Basic Math
APPRECIATION Alhamdulillah. Thank God for giving us chance to finish our Basic Math course work on the right time. Well, this task gives us a lot of experiences during the process to finish it. It was quite tough to finish this task because this problem solving task is new for us. But, we finished this course work perfectly. A big thank you also must be given to En. Mohd. Azmi because helps us a lot to finish this task. He gave us the guidelines about routine and non-routine problems and how to apply Polya’s problem solving model. It helps us a lot to finish this task.
An appreciation to our parents because always give supports during the process to finish this course work. They also gave facilities like laptop and printer so that easy for us to finish this task. Thanks you to all our friends and seniors who gave supports and some guidelines to finish this task. We shared our ideas and helped each other to produce a great work for this coursework. Lastly, we hope that we have finished this coursework without any mistake. Hopefully everyone satisfies with our work. Thank you. NON-ROUTINE PROBLEM Non-routine problem solving serves a different purpose than routine problem solving.
A routine is a sequence of actions regularly followed. Non-routine would be something you wouldn’t do at all regularly. Our evening routine is home by six and dinner on the table by seven. Sleeping late is not or non routine in our family. Non-routine problem solving is mostly concerned with developing students’ mathematical reasoning power and fostering the understanding that mathematics is a creative endeavor. From the point of view of students, non-routine problem solving can be challenging and interesting. * Non routine problems means unusual or unique problems Do not know any standard procedure * Requires the application of skills, concepts or principles which have been mastered * The method cannot be memorized * Needs a set of systematic activities : * planning * strategy * suitable methods PROBLEM 1 A florist is going to make flower by paper for her customer. She has red, green and purple paper. She can use silver decorations, yellow decorations or orange decorations to beautify her paper flower. She can use black or white rope to her flower paper. How many different flower papers can she make? George Polya’s problem solving steps: 1).
Understanding the problem i – 3 types color of paper : red, green, purple ii – 3 types of decorations : silver, yellow , orange iii – 2 types of rope :black and white 2). Devising a problem The possible strategies: 1. Draw a diagram 2. Making table 3). Carrying out the plan -The question is to find how we can get the flower with different color. 4). Look back – How many different flower papers can she make? – The question is to find how we can get the flower with different color. – There are 18 different flowers she can makes. Solution: DRAW DIAGRAM Symbol for the Tree Diagram: RED| R|
GREEN| G| PURPLE| P| SILVER| S| YELLOW| Y| ORANGE| O| BLACK| B| WHITE| W| First Tree Diagram: B S W B Y R W B O W For the first tree diagram that is the paper, second is the decorations and the third is the type of wire. From the first tree diagram we get 6 types flower of papers which are: = RSB, RSW, RYB, RYW, ROB, ROW Second Tree Diagram: B S W G Y B W B O W From the second tree diagram we get 6 types of flower which are = GSB, GSW, GYB, GYW, GOB, GOW Third Tree Diagram: B S W B O P W B Y W From the second tree diagram we get 6 types of flower which are = PSB, PSW, PYB, PYW, POB, POW
From the tree diagrams shown, there are 18 ways that the florist can produce paper flowers. This is because each tree diagram provides 6 different colors of flowers. There are 3 tree diagrams multiply with 6 are 18. So, there are 18 different flowers she can makes. MAKING TABLE | RED| GREEN| PURPLE| SILVER (BLACK WIRE)| YELLOW (BLACK WIRE)| ORANGE (BLACK WIRE)| RED| | | | /| /| /| GREEN| | | | /| /| /| PURPLE| | | | /| /| /| SILVER (WHITE WIRE)| /| /| /| | | | YELLOW (WHITE WIRE)| /| /| /| | | | ORANGE (WHITE WIRE)| /| /| /| | | | I. From the table, shown that there are 18 ways the florist can make the different color of flower.
II. So, there are 18 different flowers she can makes. Justification The best method to solve this problem is making a diagram. This is because we can see clearly the situation of colour and it’s different. Besides, using table we can see the combination with the color, decoration and wire. Using table also can be use for this problem, but it is quite hard for people to see the solution clearly. PROBLEM 2 If Yaya had 17 cents, what is the smallest number of coins she could have? If she had 1 nickel, what other coins could she have? George Polya’s problem solving steps: 1). Understanding the problem Yaya has 17 cent. -If she had 1 nickel. – What other coins could she have? 2). Devising a problem The possible strategies: 1. Make a combination table 2. Guess and check 3). Carrying out the plan -The question is to find the other coins must Yaya have in a smallest number of coins. 4). Look back – What other coins could she have? – To find the other coins must Yaya have in a smallest number of coins. Solution: COMBINATION TABLE Pennies ( 1 cent)| Nickels (5 cent)| Dimes (10 cent)| Total of coins| 17| 0| 0| 17 cent| 12| 1| 0| 17 cent| 7| 2| 0| 17 cent| 2| 3| 0| 17 cent| | 0| 1| 17 cent| 2| 1| 1| 17 cent| i) By making a combination table (shown above), Yaya has to fill it out until she can total of the coins for a 17 cent in every row and column. ii) The first row has the types of coins in a smallest number and the first column the numbers of coins for to total to 17 cents. iii) The remaining cells are the combinations of the two. GUESS AND CHECK i) Using the hint, she only has 1 nickel coins, so she has to add other smallest coins to equals with 17 cent. ii) A smallest coin is like a penny is a 1 cent, nickel that a 5 cent and dimes is a 10 cent. ii) Since, she has a 6 of group smallest coins that she can have for a smallest numbers of coins. She has a nickel, pennies and dimes a type of coins. Justification The best method to solve this problem is making a combination of coins with a table. This is because we can see clearly the situation and the elaboration. We also can know the combination of the coins with the table. While using guess and check method is quite hard because we just guessing and checking either the solution are correct or not. So, by using table is the best way to get the solution for this problem PROBLEM 3
Bob is an overweight person and his doctor told him to lose 36 kg. If he lost 11 kg the first week, 9 kg the second week, and 7 kg the third week, and he continues losing at this rate, how long will it take him to lose 36 kg? WEEK| TOTAL KILOGRAMS LOST| 1| 11| 2| 11 + 9 = 20| 3| 20 + 7 = 27| 4| | 5| | George Polya’s problem solving steps: 1). Understanding the problem * How much does he need to lose? = 36 kg * How much did he lose the first week? = 11 kg * How much did he lose for the second week? = 9 kg * How much did he lose for the third week? = 7 kg 2). Devising problem The possible strategies: Make a combination table * Guess and check 3). Carrying out the problems * How much less does he lose the second week than first week? = 2 kg * How much less does he lose the third week than the second? = 2 kg 4). Look back – how long will it take him to lose 36 kg? – he will lost 36 kg in the sixth week. Solution: COMBINATION TABLE WEEK| TOTAL KILOGRAMS LOST| 1| 11| 2| 11 + 9 = 20| 3| 20 + 7 = 27| 4| 27 + 5 = 32| 5| 32 + 3 = 35| 6| 35 + 1 = 36| Pattern: the number of kilograms lost decreases by 2 kilogram each week. It will take the man 6 weeks to lose 36 kg. GUESS AND CHECK i.
If the man lost decreases of 11 kg the first week, 9 kg the second week, 7 kg the third week, and so on, he will lost 36 kg in the sixth week. ii. This is because the weight is decreasing 2 kg per week. Justification The best method to solve this problem is making a table. This is because we can see clearly the situation and the elaboration. By using the table, we can see the pattern of decreasing of weight. We can see the week and the total kilogram lost by the person clearly. While using guess and check method is quite hard because we just know the answer by guessing and checking the answer.
It takes quite long time either than using the table. So, the best way to get the solution of this problem is making table. Individual Reflection: (Muhammad Ikhwan Bin Samsuddin) In my experience, we have to do a lot of things when we try to complete this assignment. After doing a research, I can understand what is mean by non-routine problems. Non-routine problem solving serves a different purpose than routine problem solving. A routine is a sequence of actions regularly followed. Non-routine would be something you wouldn’t do at all regularly.
When we try to try to solve the non-routine problems, we use polya theory to find a solution. It is easy for us to find solution and solve the problems using polya theory. Furthermore, there are a lot steps from polya theory that can be used to solve that problems. But not all problems can be solved using the same steps. There are a lot of strategies of polya theory such as draw a table, guess and check, draw a diagram and many more. We need to understand the question before we start using polya theory. Moreover, there are four steps to solve the problems. Firstly, we need to understand the questions given.
Read the question carefully and underline the keywords of that question. Secondly, after we understand the question, we need to device the problems using the strategies. There many possible strategies that we can use to solve that kind of questions. Thirdly, we need to carry out the plan and how to solve the problems using those strategies. We need at least two strategies for each problem because some people cannot understand the certain strategies. Lastly, we need to look back after solve the problems. It is because we need to check whether we answer the question or not and our answer is correct or not.
Last but not least, main point of this assignment is to produce beginning teacher, who are knowledgeable and skillful and we are assigned to gather information about this topic. First, make a meaningful and rational inferences and judgements based on knowledge of ratios. Second, construct visual representation of data and to communicate findings through logical and critical analysis of information. So, we complete both of the topics for this task. There are a lot of information I can get from this task. I hope this information can use for my future. REFERENCE 1.
Malaysia Book of Records Millenium Edition, 2000. R & D Communication Sdn. Bhd. 2. Mathematics Form 1, 2000. Penerbitan Pelangi Sdn. Bhd. Johor, Malaysia. 3. A belson, H. & diSessa, A. (1980). Turtle Geometry: the Computer as a Medium for Exploring Mathematics. Cambridge, MA : MIT Press 4. von Glaserfeld, E. (1987). Preliminaries to any Theory of Representation. In C. janvier (eds. ) Problem of Representation in Mathematics Learning and Problem Solving, Hillsdale, NJ: Erlbaum. 5. Susan O’ Conell. (1992). Introduction to problem solving strategies for the elementary math classroom.
Math solution publication. 6. http://www. managementhelp. org/prsn_prd/prob_slv. htm * Surfed on 2nd March 2010 7. http://en. wikipedia. org/wiki/Problem_solving * Surfed on 2nd March 2010 8. http://www. mediafrontier. com/Article/PS/PS. htm * Surfed on 2nd March 2010 9. http://www. mathpentath. org/pdf/meba/routine. pdf * Surfed on 2nd March 2010 10. http://io. uwinnipeg. ca/~jameis/Math/N. nonroutine/NEY1. html * Surfed on 2nd March 2010 CONTENT 1. APPRECIATION 2. NON-ROUTINE PROBLEM 3. POLYA’S PROBLEM SOLVING METHOD 4. PROBLEM 1 5. PROBLEM 2 6. PROBLEM 3 7. REFLECTION 8. REFERENCE
