California State Standards for Mathematics: Grade 7

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CA.NS. Number Sense

1.0. Students know the properties of, and compute with, rational numbers expressed in a variety of forms.

1.1. Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general.

1.2. Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

1.3. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

1.4. Differentiate between rational and irrational numbers.

1.5. Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

1.6. Calculate the percentage of increases and decreases of a quantity.

1.7. Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

2.0. Students use exponents, powers, and roots and use exponents in working with fractions.

2.1. Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

2.2. Add and subtract fractions by using factoring to find common denominators.

2.3. Multiply, divide, and simplify rational numbers by using exponent rules.

2.4. Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

2.5. Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

CA.AF. Algebra and Functions

3.0. Students graph and interpret linear and some nonlinear functions.

3.1. Graph functions of the form y = nx to the power of 2 and y = nx to the power of 3 and use in solving problems.

3.2. Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).

3.3. Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (rise over run) is called the slope of a graph.

3.4. Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

4.0. Students solve simple linear equations and inequalities over the rational numbers.

4.1. Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

4.2. Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

CA.MG. Measurement and Geometry

3.5. Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.

3.6. Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

2.6. 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.

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

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

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