Washington State Standards for Mathematics: Grade 7

WA.7.1. Core Content: Rational numbers and linear equations (Numbers, Operations, Algebra) Students add, subtract, multiply, and divide rational numbers - fractions, decimals, and integers - including both positive and negative numbers. With the inclusion of negative numbers, students can move more deeply into algebraic content that involves the full set of rational numbers. They also approach problems that deal with a wider range of contexts than before. Using generalized algebraic skills and approaches, students can approach a wide range of problems involving any type of rational number, adapting strategies for solving one problem to different problems in different settings with underlying similarities.

7.1.A. Compare and order rational numbers using the number line, lists, and the symbols <, >, or =.

7.1.B. Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically.

7.1.C. Fluently and accurately add, subtract, multiply, and divide rational numbers.

7.1.D. Define and determine the absolute value of a number.

7.1.E. Solve two-step linear equations.

7.1.F. Write an equation that corresponds to a given problem situation, and describe a problem situation that corresponds to a given equation.

7.1.G. Solve single- and multi-step word problems involving rational numbers and verify the solutions.

WA.7.2. Core Content: Proportionality and similarity (Operations, Geometry/Measurement, Algebra) Students extend their work with ratios to solve problems involving a variety of proportional relationships, such as making conversions between measurement units or finding the percent increase or decrease of an amount. They also solve problems involving the proportional relationships found in similar figures, and in so doing reinforce an important connection between numerical operations and geometric relationships. Students graph proportional relationships and identify the rate of change as the slope of the related line. The skills and concepts related to proportionality represent some of the most important connecting ideas across K-12 mathematics. With a good understanding of how things grow proportionally, students can understand the linear relationships that are the basis for much of high school mathematics. If learned well, proportionality can open the door for success in much of secondary mathematics.

7.2.A. Mentally add, subtract, multiply, and divide simple fractions, decimals, and percents.

7.2.B. Solve single- and multi-step problems involving proportional relationships and verify the solutions.

7.2.C. Describe proportional relationships in similar figures and solve problems involving similar figures.

7.2.D. Make scale drawings and solve problems related to scale.

7.2.E. Represent proportional relationships using graphs, tables, and equations, and make connections among the representations.

7.2.F. Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles.

7.2.G. Determine the unit rate in a proportional relationship and relate it to the slope of the associated line.

7.2.H. Determine whether or not a relationship is proportional and explain your reasoning.

7.2.I. Solve single- and multi-step problems involving conversions within or between measurement systems and verify the solutions.

WA.7.3. Core Content: Surface area and volume (Geometry/Measurement) Students extend their understanding of surface area and volume to include finding surface area and volume of cylinders and volume of cones and pyramids. They apply formulas and solve a range of problems involving three-dimensional objects, including problems people encounter in everyday life, in certain types of work, and in other school subjects. With a strong understanding of how to work with both two-dimensional and three-dimensional figures, students build an important foundation for the geometry they will study in high school.

7.3.A. Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work.

7.3.B. Determine the volume of pyramids and cones using formulas.

7.3.C. Describe the effect that a change in scale factor on one attribute of a two- or three-dimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure.

7.3.D. Solve single- and multi-step word problems involving surface area or volume and verify the solutions.

WA.7.4. Core Content: Probability and data (Data/Statistics/Probability) Students apply their understanding of rational numbers and proportionality to concepts of probability. They begin to understand how probability is determined, and they make related predictions. Students revisit how to interpret data, now using more sophisticated types of data graphs and thinking about the meaning of certain statistical measures. Statistics, including probability, is considered one of the most important and practical fields of study for making sense of quantitative information, and it plays an important part in secondary mathematics in the 21st century.

7.4.A. Represent the sample space of probability experiments in multiple ways, including tree diagrams and organized lists.

7.4.B. Determine the theoretical probability of a particular event and use theoretical probability to predict experimental outcomes.

7.4.C. Describe a data set using measures of center (median, mean, and mode) and variability (maximum, minimum, and range) and evaluate the suitability and limitations of using each measure for different situations.

7.4.D. Construct and interpret histograms, stem-and-leaf plots, and circle graphs.

7.4.E. Evaluate different displays of the same data for effectiveness and bias, and explain reasoning.

WA.7.5. Additional Key Content (Numbers, Algebra) Students extend their coordinate graphing skills to plotting points with both positive and negative coordinates on the coordinate plane. Using pairs of numbers to locate points is a necessary skill for reading maps and tables and a critical foundation for high school mathematics. Students further prepare for algebra by learning how to use exponents to write numbers in terms of their most basic (prime) factors.

7.5.A. Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane.

7.5.B. Write the prime factorization of whole numbers greater than 1, using exponents when appropriate.

WA.7.6. Core Processes: Reasoning, problem solving, and communication - Students refine their reasoning and problem-solving skills as they move more fully into the symbolic world of algebra and higher-level mathematics. They move easily among representations - numbers, words, pictures, or symbols - to understand and communicate mathematical ideas, to make generalizations, to draw logical conclusions, and to verify the reasonableness of solutions to problems. In grade seven, students solve problems that involve positive and negative numbers and often involve proportional relationships. As students solve these types of problems, they build a strong foundation for the study of linear functions that will come in grade eight.

7.6.A. Analyze a problem situation to determine the question(s) to be answered.

7.6.B. Identify relevant, missing, and extraneous information related to the solution to a problem.

7.6.C. Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

7.6.D. Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution.

7.6.E. Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

7.6.F. Apply a previously used problem-solving strategy in a new context.

7.6.G. Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.

7.6.H. Make and test conjectures based on data (or information) collected from explorations and experiments.