9-10.1.1 Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
9-10.1.1.PO 1 Justify with examples the relation between the number system being used (natural numbers, whole numbers, integers, rational numbers and irrational numbers) and the question of whether or not an equation has a solution in that number system.
9-10.5.1 Use reasoning to solve mathematical problems.
9-10.5.1.PO 1 Select an algorithm that explains a particular mathematical process; determine the purpose of a simple mathematical algorithm.
9-10.5.1.PO 2 Analyze algorithms for validity and equivalence recognizing the purpose of the algorithm.
9-10.5.2 Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
9-10.5.2.PO 1 Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify implicit and explicit assumptions that have been made.
9-10.5.2.PO 2 Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s).
9-10.5.2.PO 3 Evaluate a solution for reasonableness and interpret the meaning of the solution in the context of the original problem.
9-10.5.2.PO 4 Generalize a solution strategy for a single problem to a class of related problems; explain the role of generalizations in inductive and deductive reasoning.
9-10.5.2.PO 5 Summarize and communicate mathematical ideas using formal and informal reasoning.
9-10.5.2.PO 6 Synthesize mathematical information from multiple sources to draw a conclusion, make inferences based on mathematical information, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning.