Mathematics, Part 19

Question 1: List some guidelines for using manipulative materials in the mathematics classroom.

Answer 1: As with all classroom supplies, the students must understand that there are rules for their use, including how to store the materials when they are not in use. In addition…the teacher should discuss with the students the purpose of the manipulatives and how they will help the students to learn,the students should understand that the manipulatives are intended for use with specific problems and activities; however, time for free exploration should be made available so students are less tempted to play when assigned specific tasks,a chart posted in the classroom of the manipulatives with their names will help the students to gain familiarity with them and develop mathematical literacy skills, and loans of manipulatives for home use with a letter of explanation to the parents about the purpose and value of the manipulatives will encourage similar strategies with homework.

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Question 2: Explain square roots.

Answer 2: A number multiplied by itself two times is squared, or raised to the power of 2; for example 4 * 4 = 16, 5 * 5 = 25, etc. The number that is squared is the square root; therefore, 4 is the square root of 16, 5 is the square root of 25. The square root of a number is indicated by a radical sign: v. For example: 2² = 4; v4 = 2 or the square root of 4 equals 2. A perfect square is a number that has an integer for a square root. There are 10 perfect squares from 1 to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (the squares of integers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10).Every number has both a positive and a negative square. For example, the square root of 9 is +3 and -3 because 3 * 3 = 9 and -3 * -3 = 9.

Question 3: Compare and contrast algorithms and estimates.

Answer 3: Algorithms result in an exact answer, while an estimate gives an approximation. Algorithms are systematic, problem-solving procedures used to find the solution to a mathematical computation in a finite number of steps. Algorithms are used for recurring types of problems, thus saving mental time and energy because they provide a routine, unvaried method, like a standard set of instructions or a recipe. A computer program could be considered an elaborate algorithm.An estimate attempts only to find a value that is close to an exact answer. A multidigit multiplication problem such as 345 * 12 can be calculated on paper or with a calculator but would be difficult to do mentally. However, an estimation of the answer based on something simpler can be done mentally, such as 350 * 10 = 3500 + 700 = 4200. This estimate is close to the actual answer of 4140. Students can practice their number sense by computing estimations.

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