Solutions to math problems are explained step-by-step.
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Communication activities become more elaborate in third andfourth grade, as students become more comfortable with symbolic andwritten representations of ideas. Students should communicate witheach other about mathematics on a daily basis, exploring problemsituations and justifying their solutions. Different types of writingassignments may be used: keeping journals, explaining solutions tomath problems, explaining mathematical ideas, and writing about thereasoning involved in solving a problem. Students continue to usemanipulatives to explore new ideas and learn to relate differentrepresentations of an idea to each other. For example, after usingbase ten blocks to solve x , students might providea pictorial representation of these blocks (at left below) followed bya written explanation of what they did to get x . Linking the use of concrete manipulatives to the pictorialand symbolic representations is critical to understanding themathematical procedures.
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Writing is an integral part of conveying both mathematical concepts and solutions. Often K-12 educators are not provided with an adequate means of teaching writing in the math curriculum without delving into the English curriculum. By teaching the students to construct heuristics and algorithms (HAL) to derive solutions to mathematical problems, then the student is learning an effective means of problem solving to the extent that they must list the givens, concepts learned, and learn to think sequentially. The construction of algorithms and heuristics stands on its own merits in the area of problem solving and critical thinking. By teaching students not only how to construct algorithms and heuristics, but also a few transitional words and phrases then the HAL can then be used by the student to write an English translation of any given problem and its solution. Obviously, HAL is a form of pseudo code.