Mathematical processes
Mathematics, Grade 8
Mathematical processes
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Study Guide Mathematical processes Mathematics, Grade 8
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MATHEMATICAL PROCESSES Mathematical processes refer to the skills and strategies needed in order to solve mathematical problems. • Problem solving skills refer to the basic mathematical techniques that must be used to solve a problem. • If a problem were to determine the perimeter of a square, a needed skill would be the knowledge of what perimeter means and the ability to add the numbers. • Problem solving strategies are also part of mathematical processes. There are many different strategies that can be used to solve a problem. If one strategy does not help to find the solution to a problem, using another strategy may help to solve it. • Once a problem is solved, the answer should be looked at to consider if the answer is correct. • Reasoning and proof are ways to show an answer is correct. An answer should be checked as proof that it is correct. If an answer cannot be checked as with an equation, it should be reasoned that it is correct based on the given information. Mathematical processes are used in everyday life in many situations. Real world connections can refer to banking situations, sporting events, advertising, driving, comparing population, calculating recipes, predicting weather and many more situations. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use mathematical processes Problem solving skills refer to the basic mathematical techniques that must be used to solve a problem. Problem solving skill refer to techniques such as PEMDAS, using formulas, knowing how to use the mathematical operations with all real numbers, such as fractions and negative numbers, and the basics for solving any mathematical problem. For example, what is the result of 3² - 6 ÷ 3 + 3? Ex. 3² - 6 ÷ 3 + 3 = 9 - 2 + 3 = 10 In order to solve this correctly, a person must know to use PEMDAS. If PEMDAS is not followed, the answer will be incorrect. Some problem solving strategies that can be used are: guess and check, draw a graph or diagram, use an equation or formula, look for a pattern, act out the situation, break down a problem into smaller problem and working backwards. There are more strategies that can be used and a problem can be solved by using one or more strategies. • For example, what strategy could be used to find the total number of pencils given out in a class if a teacher gives two pencils to her class of 18 students? o Use an equation → 2 pencils x 18 students o Break it down → 2 pencils for 9 students + 2 pencils for 9 students o Act it out → physically give 2 pencils to 18 students and then count the pencils. These are only three strategies that can be used to solve this problem. There are many others. If one strategy does not help to find the solution to a problem, using another strategy may help to solve it. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
An answer should be checked as proof that it is correct. For example, the inequality, 2x - 4y ≤ 16 is solved and the answer is y ≤ 1/2x -4 is found. Is this correct? Why? Ex. 2x - 4y ≤ 16 → -4y ≤ -2x + 16 → y ≥ 2/4x - 16/4 → y ≥ 1/2x - 4 The answer is incorrect because the inequality sign was not switched when the -4 was divided by both sides. The correct answer should be y ≥ 1/2x - 4. • If an answer cannot be checked as with an equation, it should be reasoned that it is correct based on the given information. Mathematical processes are used in every day life in many situations. Using problem solving skills, problem solving strategies and reasoning and proof help people solve problems every day. Try This! 1. What must be done first in order to solve the problem, 2(5x - 6)? 2. A table has a length of 3' and a width of 2'; what must a person know in order to solve for the area of the table? 3. What strategy can be used to find the number of different ways that 2 tops can be worn with 3 pairs of pants? 4. What strategy can be used to find which ordered pair make the equation, y = 6x - 5, true? 5. Two sides of a right triangle are 6 and 8. A student thinks the hypotenuse is 10. Is 10 the correct answer? Why? 6. Over the course of a week, Mrs. Jones makes deposits of $150 and $89. She also writes a check for $40. If her beginning balance was $375, what is her ending balance? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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