By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest). Students know about pi and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.

• 1.0 Students make decisions about how to approach problems:

  1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

  1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.

  1.3 Determine when and how to break a problem into simpler parts.

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• 2.0 Students use strategies, skills, and concepts in finding solutions:

  2.1 Use estimation to verify the reasonableness of calculated results.

  2.2 Apply strategies and results from simpler problems to more complex problems.

  2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

  2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

  2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

  2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

  2.7 Make precise calculations and check the validity of the results from the context of the problem.

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• 3.0 Students move beyond a particular problem by generalizing to other situations:

  3.1 Evaluate the reasonableness of the solution in the context of the original situation.

  3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

  3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

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