By the end of grade 6, 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.
- apply their knowledge to statistics and probability.
- understand the concepts of mean, median, and mode of data sets and how to calculate the range.
- 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.
- conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest).
- know about π and the formulas for the circumference and area of a circle.
- use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression.
- solve one-step linear equations.
By the end of grade 7, students:
- are adept at manipulating numbers and equations and understand the general principles at work.
- understand and use factoring of numerators and denominators and properties of exponents.
- know the Pythagorean theorem and solve problems in which they compute the length of an unknown side.
- know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale.
- make conversions between different units of measurement.
- know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another.
- increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest.
- graph linear functions and understand the idea of slope and its relation to ratio.
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.