HOW TO SOLVE PROBLEMS 87 Problem 3. Ruth practiced her music lesson from ten minutes after three until twenty minutes after three. How many minutes did she practice at that time? 1. What does this problem ask you to find? 2. Must you add or subtract to get the answer? 3. What is the answer? Problem 4. How long did Lois practice her lesson if she began at five minutes after two and stopped at thirty minutes after two? 1. What does this problem ask for? 2. Must you add or subtract? 3. What is the answer? Sometimes in working a problem you will have to go back to earlier problems and use their answers to get the answer to the new problem. Problem 5 uses the answers you found to Problems 3 and 4. Problem 5. Lois practiced how much longer than Ruth? 1. What numbers will you need for this problem? 2. What must you do to get the answer? 3. What is the answer? In working problems, read each problem carefully at least twice, and then ask yourself these questions: 1. What does this problem ask me to find? 3. Is there more than one part to the problem? 4. Do I need to use numbers from another problem? NEW WORK 70. How to Estimate Answers. (CLASS WORK.) Careful pupils will be interested to know that there are some easy ways to keep from making foolish mistakes. As you read a problem carefully and ask yourself the questions in this article, estimate or think what would be a reasonable answer. An "estimate" is a careful guess. A reasonable answer is one that is about right. Read Problem 1 carefully and estimate about what the answer should be. Problem 1. John has 27 cents and Harry has 24 cents. How much do both boys have? 1. What does this problem ask you to find? 2. Must you add or subtract? 3. You will keep from making a foolish mistake if you say to yourself: "27 cents is a little more than a quarter, and 24 cents is a little less than a quarter. The answer must be about two quarters or 50 cents." (25+25=50.) 4. Is 50 cents about the correct answer? What is the correct answer? 5. If a pupil worked this problem and got 41 cents for an answer, what did he probably forget to carry when he added 27 and 24? Do you think that he would have made this foolish mistake if he had first estimated that a reasonable answer would be about 50 cents? ESTIMATING ANSWERS 89 Problem 2. Joe had 26 marbles. One day he counted them and found that he had lost all but 14. How many had he lost? 1. What does this problem ask? 2. Will you have to add or subtract to find the answer? 3. Must the answer be less than 26? 4. Would it help to think to yourself: "26 is about 25, and 14 is about 15. 15 from 25 is 10. The answer must be about 10." 5. Is the answer about 10? What is the correct answer? It often helps to think of the numbers in a problem as ending in a five or a zero when you estimate a reasonable answer. Thus: (a) 27+39 might be thought of as 30+40, giving 70 as an estimate of a reasonable answer. What is the correct answer? (b) 94-33 might be thought of as 90-30, giving 60 as an estimate of a reasonable answer. How far is 60 from the correct answer? Do you think you would make a very foolish mistake in either of the two problems above if you first estimated reasonable answers? Problem 3. An automobile traveled 18 miles the first hour, 22 miles the second hour, and 29 miles the third hour. How far did it travel in the three hours? 1. What does this problem call for? 2. Must you add or subtract? 3. Do you think that 20+20+30=70 would be a good way to estimate a reasonable answer? How nearly correct is 70? Is the correct answer 69 hours or 69 miles or 69 automobiles? There is another good way to keep from making foolish mistakes. Think: When I add, the answer will be more than any one of the numbers I am adding. When I subtract, the answer will be less than the larger number in the example or problem. Now estimate reasonable answers to the three problems below. Then work the problems. See how close your estimated answer is to the correct answer. 1. On Tuesday Alice practiced her music lesson 32 minutes before school and 24 minutes after school. How long did she practice that day? 2. Two boys had 31 cents together. They wanted to buy a ball costing 75 cents. How much more money did they need? 3. Frank estimated that a reasonable answer to a problem would be 85 hours. The correct answer was 62 hours. How far did he miss the right answer? 71. Problems about Children's Presents. (WRITTEN WORK.) Read carefully the problems in this article before you try to work them. As you read, estimate an answer for each one. Write this answer after the number of the problem. and see how close the answer is to your estimate. Be sure to write the numbers in straight columns before you add them. Then work each problem Just before Christmas the children in a third-grade class planned to take presents to the Children's Hospital. They made some of the presents. The problems below tell what things they did. 1. Joe and Fred worked a little while every day for 2 weeks making a train of cars. They used 3 Nabisco boxes for flat-cars; 4 chalk boxes for box-cars; 1 cocoa can and 1 baking-powder can for the engine. How many boxes and cans did they use all together? |