# Virginia State Standards for Mathematics: Grade 7

7.1. The student will

7.2. The student will describe and represent arithmetic and geometric sequences, using variable expressions.

7.3. The student will

7.3.a) model addition, subtraction, multiplication, and division of integers.

7.3.b) add, subtract, multiply, and divide integers.

7.3.c) The additive and multiplicative identity properties;

7.3.d) The additive and multiplicative inverse properties; and

7.3.e) The multiplicative property of zero.

7.4. The student will solve single-step and multistep practical problems, using proportional reasoning.

7.4.a) Solve practical problems using rational numbers (whole numbers, fractions, decimals) and percents;

7.4.b) Solve consumer-application problems involving tips, discounts, sales tax, and simple interest.

7.5. The student will

7.6. The student will determine whether plane figures--quadrilaterals and triangles--are similar and write proportions to express the relationships between corresponding sides of similar figures.

7.7. The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

7.7.a) Estimate and find the area of polygons by subdividing them into rectangles and right triangles; and

7.7.b) Apply perimeter and area formulas in practical situations.

7.8. The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane.

7.9. The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.

7.10. The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle.

7.11. The student, given data for a practical situation, will

7.12. The student will represent relationships with tables, graphs, rules, and words.

7.13. The student will

7.14. The student will

7.15. The student will

7.16. The student will apply the following properties of operations with real numbers:

7.17. The student, given a problem situation, will collect, analyze, display, and interpret data, using a variety of graphical methods, including

7.17.a) Frequency distributions;

7.17.b) Line plots;

7.17.c) Histograms;

7.17.d) Stem-and-leaf plots;

7.17.e) Box-and-whisker plots; and

7.17.f) Scattergrams.

7.18. The student will make inferences, conjectures, and predictions based on analysis of a set of data.

7.19. The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships.

7.20. The student will write verbal expressions as algebraic expressions and sentences as equations.

7.21. The student will use the following algebraic terms appropriately: equation, inequality, and expression.

7.22. The student will

7.22.a) Solve one-step linear equations and inequalities in one variable with strategies involving inverse operations and integers, using concrete materials, pictorial representations, and paper and pencil;

7.22.b) Solve practical problems requiring the solution of a one-step linear equation.

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