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Ohio's Academic Content Standards in MathematicsMathematical Processes Standard
Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas.
| | | By the end of the K - 2 program: | | A. | Use a variety of strategies to understand problem situations; e.g., discussing with peers, stating problems in own words, modeling problems with diagrams or physical materials, identifying a pattern. (ORC Resources) | | B. | Identify and restate in own words the question or problem and the information needed to solve the problem. (ORC Resources) | | C. | Generate alternative strategies to solve problems. (ORC Resources) | | D. | Evaluate the reasonableness of predictions, estimations and solutions. (ORC Resources) | | E. | Explain to others how a problem was solved. (ORC Resources) | | F. | Draw pictures and use physical models to represent problem situations and solutions. (ORC Resources) | | G. | Use invented and conventional symbols and common language to describe a problem situation and solution. (ORC Resources) | | H. | Recognize the mathematical meaning of common words and phrases, and relate everyday language to mathematical language and symbols. (ORC Resources) | | I. | Communicate mathematical thinking by using everyday language and appropriate mathematical language. (ORC Resources) |
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| | | By the end of the 3 - 4 program: | | A. | Apply and justify the use of a variety of problem-solving strategies; e.g., make an organized list, guess and check. (ORC Resources) | | B. | Use an organized approach and appropriate strategies to solve multi-step problems. (ORC Resources) | | C. | Interpret results in the context of the problem being solved; e.g., the solution must be a whole number of buses when determining the number of buses necessary to transport students. (ORC Resources) | | D. | Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork. (ORC Resources) | | E. | Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric array, represent one-third by dividing an object into three equal parts. (ORC Resources) | | F. | Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number. (ORC Resources) | | G. | Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation. (ORC Resources) | | H. | Recognize basic valid and invalid arguments, and use examples and counter examples, models, number relationships, and logic to support or refute. (ORC Resources) | | I. | Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others. (ORC Resources) | | J. | Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language. (ORC Resources) | | K. | Use mathematical language to explain and justify mathematical ideas, strategies and solutions. (ORC Resources) |
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| | | By the end of the 5 - 7 program: | | A. | Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives. (ORC Resources) | | B. | Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations. (ORC Resources) | | C. | Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods. (ORC Resources) | | D. | Recognize whether an estimate or an exact solution is appropriate for a given problem situation. (ORC Resources) | | E. | Use deductive thinking to construct informal arguments to support reasoning and to justify solutions to problems. (ORC Resources) | | F. | Use inductive thinking to generalize a pattern of observations for particular cases, make conjectures, and provide supporting arguments for conjectures. (ORC Resources) | | G. | Relate mathematical ideas to one another and to other content areas; e.g., use area models for adding fractions, interpret graphs in reading, science and social studies. (ORC Resources) | | H. | Use representations to organize and communicate mathematical thinking and problem solutions. (ORC Resources) | | I. | Select, apply, and translate among mathematical representations to solve problems; e.g., representing a number as a fraction, decimal or percent as appropriate for a problem. (ORC Resources) | | J. | Communicate mathematical thinking to others and analyze the mathematical thinking and strategies of others. (ORC Resources) | | K. | Recognize and use mathematical language and symbols when reading, writing and conversing with others. (ORC Resources) |
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| | | By the end of the 8 - 10 program: | | A. | Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution. (ORC Resources) | | B. | Apply mathematical knowledge and skills routinely in other content areas and practical situations. (ORC Resources) | | C. | Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities. (ORC Resources) | | D. | Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions. (ORC Resources) | | E. | Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas. (ORC Resources) | | F. | Use precise mathematical language and notations to represent problem situations and mathematical ideas. (ORC Resources) | | G. | Write clearly and coherently about mathematical thinking and ideas. (ORC Resources) | | H. | Locate and interpret mathematical information accurately, and communicate ideas, processes and solutions in a complete and easily understood manner. (ORC Resources) |
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| | | By the end of the 11 - 12 program: | | A. | Construct algorithms for multi-step and non-routine problems. (ORC Resources) | | B. | Construct logical verifications or counter-examples to test conjectures and to justify or refute algorithms and solutions to problems. (ORC Resources) | | C. | Assess the adequacy and reliability of information available to solve a problem. (ORC Resources) | | D. | Select and use various types of reasoning and methods of proof. (ORC Resources) | | E. | Evaluate a mathematical argument and use reasoning and logic to judge its validity. (ORC Resources) | | F. | Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences. (ORC Resources) | | G. | Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified empirically using examples or data. (ORC Resources) | | H. | Use formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations. (ORC Resources) | | I. | Communicate mathematical ideas orally and in writing with a clear purpose and appropriate for a specific audience. (ORC Resources) | | J. | Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. (ORC Resources) |
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