1.0 Introduction Mathematics is subject-involving numbers, numbers that has value. It has been a basic for many subjects in the world. It also can explain our natural environment phenomenon. For example the natural changes of day and nigh. In understanding these, our scientist has used astronomical studies, which needs mathematics as a basic. Imagine our world without mathematics, no knowledge of mathematics, numbers, measurement and many others. We don‟t even know what is plus, minus, subtract and multiple. Our life will be equal to stone age, where they don‟t know how to value things. Students must understand the question and decide on the facts that they understand. In the process of identifying the problems, method, technical, referral and source should highlighted. First the students need to understand the predictions because it helps the students to obtain the information easily. It will make the students to make predictions what might happen, how to solve the problems and what steps to be taken. Secondly collecting information, then to rearrange the information according to the sequence. At this level the students are able to predict, evaluate and verify the information. Then the students must create a procedure and sequence to solve the problem. Thirdly is analysis, the predictions that has been done. At this level the students able to solve the problem, decide on creative analysis for verification. Lastly they will make a conclusion that is students must have obtain conclusion and solution for the problem. 2.0 Introduce Multiplication to our Students The teacher must emphasis strongly when teaching new concepts. The understanding of solely depends on the explanations of the teacher. Multiplication is on of the concept that is taught in Year 2. Teachers must use concrete materials to explain on the multiplication concept more effectively. Prior to that the teacher will request the students to write the numbers based on pictures and decide on the operation to obtain the answers. Request the students to calculate the numbers or the group, which is available. Then the students will write the group numbers. From there the students will be able to understand multiplication multiplication. is actually repeated process which if shorten is Multiplication of whole numbers is commonly known as repeated addition of the same number. In fact, we can consider it to be a “short-cut” method of adding the same number in a given number of times. The result of multiplication is the total number (product) that would be obtained by combining several (multiplier) groups of similar size (multiplicand). For example, if we are combining 4 groups with 2 objects in each group, we could arrive at the same answer by addition. For example 2 + 2 + 2 + 2 = 8 is equivalent to the multiplication equation 4 x 2 = 8. 2 + 2 + 2 + 2 = 8 means 4 x 2 = 8 REPEATED ADDITION We can also express multiplication in standard written method. x 2 7 4 8 (multiplier) (multiplicand ) (product) Suggestion teach concept multiplication as repeated addition Learning Outcome : i. To describe multiplication as repeated addition. ii. To write relevant multiplication sentences. Materials : i. Marbles ii. Boxes 1. Teacher presents repeated-addition story while students model marbles and boxes. Ah Chong has boxes. In each of the boxes, there are 4 marbles. How many marbles are there altogether? An example to illustrate 3 x 4 = 4 + 4 + 4 2. After several rounds of story modeling, teacher introduces multiplication as repeated addition and the relevant mathematics sentences such as: 3x4=4+4+4 3. In groups of five, ask each student to take turns to play each of the Follow roles: Pupils A : Take any number of boxes ( not more than 5 ) and put them at the center of. Pupils B : Put any number of marbles ( not more than 3 ) in each boxes. Pupils C : Tell the story “ 5 boxes, 3 marbles in each, 15 marbles in all.” Pupils D : Write the repeated addition sentences and multiplication sentences. 4. Teacher asks pupils to draw a question card from their pack and repeat step 3 with different numbers of boxes and marbles based on the question displayed on the card. 5. Teacher summaries the lesson on how to describe multiplication as repeated addition and how to write multiplication sentences. 3.0 Remembering Basic Multiplication Facts The basic facts of multiplication involve the products of any two 1-digit whole numbers. We shall concentrate ourselves on teaching half on the basic facts to our Year 2 students, that is, till 9 x 5 = 45. As we can organize in a similar manner. In fact organizing the basic facts into a table could help our students to remember and master the basic facts systematically and easily. Before helping students to construct a table of basic facts of the basic facts of multiplication, we should make sure that they understand them well. Here are some of the important basic multiplication facts: 1. 2. Multiplying by 0 : Any number multiplied by 0 equals 0. Multiplying by 1 : Any number multiplied by 1 equals that number. 3. Multiplying by 2 and 3 : TWO 0x2= 0 5 x 2 =10 1x2= 2 6 x 2 =12 2x2= 4 7 x 2 =14 THREE 0x3= 0 5 x 3 =15 1x3=3 6 x 3 =18 2x3=6 7 x 3 =21 3x3= 9 8 x 3 = 24 4 x 3 = 12 9 x 3 = 27 3x2= 6 8 x 2 =16 4x2= 8 9 x 2 =18 4. Multiplying by 4 and 5. FOUR 0x4= 0 5 x 4 =20 1x4= 4 6 x 4 =24 2x4= 8 7 x 4 =28 FIVE 0x5= 0 1x5=5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 3 x 4 =12 8 x 4 =32 4 x 4 =16 9 x 4 =36 There are 4 important things that a teacher must practice at school, to help the students to remember the basic factor in multiplication more easily and accurately. Besides the above the teacher can use other technique more effectively. 1. 2. Always ask random questions Practice by filling empty zero box The teacher uses 3 minutes for each teaching session. 4.0 Multiplication algorithms There are many different ways to perform multiplication. Usually, we perform the task of multiplication by the standard form, which is writing the numbers to be multiplied in vertical order. 4.1 Algorithm 1 1 1 2 x 7 3 0 4 3 2 Algorithm is written in a standard written method, which is commonly used in the class. Multiplication in regrouping in ones will place ones inside and tens in put up. This type will not use bigger space and less numbers to provide the answers. It‟s easier to teach students using this method and uses less time to solve the questions, and can be implemented on all levels. 4.2 Algorithm 2 2 x 1 3 1 9 0 4 3 2 + 6 7 2 Algorithm 2 is written in a standard written method. Each multiplication will be written in the space provided. Work flow is very clear. This method uses bigger space and more numbers to obtain answers. Convenience for students to use these methods. Uses more time solve the questions and advisable to be used for students on marginal performance. 4.3 Algorithm 3 2 x 1 3 1 9 0 0 4 3 2 0 0 2 4x3 30 x 3 200 x 3 + 6 7 Algorithm 3 is written in a standard written method. Each multiplications students must understand to write the value of the digits correctly. Each digits must be multiple outside. Each multiplication will be written clearly at the space provided. This method uses bigger space to provide the answers to the questions. A lot of numbers will confused the students and they tend to make mistakes. They need more time to solve the questions and recommended for students with good performance 4.4 Algorithm 4 x 3 200 600 30 90 4 12 234 x 3 = 600 + 90 + 12 = 702 Algorithm 4, uses a different solution on the whole. This times its uses Box System. The students must understand to write the value of the digit correctly. The digit value will be multiplied and the answers will b written inside the box provided. This method uses bigger pace and many numbers to solve the questions. Many numbers will confuse the students and will make more mistakes when the doing the process. There is another method that additional. Needs more time to solve the problem and its advisable to teach students with good performance. No recommended for Year 2 students and only applicable for as an additional way for multiplication and only for exposure. My opinion, Algorithm 1 is advisable to be used at school and daily life. This is based on the below matters: i) ii) iii) iv) v) Easy to understand and easy to write Does not use deep numbers and gives fast answers. Does use many symbols in getting the answers. Appropriate for all levels. Currently have been practice in daily life and easy for parents to guide and teach since it uses the old method. 5.0 Lesson Plan Solve Multiplication Problem Date Time Year Number of students Subject of teaching : 3 rd March 2008 : 60minutes : 2 MAWAR : 38 pupils : Multiplications Within 2,3,4,and 5 Times-Table Learning Outcome : Pupils will be able to solve problems involving Multiplication in real life situations. Learning Objectives : Pupils will be taught to use and apply knowledge of Multiplication in real life. Induction Set ( 5 mininutes ) Narrates the story that happened in the orchard. Teachers tells the incident that happened at fruit orchard. „Pak Mat has a fruit orchard. Every morning he collects durian fruit to be sold in the market. Each basket can accommodate 5 fruits. But on that day Pak Mat only be able to collect 5 baskets only.‟ : “ What is the story?” : “ It‟s about Pak Mat and his durians.” : “ Did Pak Mat collected many durians?” : “Yes a lot.” : “ Can you count how many durians he collected?” Teacher Pupils Teacher Pupils Teacher Some students says yes, and some says no. Teacher : “ You can count each basket has 5 fruits and he has 4 baskets.” The teacher wrote this on the blackboard 5+5+5+5= Teacher : “ You can repeated addition or multiply.” Students calculated and gave the correct answer. Teacher : “If we change the sum operation to multiple the answer is also 4 x 5 = 20.” Step 1 (10 minutes ) Explanation of solve problems involving multiplication in real life situations (used Polya Model) Teacher ask the whole class to read the question. Teacher : “Class please find the important information in the question.” “Can you give me.” Teacher wrote the important information on the black board.” The students read the information. Teacher ask the students to create mathematic sentence.” The students solved the problems The verified the answer by using the divide operation. Step 2 ( 20 minutes ) Activities Group to solve the problem. The teacher divides the students to group of five. Each group has 3 questions. Teacher : “In your group, read the question and underline the important information using color pencil.” “After that create mathematic sentences and lastly solve the problems. The students present their findings. : “What information did you underline?” : “2 cupboards, a week and how many.” : “a week equal 7 days.” “So write in mathematics sentences is 7 x 2 = 14.” “You can verify your answer by 14 ÷ 7 = 2. “Now you understand how to solve the problems.” Teacher Pupils Teacher The group with the correct answers is the winner. Step 3 ( 10 minutes ) Activities Individually to solve problems. Each student receives one question. The teacher asks the students to solve the question according to the method they learned recently. To verify the answers together ( follow step of Polya Model ) : “Let‟s check your answer.” Teacher Step 4 ( 10 minutes ) Evaluation (questionnaires). The teacher hands out the questionnaires to the students. Students answer all the questions provided. Check the answers. Closing ( 5 minutes ) The teacher makes a conclusion of the overall students. The teacher ask the students to tell the steps in solving the problems according to Polya Model. Step of Polya Model 1. 2. 3. 4. Understand the question Plan the strategy Used strategy Check the answer Teacher summaries the lesson on the importance of solving story problems involving real life. Moral Value Teaching aids : Honest : Worksheets, Polya Model Chart 6.0 Conclusion Multiplication is the important concept for any topics in Mathematics. Suitable the task that had given this semester including method teacher to introduce multiplication, memories the basic facts and ability to plan the lesson. The Teacher must explain clearly multiply concept for students Year 2. The skills is to be used forever. Therefore, the teacher will be try to find the simple ways help students solve problem in memories basic facts. There are 4 method are suggested here are multiplying by 0, multiplying by 1, multiplying 2 and 3, and multiplying 4 and 5. Teacher also have done every particular to make it concept multiply in memories. There are 4 multiplication algorithm that try to discussion for get more advantage and benefit in each. After work chose either one that better algorithm and give the reason. Lastly, write lesson plan to teach the students how to solve multiplication problem. The Lesson plan 1 hour have induction set, step 1, step 2, step 3, step 4 and closing. This Lesson plan are focusing to works method by using solve problem in „Polya Model‟. The Model consist 4 step there are understand the solving problem, plan the strategy, used the strategy and check the answer solving problem used versa.