Math word problems are frequently used to gauge students' ability to decipher pertinent information and also to assess students' ability to use their analytical and mathematics skills to solve problems. Math word problems are often used to relate mathematics to real life situations. For instance, Physics applications, finance applications, Economics applications, surveying and other fields heavily rely on Mathematics.
Consequently, word problems appear in a lot of standardized exams as well as in everyday assignments that students face. Standardized exams like the SAT test love word problems since they can be used to integrate many fields of mathematics; and they are a higher order thinking assessment tools.
Teachers and math tutors need to know how help students solve seemingly complicated word problems using innovative approaches, as well as emphasis on tried and tested methods.
Math word problems are frequently used in mathematics exams not only for reasons previously mentioned, but also because they are used to integrate many areas of mathematics in the same problem. An example would be a math word problem that tests a student's knowledge of both Geometry and Algebra. There are many strategies that help students achieve the capability to solve word problems.
While the enlisted strategies are different from topic to topic, teachers and math tutors should inform students of the importance of consistently writing down known and unknown quantities upon reading a word problem, underlining key words, and drawing charts. After doing so, students will should also review the specific topics in mathematics with which the word problem is involved. After efficient, effective and in depth assistance in the specific topic of a word problem, students will be able to complete a problem and reach a satisfying solution.
To successfully teach math, it's important to appeal to the learning styles of students in a way that will maximize the effectiveness of students in being able to draw out pertinent information in word problems and using their Mathematics skills to complete a solution for a word problem. Expert teachers and math tutors are also good at relating word problems to real life and often offer students many options of visualization and/or relations of a particular problem.
Snowtime fun math problem (and answer!)
Question: Alex and Alicia have piled up the snow in their front yard so that their children can learn some math and have some fun. They have made a conical pile of snow six feet high and eight feet across. They will let their children, Sandy and Sam, slide down the hill if the children can determine (a) the volume of the snow piled up to make the hill and (b) the angle down which they will slide from the top. Can you help Sandy and Sam to find the volume and the angle?
Answer: The volume of a cone is calculated using the formula V= 1/3pi r^2(h), or 1/3 the number pi (approximately 3.14) times the radius squared times the height. Alex and Alicia's snow cone is eight feet across, which means that the radius is four feet. The height is six feet. Therefore, that volume is 1/3 (3.14) (4^2) (6), 100.48, or a little over 100 cubic feet. That's a lot of snow for parents to shovel!
The angle down which they slide may be calculated by the dimensions of the triangle formed by the mound. If the height is 6 and the base of the triangle is 4, as shown above, using the Pythagorean theorem shows us that the outside(or the hypotenuse of the triangle) is the square root of the sum of the squares of 4 and 6, or the square root of 52. Using the arc sin function of 6/square root of 52, the angle is approximately 56 degrees. Sam and Sandy will surely have a wild ride down their man-made mountain! |
