is given in the second circle) = 2(3.14 x 8cm) = 50.24cm 3

TRY THESEDo what is asked.1. A circular flower garden has a diameter of 10 meters. What is the circumference of the flower garden?2. Carla has a circular tablecloth. Its radius is 1.5 m. What is its circumference?3. d = 15 cm 4. r = 9 cm 5. d = 25 cm C = ___ C = ___ C = ___ WRAP UP Circumference of a circle is the distance around the circle. To getthe circumference of a circle, use any of the following formulas. C = d (if the diameter is given) C = 2r (if the radius is given) ON YOUR OWNFind the circumference of the circle with the given diameter or radius. Write yoursolutions and answers in your notebook. 4

1. d = 17 cm2. d = 13 cm3. r = 6.15 m4. d = 8.5 cm5. r = 2.25 cm 5

WORD PROBLEMS INGVROALDVEIVNG CIRCUMFERENCE WORD PROBLEMS INVOLVING CIRCUMFERENCEObjective: Solve word problems involving the circumference of a circle REVIEWCalculate the circumference of a circle with the given diameter or radius.1) r = 8.5 cm2) d = 26 cm3) r = 15 cm4) d = 6 m5) r = 3.5 mSTUDY AND LEARNRead the problem.Example 1: Mayor Jonathan Garcia of Mogpog, Marinduque built a fountain on the municipalplaza. The fountain stood on a circular pond with a diameter of 8.4 meters. Find thedistance around the pond.READ AND What is asked for in the problem?UNDERSTAND (distance around the pond) What data was given?PLAN (diameter of the pond is 8.4 meters) What must be done to solve the problem? The phrase “distance around” tells us that we 1

need to find the circumference of the circular pond. Since C = d, the number sentence for this problem is 3.14 x 8.4 = n SOLVE Carry out the plan. ANSWER 3.14 CHECK x 8.4 1256Let us try another problem. 2512 .Example 2: 26.376 The circumference of the circular pond is 26.376 meters. Is the answer correct? Check by division. 8.4 → diameter 3.14 26.376 → circumference 2512 1256 1256 0 A circular swimming pool has a radius of 9 meters. Find the distance covered byAcela if she walks along the rim of the pool. What is asked in the problem? What are given? What must be done to solve the problem? What is the number sentence?(2 x 3.14) x 9 = nCarry out the plan. (2 x 3.14) x 9 = n 6.28 x 9 = 56.52 2

The answer is 56.52 meters.Example 3: Vangie bought 8.5 meters of lace to be sewn around the edges of the circular tablecloth. If the lace fits exactly the edge, find the diameter and radius of the table cloth.We need to divide 8.5 by 3.14 to get the diameter. 2.7073.14 8.50000 628 2220 2198 220 0 2200 2198 22To get the radius, divide 2.71 by 2.r = 2.71  2 = 1.355 meters or about 1.36 meters TRY THESECan you now solve the problems involving circumference of a circle on your own? Get apiece of paper and solve the two problems below.1. How many meters of fencing is needed to enclose a circular garden whose diameter is 10.50 meters?2. If a buko pie has a circumference of 94.20 cm, what is its diameter? 3

You are now ready to solve problems on your own. Write your answers on a sheet of paper and present this to your teacher for checking. Or, you may have other members of the family check it first before giving it to your teacher. ON YOUR OWNRead and solve. Write your solutions and answers in your notebook. 1) A round tissue holder has a radius of 7.5 cm. If a red ribbon is to be placed around it, how much ribbon is needed? 2) A small plate has a diameter of 20 cm. What is its circumference? 3) The wheel of a vehicle has a radius of about 25 cm. Find its circumference. 4

AREA GORFADAECVIRCLE AREA OF A CIRCLE Objective: Find the area of a circle REVIEW Identify the parts of circle referred to. 1. A segment that passes through the center of a circle and has both endpoints on the circle. 2. A segment that has one endpoint on the circle. 3. The length of the radius is always half of the _______. STUDY AND LEARN Read this problem and learn how to find the area of a circle.Example 1: What is the area of a circular mirror with a radius of 16 cm? What are you asked for to find in the problem? What is given? How do we find the area of a circle? The area of a circle: A = r2 where  means pi whose value is about 3.14 The exponent 2 means that we are going to multiply the radius by itself. 1

Let us substitute the value of each symbol and perform the operation. A = r2 = 3.14 x (16)2 = 3.14 x 256 = 803.84The area of the circular mirror is 803.84 square centimeter or 803.84 cm2.Let us try another one.Example 2: What is the area of a circle whose diameter is 15 meters?Since the given is the diameter, divide 15 by 2 to get the radius. So: A = 3.14 x (7.5)2 = 3.14 x 56.25 = 176.63 sq. mTRY THESETest yourself whether you can now find the area of circle. Go back to the previous pagesof this module if you want to review how to find the area.1. What is the area of a circle whose radius is 8 cm?2. A revolving sprinkler sprays a lawn for a distance of 7 m. How many square metersdoes the sprinkler spray in 1 revolution?3. r = 12 m 4. r = 6 m 5. d = 17 cmA = ____ A = ____ A = ____ WRAP UP The area of a circle is the surface covered by a circular region. The formula infinding the area of a circle is r2, where  (pi) is approximately 3.14 and r is theradius of the circle. 2

ON YOUR OWNRead and solve. Write your solutions and answers in your notebook.1) Find the area of a circle having a radius of 5 meters. 5m2) Find the area of a circle having a diameter of 22 meters.  22 m3) What is the area of a circle whose diameter is 26 dm?4) r = 4.5 m A = ____5) d = 23 cm A = ____ 3

AREA OFGRAATDRE AVPEZOID AREA OF A TRAPEZOID Objective: Find the area of a trapezoid REVIEW 1. What is the area of a triangle if its height is 10 cm and the base is 8 cm? 2. Find the area. 8 cm 6 cm STUDY AND LEARN Look at the trapezoid below. We have two bases of different lengths. b1height b2 1

If we take another trapezoid congruent to the first we can form a parallelogram as shown. b1 b1 b1 b2h b2 b2 b2 b1 Notice that the base of the parallelogram is the sum of b1 and b2 of the trapezoid. To get the area of the original trapezoid we can use half the area of the parallelogram 1 b1 + b2 formed. Therefore, A = 2 ( b1 + b2)h or A = ( 2 ) x h Let’s solve for the area of the trapezoid where h = 3 units, b1 = 3 units, b2 = 5 units. Let us substitute the value of each symbol and perform the operations. Area b1 + b2 = ( )x h 2 3+5 = ( ) x3 2 8 = x3 2 =4x3 = 12 The area of the trapezoid is 12 sq. units. Here’s another example. Example 1: Let us find the area of this trapezoid. 6 cm 4 cm 8 cm Area b1 + b2 = ( )xh 2 6+8 = ( ) x4 2 2

14 = x4 2 =7x4 = 28The area of the trapezoid is 28 square cm or 28 cm2.Let us try another one.Example 2: 8 cm b1 + b2 Area = ( 2 )x h 5 cm 8 +10 = ( )x5 2 10 cm 18 = x5 2 = 9x5 = 45 sq. cmTRY THESEA. Find the area of a trapezoid with bases 9 cm and 5 cm and a height of 8 cm. 5 cm Area = ( b1 + b2 )x h 8 cm 2 9 cmB. What is the area of a trapezoid if the height is 7 cm and the parallel sides are 8 cm and 12 cm long? 3

WRAP UP The formula for the area of a trapezoid is: A= 1 (b1  b2 ) x h 2 ( b1 + b2)h or A = 2ON YOUR OWNFind the area of each trapezoid. Answer in your notebook.1) h = 8 cm 2) h = 5 m 3) h = 9 m 4) h = 6 cm b1 = 4 cm b1 = 8 cm b2 = 10 cm b1 = 9 m b1 = 5 m b2 = 12 cm b2 = 13 m b2 = 7 cm 4

VOLUME OF A RGERACDTEAVNGULAR PRISM VOLUME OF A RECTANGULAR PRISMObjective: Find the volume of a rectangular prism REVIEW 15 cmFind the area of the following rectangles. 8 cm 12 cm 5)1) 2) 9m 4m 5 cm 6 cm3) 4) 5 cm 6 cm 14 cm STUDY AND LEARNYou have learned that the volume of any solid is the number of units of cubic measurecontained in the solid. Volume is measured in cubic units.Look at the rectangular prism below. h = 4 units l = 5 unitsw = 4 units 1

Answer these questions:In the figure, how many square units make up the length of the rectangular prism? thewidth? the height?Volume of rectangular prism =lxwxhWhere l or length = 5cm w or width = 4cm h or height = 4cmVolume =lxwxh = 5cm x 4cm x 4cm = 80 cubic cm or 80cm³Let us have another example.Example 2:Find the volume of a rectangular solid 8 meters long, 5 meters wide and 7 metershigh.7m V=lxwxh 5m V = 8m x 5m x 7m V = 280 cubic metres or 280 m3 8mTRY THESETry to answer the exercises below by simply applying the formula V = l x w x h.Find the volume of the following rectangular prisms. Write your answers in yournotebook.1) 2) 6m 10 dm 8m 5m3) l = 16 cm 6 dm 4) l = 9 m 5 dm 2

w = 7 cm w=3mh = 8 cm h=7mV=? V=?5) What is the volume of a rectangular box if it is 16 cm long, 10 cm wide and 6 cm high?WRAP UP The formula for the volume of a rectangular prism islength x width x height. Or it can be written as, Vrectangular prism = l x w x hVolume is given in cubic units.ON YOUR OWNA. How much can this prism contain or hold?1. L = 15 cm 2. L = 12 m 3. L = 20 dm W = 7 cm W=6m W = 10 dm H = 5 cm H=8m H = 5 dm V = ____ V = ____ V = ____4. L = 7 m 5. L = 9 mW = 3.5 m W = 4.5 mH=6m H=6mV = ____ V = ____B. Read and solve. 1. What is the volume of a rectangular solid if it is 7 cm long, 4 cm wide and 9 cm high? 2. Marlon bought a rectangular box. If it is 15 cm long, 12 cm wide and 10 cm high, what is its volume? 3

PARTS OF A THERMOMETER/READING A THERMOMETER GRADE VPARTS OF A THERMOMETER / READING A THERMOMETER Objective: Identify the parts of a thermometer Read a thermometerREVIEWTell whether each of the following objects below is hot or cold. Write your answers inyour notebook.1. 2. 3.4. 5. 6. 1

STUDY AND LEARNAre there health workers in your barangay? They use a thermometer to measure thebody temperature of their patients. In hospitals or in some houses, they also usethermometers. Look at the thermometer drawn below. CThe thermometer is used to measure temperature. Temperature tells how hot orcold something is. A unit for measuring temperature is the degree Celsius (C).The thermometer, has a glass tube containing mercury, a liquid that goes up anddown the tube, depending on the temperature of the object.When the temperature is hot, the mercury goes up the glass. It goes down whenthe temperature gets cold. 2

The thermometer has marks labeled by numerals. The numerals tell the number ofdegrees at a particular temperature.Through a thermometer you can verify that the boiling point of water is 100 C. It isread as 100 degrees Celsius. It is written as 100 C.What is the normal body temperature? the normal room temperature?What is the temperature at which water freezes? 37 C is read as 37 degrees Celsius. 20 C is read as 20 degrees Celsius. 0 C is read as 0 degree Celsius.TRY THESEWrite in your paper the reading in each thermometer. 3.1. 2.4. 5. 6. 3