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 write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:

  1.1 Write and solve one-step linear equations in one variable.

  1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.

  1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

  1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.

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• 2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:

  2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

  2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.

  2.3 Solve problems involving rates, average speed, distance, and time.

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• 3.0 Students investigate geometric patterns and describe them algebraically:

  3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pi(d) - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

  3.2 Express in symbolic form simple relationships arising from geometry.

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