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 teenager 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 that 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. Don’t forget lists and tables, or working backward after an initial prediction. In geometry or 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 finding the area under a curve. 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, cooking, athletic events, tracking temperatures or even on road trips.
Keep in mind that math today is taught differently from generations past. Instead of teaching subjects in lock step, concepts presented in previous years are constantly built upon. 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. “A child in high school may discover he is having a hard time in algebra. However, it may not necessarily be the algebra but that he hasn’t mastered multiplication or division.”
Many Web-based resources offer excellent visual and interactive problems. For basic review, 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.
Also check the Web offerings from your own school or district. Often, state standards are supported by readily available test prep and curricular materials. One district-authorized site that offers insight into calculus, statistics, and more is www.fcps.edu/DIS/OHSICS/math/socha/index.html. For additional practice with problems ranging from statistics to algebra, see the attached worksheet. Each problem may be solved with the aid of a drawing.
By Emmet Rosenfeld
High School Worksheet
1. For a new car priced at $24,000, Martha takes a five-year loan with an interest rate of 6.5%. By the time she owns the car, how much will she have paid including principal (the original cost) and interest? (note: the formula for Interest = Principal x Rate x Time)
2. In Sally’s sock drawer, there are two pairs of blue socks and two pairs of red socks. Sally decides to wear the first two socks she pulls from the drawer. What are the odds that her socks will match?
3. Tania needed to borrow some money from David. She agreed to pay him back one and a half times the original sum, plus $60. She paid David a total of $228. What was the original amount she borrowed?
4. Two cars belonging to two brothers are in two towns two hundred miles apart. The brothers decide to meet for a cup of coffee. The first brother starts at 9:00 a.m. driving 60 mph. The second brother starts at 9:00 a.m. driving 40 mph. What time do they meet?
5. Water flows into a sink at six ounces per minute and drains out at two ounces per minute. The sink holds 180 ounces. How long does it take to fill the sink?
6. Jack eats three lollipops in one minute. Jill eats two lollipops per minute. How many do they eat in total in 12 minutes?
7. Farmer Joe’s rectangular field is 140 feet in perimeter. The length is six times the width. What are the dimensions of his field?
8. A can of beans has a radius of three inches and a height of seven inches. What is the volume of the can?
9. An astronaut is driving along the edge of a round crater in his space pod. The crater’s diameter is 14 kilometers. In one revolution around the crater, how far does the pod travel?
10. A carpenter is building a ramp to a platform that is nine feet off the ground. The ground is perfectly level, and he begins 16 feet away from the structure. How long will the face of the ramp be?
1. Martha’s car will cost $31,800, including $7800 interest.
2. Sally has a 3/7 or 42.9% chance of pulling matching socks from the drawer.
3. Tania originally borrowed $112.
4. The brothers meet for coffee at 11:00 a.m.
5. It takes 45 minutes to fill the sink.
6. Jack and Jill eat 60 lollipops.
7. Farmer Joe’s field is 10 feet wide and 60 feet long.
8. The can of beans holds 198 cubic inches.
9. The circumference of the crater is 44 kilometers.
10. The face of the ramp will be 18.36 feet long.