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.
All classes meet the California Mathematics Content Standards for California Public Schools. Click the link below to view academic content standards for Mathematics, adopted by the California State Board of Education: