UNIVERSITY OF CAPE COAST COLLEGE OF EDUCATION STUDIES SCHOOL OF EDUCATIONAL DEVELOPMENT AND OUTREACH INSTITUTE OF EDUCATION COURSE NAME: TEACHING PROBLEM SOLVING IN MATHEMATICS COURSE CODE: EMA 402 SW QUESTIONS 1. Which of the following is the theoretical basis guiding the principle of problem solving? A. Cognitivist Theory B. Behaviorist Theory C. Constructivist Theory D. Pavlovian Theory 2. All the following are heuristic strategies except A. Acting it out B. Working backward C. Carrying out the plan D. Looking at all possibilities 3. The model with Entry, Attack and Review phases is attributed to A. Carpenter B. Mason C. Harrison D. Polya 4. The Mathematics master of Nhame JHS when teaching usually presents the mathematics, his students practice the skills involved and finally, the students solve story problems that require using the skill. In problem solving this teacher is A. Teaching for problem solving B. Teaching about problem solving C. Teaching through problem solving D. None of the above Sally has some beds and sofas. All of them are equal in length. The total length is 14 metres. Each bed is 2 metres long. Sally has 1 fewer bed than sofas. What is the total length of the sofa? A student attempts solve the problem using four phases of a model. Use the above information to answer question 5 to 8 5. The student make a choice by restating the problem in another way. At what phase will he do that? A. Understanding the problem B. Devising a plan C. Carrying out the plan D. Looking back 6. If the student does the following: What to find: Total length of the sofas. What is known: Each bed is 2 metres long. Each sofa is 2 metres long. Total length of beds and sofas is 14 metres. Sally has 1 more sofa than bed The student is at what phase here? A. Understanding the problem B. Devising a plan C. Carrying out the plan D. Looking back 7. At what phase will the student then check the following; How many sofas are there? 8 m ÷ 2 m = 4 How many beds are there? 4 – 1 = 3 How many beds and sofas altogether? 4 + 3 = 7 What is the total length of beds and sofas? 7 × 2 m = 14up A. Understanding the problem B. Devising a plan C. Carrying out the plan D. Looking back 8. The phase where the student solve the problem as follows is called: If we add 1 more bed, Sally will have the same number of beds and sofas. New total length = 14 m + 2 m = 16 m Sally has the same number of beds and sofas Total length of sofas = 16 m ÷ 2 = 8 m A. Understanding the problem B. Devising a plan C. Carrying out the plan D. Looking back 9. One of the factors that determine the strategies used to solve problems and investigative tasks are A. The skill and understanding level of the problem solver or investigator B. The skill and heuristic level of the problem solver or investigator C. The skill and the sophistication level of the problem solver or investigator D. The skill and the investigative level of the problem solver or investigator 10. All the following explains heuristics except A. It is independent of any topic B. It is a general suggestion C. It is dependent on a subject D. It is general strategies SECTION B 1. Yaw uses the number cards given below to form as many 3-digit odd numbers as he can. List all the numbers that Yaw can form. SOLUTION Understand: What to find: All the 3-digit odd numbers that Yaw can form from the 4 number cards. What is known: Odd numbers end with 5 or 7. Devise a plan: Make a systematic list Carry out the plan: Odd numbers that end with 5: 245 275 425 475 725 745 Odd numbers that end with 7: 247 257 427 457 527 547 Yaw can form 12 3-digit odd numbers. Look back: Did I form 3-digit numbers? Yes Did I form odd numbers? Yes Did I form all possible numbers? Yes 2. David sold a total of 15 $4 coupons and $5 coupons for a funfair. He received $65 for the sale of the coupons. How many $4 coupons and how many $5 coupons did he sell? Solution: Solution: Understand: What to find: The number of $4 coupons and the number of $5 coupons David sold? What is known: He sold 15 coupons. He received $65. Devise a plan: Guess and check Carry out the plan: $4 + $5 = $9. (7 × 9) = 63 is close to 65. I can start the first guess with 7 $4 coupons. David sold 10 $4 coupons and 5 $5 coupons. Look back: What is the total number of coupons? 10 + 5 = 15 What is the total value of coupons? $40 + $25 = $65 3. In a quiz, 5 marks were awarded for each correct answer and 3 marks were deducted for each wrong answer. Darren answered 14 questions and scored 30 marks. How many questions did he answer correctly? Solution: Understand: What to find: The number of questions Darren answered correctly. What is known: Add 5 marks for each correct answer. Minus 3 marks for each wrong answer. He answered 14 questions. He scored 30 marks. Devise a plan: Guess and check Carry out the plan: I can start the first guess with the same number of correct answers and wrong answers. Look back: What is the total number of questions? 9 + 5 = 14 What is the total marks scored? 45 – 15 = 30 4. Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart? Solution After t hours the distances D1 and D2, in miles per hour, travelled by the two cars are given by D1 = 40 t and D2 = 50 t After t hours the distance D separating the two cars is given by D = D1 + D2 = 40 t + 50 t = 90 t Distance D will be equal to 450 miles when D = 90 t = 450 miles To find the time t for D to be 450 miles, solve the above equation for t to obtain t = 5 hours. 5 am + 5 hours = 10 am 5. At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? Solution After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm 6. Two trains, traveling towards each other, left from two stations that are 900 miles apart, at 4 pm. If the rate of the first train is 72 mph and the rate of the second train is 78 mph, at what time will they pass each other? Solution After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by D1 = 72 t and D2 = 78 t After t hours total distance D traveled by the two trains is given by D = D1 + D2 = 72 t + 78 t = 150 t When distance D is equal to 900 miles, the two trains pass each other. 150 t = 900 Solve the above equation for t t = 6 hours.
