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If a picture is worth a thousand words, isn’t a word problem worth at least one picture? Word problems are common at every level of math, from addition to calculus. Help your child draw conclusions the easy way. Understand the concepts involved in a particular word problem. Look for key words such as simplify, represent or solve for. Make sure your child is familiar with these general operations and terms. Also, be sure to correctly isolate elements of the equation. Does the answer require that she simply solve a multi-step equation in one variable or does it require her to solve and then graph? Next, create a diagram, sketch or chart with the appropriate elements. There are several strategies available here. Don’t forget lists and tables, or working backward after an initial prediction. In geometry or pre-algebra, a word problem often requires a graphic solution in addition to, or in place of, a calculation. Make the conceptual shift from a drawing to an equation. It is important to emphasize that this method is not meant to provide a “short cut,” so much as a bridge. Check your child’s understanding of the concept by asking her to explain, for example, the process of graphing a line. Getting the right answer is important, but equally important is learning the route taken. Richard E. Bavaria, Ph.D., vice president of education for Sylvan Learning Center, says bringing math into everyday situations is a great learning tool. “Any time parents can help their child recognize that math is a part of everyday life and not just a series of problems on a worksheet, they are doing their child a favor,” Bavaria says. “If parents can talk about how they use math in their everyday life, children can easily relate.” He says parents can help children become familiar with math by using it in familiar situations such as at the tool bench, athletic events, cooking, tracking temperatures or even on road trips. Keep in mind that math today is taught differently than in generations past. Concepts presented during a child’s early years are constantly built upon. As early as sixth grade, students are taught logistics, statistics and probability, which prepares them for more complicated high school math. If a student doesn’t grasp these fundamentals, he never can fully understand more advanced concepts until he reviews the basics. Under-achieving students often develop coping strategies that mask their lack of a firm foundation in the fundamentals. “Math is very much a sequential subject and it requires a strong foundation,” Bavaria says. “When students recognize they are having difficulty in math, the problem might now be in the lesson that they are learning, but that they haven’t mastered the lesson from three weeks ago.” Many Web-based resources offer excellent visual and interactive problems. Younger students will like the games and friendly graphics offered at www.coolmath.com. Another site maintained by Drexel University, mathforum.org, offers excellent reviews of concepts along with resources for students and teachers. For additional practice, see the attached worksheet, with problems covering basic operations, fractions, decimals and percents. Each problem may be solved with the aid of a drawing. By Emmet Rosenfeld Junior High Worksheet Basic Operations Review 1. Nell has been collecting cards for three years. She bought 29 the first year, 40 the second, and 63 this year. Last year, she gave away seven, and this year, she traded away 17 cards in return for two. How many cards are in her collection now? 2. Megan charges $6 an hour to baby-sit one child, and $2 for each additional child. She babysat for the Smiths, who have two boys, last Friday from 5:00 p.m. to 6:30 p.m. At 6:30 p.m., the boys’ friend came over. The Smith’s came home at 9:00 p.m. How much did Megan earn? Multiplication and Division with Decimals 3. Bill drives 13.4 miles to and from work each day, and his total commuting time is 39 minutes. What is his average speed in miles per hour? 4. Marty pays $1.28 for enough lemons to make a gallon of lemonade, and $2.23 for cups and sugar. At his stand, he sells cups of lemonade for 50 cents. Last Saturday, he sold 23 cups. How much money did his business make, counting both supplies and sales? Fractions 5. Dennis has to read a 234-page book in one week. He decides to read 2/3 of the book between Monday and Friday, and the rest on the weekend. If he reads the same number of pages on Saturday and Sunday, how many pages will he read on each of those days? 6. Bart ate 3/5 of a pie at the pie-eating contest. Sharon ate 2/3 of a pie. Mark ate 7/15 of a pie. Who got first, second and third place? 7. Miranda was feeding the animals at the farm. She noticed that 2/3 of the pigs came when she called, but only 1/6 as many horses as pigs responded to her call. There are 27 pigs. How many horses came right away to eat some hay? Decimals and Percents 8. John planned to hike 10 miles of the Appalachian trail. He hiked 3.43 miles on the first day, and 5.02 miles on the second day. After hiking 1.2 miles on the third day, he realized he’d forgotten his tent. He went back to the last campsite to get it, then finished his trip. How many miles did he hike in total? 9. Becky wanted to buy some towels that cost $120. She waited until they were marked down on sale, “40% off list price.” How much were the towels? 10. Twenty-five children were supposed to go on the fieldtrip but only 80% brought in their permission slips. 80% of those who brought permission slips were present on the day of the trip. How many children went? Answers: 1. Nell currently has 110 cards. 2. Megan earned $37 babysitting. 3. Bill’s average speed is a little over 41 mph. 4. Marty’s lemonade stand makes him $7.99. 5. Dennis will read 39 pages each weekend day. 6. Sharon got 1st, Bart got 2nd, and Mark got 3rd. 7. 3 horses came when Miranda called. 8. John hiked 12.4 miles in all. 9. Becky paid $72. 10. 16 children went on the trip. |
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