Washington State Standards for Mathematics: Grade 6

WA.6.1. Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Students have done extensive work with fractions and decimals in previous grades and are now prepared to learn how to multiply and divide fractions and decimals with understanding. They can solve a wide variety of problems that involve the numbers they see every day - whole numbers, fractions, and decimals. By using approximations of fractions and decimals, students estimate computations and verify that their answers make sense.

6.1.A. Compare and order non-negative fractions, decimals, and integers using the number line, lists, and the symbols <, >, or =.

6.1.B. Represent multiplication and division of non-negative fractions and decimals using area models and the number line, and connect each representation to the related equation.

6.1.C. Estimate products and quotients of fractions and decimals.

6.1.D. Fluently and accurately multiply and divide non-negative fractions and explain the inverse relationship between multiplication and division with fractions.

6.1.E. Multiply and divide whole numbers and decimals by 1000, 100, 10, 1, 0.1, 0.01, and 0.001.

6.1.F. Fluently and accurately multiply and divide non-negative decimals.

6.1.G. Describe the effect of multiplying or dividing a number by one, by zero, by a number between zero and one, and by a number greater than one.

6.1.H. Solve single- and multi-step word problems involving operations with fractions and decimals and verify the solutions.

WA.6.2. Core Content: Mathematical expressions and equations (Operations, Algebra) Students continue to develop their understanding of how letters are used to represent numbers in mathematics - an important foundation for algebraic thinking. Students use tables, words, numbers, graphs, and equations to describe simple linear relationships. They write and evaluate expressions and write and solve equations. By developing these algebraic skills at the middle school level, students will be able to make a smooth transition to high school mathematics.

6.2.A. Write a mathematical expression or equation with variables to represent information in a table or given situation.

6.2.B. Draw a first-quadrant graph in the coordinate plane to represent information in a table or given situation.

6.2.C. Evaluate mathematical expressions when the value for each variable is given.

6.2.D. Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.

6.2.E. Solve one-step equations and verify solutions.

6.2.F. Solve word problems using mathematical expressions and equations and verify solutions.

WA.6.3. Core Content: Ratios, rates, and percents (Numbers, Operations, Geometry/Measurement, Algebra, Data/Statistics/Probability) Students extend their knowledge of fractions to develop an understanding of what a ratio is and how it relates to a rate and a percent. Fractions, ratios, rates, and percents appear daily in the media and in everyday calculations like determining the sale price at a retail store or figuring out gas mileage. Students solve a variety of problems related to such situations. A solid understanding of ratios and rates is important for work involving proportional relationships in grade seven.

6.3.A. Identify and write ratios as comparisons of part-to-part and part-to-whole relationships.

6.3.B. Write ratios to represent a variety of rates.

6.3.C. Represent percents visually and numerically, and convert between the fractional, decimal, and percent representations of a number.

6.3.D. Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions.

6.3.E. Identify the ratio of the circumference to the diameter of a circle as the constant pi, and recognize 22/7 and 3.14 as common approximations of pi.

6.3.F. Determine the experimental probability of a simple event using data collected in an experiment.

6.3.G. Determine the theoretical probability of an event and its complement and represent the probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100.

WA.6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Students extend what they know about area and perimeter to more complex two-dimensional figures, including circles. They find the surface area and volume of simple three-dimensional figures. As they learn about these important concepts, students can solve problems involving more complex figures than in earlier grades and use geometry to deal with a wider range of situations. These fundamental skills of geometry and measurement are increasingly called for in the workplace and they lead to a more formal study of geometry in high school.

6.4.A. Determine the circumference and area of circles.

6.4.B. Determine the perimeter and area of a composite figure that can be divided into triangles, rectangles, and parts of circles.

6.4.C. Solve single- and multi-step word problems involving the relationships among radius, diameter, circumference, and area of circles, and verify the solutions.

6.4.D. Recognize and draw two-dimensional representations of three-dimensional figures.

6.4.E. Determine the surface area and volume of rectangular prisms using appropriate formulas and explain why the formulas work.

6.4.F. Determine the surface area of a pyramid.

6.4.G. Describe and sort polyhedra by their attributes: parallel faces, types of faces, number of faces, edges, and vertices.

WA.6.5. Additional Key Content (Numbers, Operations) Students extend their mental math skills now that they have learned all of the operations - addition, subtraction, multiplication, and division - with whole numbers, fractions, and decimals. Students continue to expand their understanding of our number system as they are introduced to negative numbers for describing positions or quantities below zero. These numbers are a critical foundation for algebra, and students will learn how to add, subtract, multiply, and divide positive and negative numbers in seventh grade as further preparation for algebraic study.

6.5.A. Use strategies for mental computations with non-negative whole numbers, fractions, and decimals.

6.5.B. Locate positive and negative integers on the number line and use integers to represent quantities in various contexts.

6.5.C. Compare and order positive and negative integers using the number line, lists, and the symbols <, >, or =.

WA.6.6. 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 six, students solve problems that involve fractions and decimals as well as rates and ratios in preparation for studying proportional relationships and algebraic reasoning in grade seven.

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

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

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

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

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

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

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

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