Students analyze and decompose routine and non-routine problems by identifying relevant, irrelevant, and missing information; representing relationships with diagrams, tables, graphs, equations, expressions, and number lines; and working with whole numbers, integers, fractions, decimals, ratios, rates, percentages, and familiar measurements. They select efficient operations, tools, and strategies; work backward or use logical elimination; estimate before and after calculating; check precision, rounding, units, inverse operations, and algebraic solutions by substitution; and interpret results in context. They communicate complete justifications, compare and critique strategies and solutions, create related problems and statistical questions, recognize and generalize patterns, organize cases, and form, test, support, or disprove conjectures using examples and counterexamples.