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-1352550-1310005<br />ADRIEL G. ROMANMYRICHEL ALVAREZAUTHORSNOEL A. CASTROMODULE CONSULTANTFOR-IAN V. SANDOVALMODULE ADVISER<br />-95250-6667504972050-781050VISION<br />A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly, Asian countries. <br />MISSION AND MAIN THRUST<br />The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technology and other related fields. It shall also undertake research and extension services, and provide a progressive leadership in its areas of specialization. <br />GOALS<br />In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness.<br />OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION (BSEd)<br />Produce graduates who can demonstrate and practice the professional and ethical requirements for the Bachelor of Secondary Education such as:<br />1. To serve as positive and powerful role models in the pursuit of learning thereby maintaining high regards to professional growth.<br />2. Focus on the significance of providing wholesome and desirable learning environment.<br />3. Facilitate learning process in diverse types of learners.<br />4. Use varied learning approaches and activities, instructional materials and learning resources.<br />5. Use assessment data, plan and revise teaching-learning plans. <br />6. Direct and strengthen the links between school and community activities.<br />7. Conduct research and development in Teacher Education and other related activities.<br />-1406525-927735<br />Overview In this unit, you will understand the concept of the basic fundamental operations dealing with whole numbers. This workbook will help you to master and to become skilled in the fundamental operations.This modular workbook provides information about four operations and how to perform such kind of operation in solving word problem. It also provides exercises and activities that will help you become skilled and for you to master the fundamental operations.Objectives:After studying this unit, you are expected to:discuss the four fundamental operations;perform the operations well;check the answers in addition and multiplication using their inverse operation.<br />-1371600-914400  <br />IntroductionIn this chapter, you will learn deeply the addition operation, the different parts of it, the different properties and the use of this operation in solving a word problem.       This chapter will serve as your first step in mastering the basic fundamental operations for this chapter will discuss how to solve a word problem using systematic ways. All the information you need to MASTER THE FUNDAMENTAL OPERATIONS DEALING WITH WHOLE NUMBERS is provided in this chapter. <br />Lesson 1<br />WHAT IS ADDITION?<br />Objectives: <br />After this lesson, the students are expected to:<br />define what addition is;<br />identify the different properties of addition;<br />perform the operation (addition) correctly.<br />      326 + 258 = 584     SumAddends                How well do you remember your basic addition facts? In addition sentence,                            326 + 258 = 584, which are the addends and which is the sum?<br />386766570931 <br />Addition is a mathematical method on putting things together. Adding whole numbers together is a method that requires placing the numbers in column to get the answer. Addition is represented by the plus sign (+). The addends and the sum are the two parts of addition. The sum is the total and the addends are the numbers needed to add.<br />Examples:<br />27 +31=58the addends are 27 and 31 and the sum is 58.<br />11+21=32the sum is 32 and the addends are 11 and 21.<br />-484156-487832WORKSHEET NO. 1<br />NAME: ___________________________________DATE: _____________ <br />816491221295YEAR & SECTION: ________________________RATING: ___________<br />,[object Object]
 ADDITION-
-4238625524629__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
ADDENDS-
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
SUM-
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
-508026-4977594238625238446ADD THE FOLLOWINGSOLUTION<br />,[object Object]
4333+9586=__________________
423381+46537=_______________
546263+9520=________________
-420052547752031481+369=__________________
23634+12438=________________
3497+6826=__________________
81650+3897601=______________
 7333+62766=_________________
 178654321+236754=___________Lesson 2<br />PROPERTIES OF ADDITION<br />Objectives: <br />After this lesson, the students are expected to:<br />define the properties of addition;<br />use the different properties of addition in solving;<br />perform an operation using the properties of addition.<br />PROPERTIES OF ADDITION<br />,[object Object],Examples:<br />8 + 0 = 827 + 0 = 27<br />10 + 0 = 1031 + 0 = 31<br />,[object Object],This property states that changing the order of the addends does not change the sum. This means you need to remember only half of the basic facts. In symbols, the property says that a + b = b + a, for any numbers a and b.:<br />Examples: <br />6 + 8 = 148 + 6 = 14<br />11 + 27 = 38             27 + 11 = 3<br />,[object Object],Examples:<br />(4 + 3) + 8 = 4 + (3 = 8) = 15<br />9 + (8 + 6) = (9 + 8) + 6 = 23<br />Remember to work in the parenthesis first.<br />Summary:The 0 Property in AdditionIf “a” is any number, a + 0 = a.The Commutative Property of AdditionIf a + b = b + a, for any numbers a and b.The Associative Property of AdditionIf a, b and c are any numbers,(a + b) = c = a + (b + c).<br />-490623-361950WORKSHEET NO. 2<br />NAME: ___________________________________DATE: _____________ <br />433070227330YEAR & SECTION: ________________________RATING: ___________<br />,[object Object],1.  265 + 547 = 547 + 265___________________________<br />2.  85 + 78 = 78 + 85_______________________________<br />-42195753982643.  15 + 0 = 15____________________________________<br />4.  3 + (5 + 9) = (3 + 5) + 9 =17_____________________<br />5.  31+ (21+15) = (31+21) +15 = 67__________________<br />6.  59 + 0 = 59___________________________________<br />7.  100 + 0 = 100_________________________________<br />8.  65 + 498 = 498 + 65____________________________<br />9.  9 + 5 = 5 + 9__________________________________<br />10. (10+10) + 10 = 10+ (10+10) =30_________________<br />Lesson 3 <br />MASTERING SKILLS IN ADDING WHOLE NUMBERS USING ADDITION TABLE<br />Objectives: <br />After this lesson, the students are expected to:<br />use the addition in table properly;<br />mastering skills in addition using tables;<br />discuss the use of addition table.<br />Addition Table<br />The Addition Table can help you to master the addition operation<br />+     0     1     2    3     4     5    6    7    8     9   10 11 12001234567891011121123456789101112132234567891011121314334567891011121314154456789101112131415165567891011121314151617667891011121314151617187789101112131415161718198891011121314151617181920991011121314151617181920211010111213141516171819202122How to useExample: 3 + 5Go down to the quot;
3quot;
 row then along to the quot;
5quot;
 column,and there is your answer! quot;
8quot;
 +12345671234567823456789345678910456789101156789101112<br /> <br /> <br />-6799006788526You could also go down to quot;
5quot;
and along to quot;
3quot;
, or along to quot;
3quot;
 and down to quot;
5quot;
to get your answer. +12345671234567823456789345678910456789101156789101112<br />-467114-309746WORKSHEET NO. 3<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />,[object Object],4582632297047<br />,[object Object]
Have your own addition table
With your addition table, add the following
1+4, 0+1, 3+4, 5+0, 5+4
6+4, 7+2, 8+0, 9+2, 10+4
1+6, 3+6, 5+6, 3+10
6+6, 10+6, 6+8, 10+10
-4191000367665After adding, try to put dots in every sum. Try to connect the dots by a line in every number to find what the mother of all science is.                       <br />-503764-485775-486410-498475Add the following numbers correctly.<br />,[object Object]
593423+4467=_____________________
359+4843=________________________
1297+4548=_______________________
696493+266=______________________
1898976+219876=__________________
78589+66533=_____________________
-4219575857266485092+1764243=_________________
828637+86464=____________________
12379+2873=______________________
  53746+783579=___________________
642578+325646=___________________
12398+6327355=___________________
563745+654689=___________________
57684+8765358=___________________
425778+87654=____________________Lesson 4<br />DIFFERENT METHODS IN ADDING WHOLE NUMBERS<br />   Objectives: <br />After this lesson, the students are expected to:<br />solve addition using other methods;<br />discuss the different methods in adding whole numbers;<br />solve mathematical problems using the other method.<br />There are some easy ways in adding whole numbers.<br /> Adding the column separately. <br />413385080010 Let 326+258 use as our illustrative example.<br />Adding in reverse order<br />326            300+20+6<br />     +258           200+50+8<br />Add the numbers in the hundreds place.Add the numbers in the tens place.Add the numbers in the ones place.Then add their sum to get the total sum.                                             500<br />300+20+6<br />200+50+8                                                                                                                   500+70<br />,[object Object],200+50+8                                                                                                           500+ 70+14<br />,[object Object],Adding in column separately<br />389692160679EXAMPLE: <br />   526<br />   + 278                                                                                                                                             <br />        14<br />                        +   9<br />                           7<br />Arrange the numbers vertically.Add the numbers in the ones place.Then add the tens place and place the sum under the tens place.Then add the numbers in column.                           804<br />Tocheck;<br />Add it upward.<br />Subtract the sum to one of the addends.<br />Add the numbers in the addends and in the sum if your answer in the sum is the same as in the addends, then your answer is correct.<br />-479127-394796WORKSHEET NO. 4<br />-42100503688715NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />19051-3913<br />,[object Object]
39, 28_________________
43, 29_________________
69, 51_________________
70, 623________________
890, 431_______________
343, 86________________
987, 652_______________
6232, 7434_____________
853 234, 578____________
6 754 236, 643 123_______SOLUTION:<br />-498517-447453-516435-394290B. Perform the operation using the procedure discussed. Check your answer by using the short method.<br />,[object Object]
367+201=____________________________
9 632+2 330=_________________________
1 423+54 673=________________________
543 265+65 223=______________________
673 895 462+54 289=___________________
629 075+57823=_______________________
-4209415218440642 890+57 829=______________________
564 872 389+54 738=___________________
12 345+42 321=________________________
3255+6472865=________________________
6437286+56387=_______________________
54390+529=___________________________
6348901+65890=_______________________
7395+7598043=________________________Lesson 5<br />SOLVING WORD PROBLEM<br />Objectives<br />        After this lesson, the students are expected to:<br />discuss how to solve a word problem;<br />solve any given problems systematically;<br />use problem solving plan in solving any given word problem.<br />Throughout this lesson, we will be solving problems that deal with real numbers. In solving word problems, the following plan is suggested:         <br />         <br />This problem solving plan should be used every time we solve word problems. Careful reading is an important step in solving the problem. This lesson serves as an introduction to the next chapter.<br />563880316865<br />PROBLEM SOLVING PLAN<br />Understand the problem.<br />Devise a plan. <br />Carry out the plan.<br />Check the answer. <br />One harvest season, a farmer harvested 531 sacks of rice. This was 87 more than his previous harvest. How many sacks did he harvest during the previous season?<br />Example: <br />PROBLEM SOLVING PLAN<br />1. UNDERSTAND THE PROBLEM            <br />What is the problem about?What information is given?What is being asked?Understand the problem and get the general idea. Read the problem one or more times. Each time you read ask:<br /> <br />Represent what is asked with a symbol. {The problem is about the number of sacks harvested. Let S be the number of sacks during the previous harvest.}<br />2. DEVISE A PLAN                                       <br />This is a key part in the 4 step plan for solving problems. Different problem solving strategies have to be applied. A figure, diagram, chart might help or a basic formula might be needed. It is also likely that a related problem can be solved and can be used to solve the given problem. Another devise is to use the “trial and learn from your errors” process. There is a lot of problem solving strategies and every problem solver has own special technique.<br />“87 more” suggests addition and we can write a formula:87+S=531.<br />3. CARRY OUT THE PLAN<br />Solve the equations:      87+S=531      S=531-87      S=444 sackIf step two of the problem solving plan has been successfully completed in detail, it would be easy to carry out the plan. It will involve organizing and doing the necessary computations. Remember that confidence in the plan creates a better working atmosphere in carrying it out<br />.<br />4. CHECK THE ANSWER<br />This is an important but most often neglected part of problem solving. There are several questions to consider in this phase. One is to ask if we use another plan or solution to the problem do we arrive at the same answer.<br />.<br />It is reasonable that the farmer harvested 444 sacks during the previous harvest. His harvest now which is 531 is more than the last harvest<br />401002510795<br />-400049-278130WORKSHEET NO. 5<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />-637951285<br /> <br />           A. Discuss the different problem solving plan briefly.<br />            1. Understand the problem<br />___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />-40936311756582. Devise a plan-___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />3. Carry out the plan<br />___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br /> Check the answer<br />___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />-421738-462758B. APPLICATION: Solve the given word problem correctly.<br /> Maria has 17 candies and her friends gave her 3 candies each. If she has 3 friends, how many candies did she have?<br />___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />     <br />,[object Object],-4156710616585___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />Lesson 6<br />APPLYING ADDITION OF WHOLE NUMBERS IN WORD PROBLEM<br />Objectives <br />After this lesson, the students are expected to:<br />,[object Object]
to develop the skills and knowledge in solving word problems;
identify the different steps in word problems involving addition.        LOOK AT THE EXAMPLE<br />A farmer gathered 875 eggs from one poultry house and 648 from another. How many eggs did he gather? We want the answer to 875 + 648 =?<br />,[object Object]
Write 3 in the ones column and bring the 1 ten to
      the  tens column.
Add the tens: 1 +7 +2 = 12 tens = 1 hundred + 2
      tens.
Write 2 under the tens column and bring the 1
      hundred to the hundreds column.
Add the hundreds: 1 + 8 + 6 = 15 hundreds = 1
      thousand + h hundreds. Write 15 to the left of 2.                                   The farmer gathered 1 523 eggs.<br />      Here is another example:<br />1 11  5 986                                                     +3 759 9 745<br />Add: 5 986 + 3 759 =?<br />,[object Object]
1 ten + 8 tens + 5 tens = 14 tens = 1 hundred + 4 tens.
1 hundred + 9 hundreds +7 hundreds = 17 hundreds = 1
             thousand + 7 hundreds.
1 thousand +5 thousands + 3 thousands = 9 thousands.                 Thus, 5 986 + 3 759 = 9 745<br />   15 326   + 1 456       6782<br />Add: 5 326 + 1 456 =?<br />,[object Object]
1 ten + 2 tens + 5 tens = 8 tens
3 hundred + 4 hundreds=7 hundreds
5 thousand +1 thousands= 6 thousands.    Thus, 5 326 + 1 456 =678<br />-580028-289408WORKSHEET NO. 6<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />Answer the following problem solving<br />,[object Object]
Miss Callanta drove her car 15 287 kilometers and 15 896 kilometers the next year. How many kilometers did she drive her car in two years?__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />The monthly production of cars as follows: January-4,356, February- 4,252, and March- 4425, June-4456, July-4287, August-4223, September-4265, October-4365, November-4109, and December- 4270. How many cars were produced in the whole year?<br />-4178300462915__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />If a sheetrock mechanic has 3 jobs that require 120 4x8 sheets, 115 4x8 sheets, and 130 4x8 sheets of sheetrock respectively. How many 4x8 sheets of sheetrock are needed to complete the 3 jobs?<br />________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________<br />-1362576-900363-1379846-914400<br />IntroductionIn this chapter, you will learn the subtraction operation, the different parts of it and the use of this operation in solving word problem. You will also learn the different ways on how to solve and check the answer or the difference which you can use in your everyday life. This chapter provides the information that will help you master the subtraction as one of the fundamental operation in Mathematics.<br />Lesson 7<br />WHAT IS SUBTRACTION?<br />Objectives<br />After this lesson, the students are expected to:<br />define what is subtraction;<br />identify the parts in subtraction;<br />differentiate the subtraction from addition.<br />What is Subtraction?<br />-224394185272<br />After learning and describing addition as a process of combining two or more groups of objects, we can now consider its opposite operation --- Subtraction. If addition is combining of group of object, subtraction is the process of taking away or of removing something. The symbol used for subtraction is the minus sign (-).<br />When we write 12 – 6, we wish to subtract 6 from 12 or to take away 6 from 12. To find the difference between two numbers, we have to look for a number which when added to the subtrahend, will give the minuend.  The table shows the relation between addition and subtraction. One undoes the work of the other.<br />346710091440<br />        12           addend     +   6  addend                               18              sum                        Minuend            18                                              Subtrahend           - 6      Difference     12Let us consider the notation below.<br />Difficulties may arise in subtraction when a digit of the subtrahend is larger than the corresponding digit in the minuend. The process of doing a subtraction of this type is called barrowing or regrouping.<br />-428625-390526WORKSHEET NO. 7<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />-29210121920<br />A. Give the meaning of the following words.<br />-41444824792811. Subtraction-________________________________________________<br />2. Minuend-__________________________________________________<br />3. Subtrahend-________________________________________________<br />4. Difference-_________________________________________________<br />B. Name the following parts of the mathematical expression given below.<br /> 12638         _____-   3630         ________             9008  <br />433387529845<br />-428721-542219C.Find the difference<br />1.  349   -265 2.  1243     -360 3.  5428    -2001 4.  10,000      -6,543<br />D. Solve the following to get the difference<br />WRITE YOUR SOLUTION HERE:1. 5637584-43675=________________<br />-41357553086102. 5389-782=_____________________<br />3. 43674-768=____________________<br />4. 376598-5281=__________________<br />5. 67396-683=____________________<br />6. 57290-7849=___________________<br />7. 56284-6847=___________________<br />8. 683963-68363=_________________<br />9. 6254-978=_____________________<br />10. 654-87=______________________<br />Lesson 8<br />MASTERING SKILLS IN SUBTRACTING WHOLE NUMBERS<br />Objectives <br />After this lesson, the students are expected to:<br />enhance the knowledge in terms of subtracting whole numbers;<br />develop the speed in solving subtraction;<br />perform the steps in subtracting whole numbers.<br />Cain Kiblah typed his report in physics at the computer shop for about 5 hours and 17 minutes while Lane Margaret types her report for only 3 hours and 28 minutes. How fast does Lane Margaret type her report than Cain kiblah? <br />       5 hrs + 17 mins    - 3 hrs + 28 mins     ?<br />To make the subtraction convenient, we borrow 1 minute so we have:<br />        5 hrs + 17 mins      77mins    - 3 hrs + 28 mins      28mins      1 hr   +                  49mins<br />-426067-200025WORKSHEET NO. 8<br />NAME: ___________________________________DATE: _____________ <br />4876800212090YEAR & SECTION: ________________________RATING: ___________<br />,[object Object],Subtract 381 from 1895<br />Subtract 852 from 1682<br />Subtract 665 from 694<br />-413606559971Subtract 443 from 1084<br />Subtract 154 from 1284<br />Subtract 46 from 850<br />Subtract 132 from 957<br />Subtract670 from 2064<br />Subtract 739 from 1591<br />Subtract 754 from 772<br />,[object Object],10327-1685=____________<br />74577-7658=____________<br />9443-99195=____________<br />14652-9195=____________<br />19919-8881=____________<br />8322-4909=____________<br />8851-8453=____________<br />7609-6957=____________<br />8858-182=_____________<br />8905-18=______________<br />Lesson 9<br />PROBLEM SOLVING INVOLVING SUBTRACTION<br />Objectives<br />After this lesson, the students are expected to:<br />,[object Object]
discuss the different steps in problem solving;
develop the knowledge in problem solving.4126089481542<br />To master the application of subtraction in problem solving, here are some examples:<br />Pedro had marbles. He gave away two of his marbles to Juan. If Pedro had twelve marbles, how many marbles left to Pedro after he gave two to Juan?<br />We can use the problem solving plan:<br />1.Know what the problem is.<br />a.What is asked?   How many marbles left to Pedro?<br />b.What are given?  12 marbles of Pedro and 2 to Juan<br />c.What operation to be used?  Subtraction<br />12 – 2 = n12 – 2 = 10   <br />N = 10 marbles left to Pedro.<br />Checking:<br />2 + 10 = n  2 + 10 = 12<br />Another example:<br />Mt. Everest, is 29 028 ft. high, while the Mt. McKinley is 20 320 ft. high. How much is Mt. Everest higher than Mt. McKinley? <br />1.What is asked?  <br />How much Mt. Everest higher than Mt. McKinley?<br />2.What are given?<br />Mt. Everest, is 29 028 ft. high and Mt. McKinley is 20 320 ft. high.<br />3.What operation to be used?<br />Subtraction<br />29 028 – 20 320 = n<br />29 028 – 20 320 = 8 708 ft. <br />Checking:<br />8 708 + 20 320 = n<br />8 708 + 20 320 = 29 028 <br />-534172-167858WORKSHEET NO. 9<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />A. Get one whole sheet of paper and solve the following problem. <br />      <br />,[object Object],-4263390263525___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],-404241017145___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],____________________________________________________________________________________________________________________________________________________________________________________________________________<br />___________________________________________________________________. <br />,[object Object],__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],-40386001092835___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />,[object Object],___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.<br />-1379855-914400<br />       <br />           <br />IntroductionIn this chapter, you will learn about the multiplication operation, its different parts and ways in solving it and the use of this operation in word problem. This chapter provides lessons and exercises that will help you to master the multiplication of whole numbers.<br />Lesson 10<br />WHAT IS MULTIPLICATION?<br />Objectives: <br />After this lesson, the students are expected to;<br />,[object Object]
identify the part of multiplication.
perform the multiplication operation properly.4387755318258<br />Multiplication is a repeated addition. It can be thought of as addition repeated a given number of times.<br />         3    multiplicand        ×5      multiplier                  15 productsFor example, 3 x 5 = 15 can be solving as 5 + 5 + 5 =15. 3 mean that the 5 is to be used three times. The same problem can also be thought of as 5x 3, or 3 + 3 +3 + 3 + 3 =15. Written this way, the three is used as a total of five times in either case is 15.<br />The number in the upper part is called the multiplicand and in the lower position is called the multiplier. The answer in the multiplication is called product.<br />-315310-298231WORKSHEET NO. 10<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />A.Identify the following.<br />                                           7         __________<br />                                        × 2          __________<br />                                         14         ___________<br />-404304555245<br />B.Get the product of the following.<br />1.32 x 25=6. 14 x 193=<br />     2.      10 x10 =                 7. 66 x 15=<br />3.25 x 68=8. 157 x 11=<br />    4.     31 x1545=     9. 655 x 8=<br />5.27 x 17781=10. 856 x 18=<br />Lesson 11<br />PROPERTIES OF MULTIPLICATION<br />Objectives<br /> After this lesson, the students are expected to:<br />,[object Object]
develop the knowledge in the properties of multiplication;
apply the properties of multiplication in solving problem.
IDENTITY PROPERTY The product of the 1 and any number a is a, that is, 1 x a = a for any number.Example:<br />21 x a = 2127 x a =2731 x a = 31<br />11 x a = 115 x a = 513 x a = 13<br />2.   ZERO PROPERTY The product of 0 and any number a is 0, that is a x 0 = 0 for any   number a.<br />Example:<br />0 x 87 = 00 x 98 = 015 x 0 = 0<br />45 x 0 = 014 x 0 = 058 x 0 = 0<br />3.  COMMUTATIVE PROPERTYChanging the order of the factors does not change the product,    that is,a x b = b x a for any number of a and b.PROPERTY<br />Example:<br />7 x 4 = 28 = 4 x 75 x 12 = 60 = 12 x 5<br />5 x 6 = 30 = 6 x 54 x 11 = 44 = 11 x 4<br />4.  ASSOCIATIVE PROPERTY Changing the grouping of the factors does not affect the product, that is, a x (b x c) = (a x b) x c for any number of a, b, and c.<br />Example:<br />(7 x 4) x 5 = 140 = 7 x (4 x 5)<br />(4 x 6) x 8 = 192 = 4 x (6 x 8)<br />5.  DISTRIBUTIVE PROPERTY   If one factor is a sum of two numbers, multiply the addends to the multiplier before adding will not change the answer, that is a x (b + c) = (a x b) + (a  x c).<br />Example:<br />5 x (6 + 7) = 30 + 35 = 65<br />6 x (7 + 9) = 42 + 54 = 9<br />-580292-231531WORKSHEET NO. 11<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />,[object Object],1. 6 x 7 = __ x 66. (7 x __) + (__ x 6) = 7 x (3 +6)<br />2. 5 x 0 = __7.  27 x __ = 27<br />3. 8 x 1 __8. 8 x __ = 0<br />-4323080736604. (4 x 5) x 7 = 4 x (__ x 7)9. 6 x (3 x 4) = (6 x __) x 4<br />5. 8 x (2 + __) = (8 x 2) + (8 x __)10. 4 x 9 =__ x 4<br />B.Fill the missing number. Use the property of multiplication to get product<br />.<br />1. (8 x 4) + (8 x 6) = 8 x (__ + 6) = ______<br />2. (7 x 5) x 2 = 7 x (__ x __) = ______<br />3. (9 x 5) = 25 x__ = _______<br />4.8 x 0 = ______<br />5. (12 x 3) + (12 x 7) = _____<br />Lesson 12<br />MASTERING SKILLS IN MULTIPLYING WHOLE NUMBERS<br />Objectives <br />After this lesson, the students are expected to:<br />,[object Object]
develop the speed in multiplying whole numbers;
perform multiplication correctly.Since multiplication is a shortcut for repeated addition, we can get the product of a two factors without the use of a two factors without the use of repeated addition. Take a look at the example:<br />11 Carries<br /> 2   4<br />3467100168910       3   5  8Multiplicand<br />x                  2  5Multiplier<br />  1 7   9  01st partial product<br />+7 1   62nd partial product<br />  8 9   50Product<br />How to use multiplication table?<br />In mastering the multiplication operation, knowing how to multiply using multiplication table helps you to become fluent in multiplying numbers.<br />2522482238497<br />19050-4204<br />Multiplication Table<br />X012345678910111200000000000000101234567891011122024681012141618202224303691215182124273033364048121620242832364044485051015202530354045505560606121824303642485460667270714212835424956637077848081624324048566472808896909182736455463728190991081001020304050607080901001101201101122334455667788991101211321201224364860728496108120132144<br /> Example: <br />Remembering 9's<br />What's 9 x 7? Use the 9-method! Hold out all 10 fingers, and lower the 7th finger. There are 6 fingers to the left and 3 fingers on the right.The answer is 6.<br />-419100-65033WORKSHEET NO. 12<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />6096015875<br />,[object Object],WRITE YOUR SOLUTION HERE:1. 59x 8 =________________<br />2. 48 x 3 =_______________<br />-41675054229103. 31 x 6 =_______________<br />4. 27 x 21 =______________<br />5. 11 x 15 =_______________<br />6. 21 x 27 =_______________<br />7. 14 x 17 =_______________<br />8. 8 x 32 = ________________<br />9. 78 x 45 =_______________<br />10. 11 x 23 =_____________<br />Lesson 13<br />“THE 99 MULTIPLIER” SHORTCUT IN MULTIPLYING WHOLE NUMBER<br />Objectives<br />After this lesson, the students are expected to:<br />,[object Object]
appreciate exploring the world of multiplication;
appreciate the multiplication operation.This lesson is concern in one of the easy ways in getting the product in multiplication. If the digits in the multiplier (or even multiplicand) are all 9 such as 9, 99, 999…, annex to the multiplicand as many zeros as there are 9’s in the multiplier and from it, subtract the multiplicand.<br />3944664154348Here some examples:<br />999×364= 364 000-364= 369 636 Why?<br />2834×99= 283 400-2834= 280566 Why? <br />,[object Object],-551793-496614WORSHEET NO. 13<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />,[object Object]
99×99=________________________
33×99=________________________
47x99=________________________
65x9=_________________________
21x99=________________________
81x99=________________________
72x999=_______________________
-426497817176856x9999=______________________
34x9=_________________________
8x9=__________________________
-341135346B. Solve the following<br />,[object Object]
Find the product of  132 and 999=_________________________
Find the product of  665 and 99=__________________________
Find the product of  670 and 9=___________________________
Find the product of  154 and 9999=________________________
Find the product of  1063 and 999=________________________

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