Grade 6 Introduction: Math Practice Problems
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WASHINGTON GRADE 6 MATHEMATICS STANDARDS
Students multiply and divide fractions and decimals with accuracy, efficiency, and understanding, building on their previous experience with fractions and their knowledge of the relationship between multiplication and division. By using approximations of complicated numbers, students estimate the results of computations in order to check the reasonableness of their answers. With these new skills, students are able to solve a wider variety of contextual problems.
Operations, Geometry, Algebra
Students continue to develop their understanding of variables and begin to see how and why variables are helpful in solving problems. They use variables to represent quantities in formulas, expressions, and equations. Students construct and analyze tables of values for a given situation, and use words, equations, and graphs to describe simple linear relationships. They write and evaluate expressions and write and solve equations.
Numbers, Operations, Geometry, Measurement, Data/Statistics/Probability
Students extend their knowledge of fractions to develop an understanding of ratios, rates, and percents. They work with ratios, rates, and percents in preparation for important future work with proportional relationships. Students convert among fractions, ratios, rates, and percents and describe the advantages of each for different purposes. Students also use ratios and rates as they work with probability.
Students apply formulas to determine the circumference and area of circles and the perimeter and area of triangles, rectangles, and parallelograms, and extend their knowledge of perimeter and area to solve problems involving more complex figures. Students continue their work in geometry by making conjectures concerning general properties of geometric figures.
Numbers, Operations, Data/Statistics/Probability
Students extend their work with statistics and apply their knowledge of decimals and fractions to describe, organize, represent, and summarize data. They use prime factorization as they learn about exponents and use factorizations to simplify fractions. Students reinforce their ability to add, subtract, multiply, and divide positive decimals and fractions, focusing on the use of mental calculations with these numbers.
Reasoning, problem solving, and communication
Students use reasoning and problem solving to deepen their understanding of mathematics content and the problem-solving process. They use relevant information, choose an appropriate strategy, solve a problem, and communicate their thinking. Students move easily among representations—words, models, pictures, or symbols—to understand and communicate mathematical ideas, justify solutions, make conjectures, draw logical conclusions, and verify the reasonableness of their solution. Problems in sixth grade reinforce students’ work with fractions and decimals and involve rates and ratios in preparation for studying proportional relationships and algebraic reasoning. As they solve problems with two-dimensional geometric figures, students prepare for work involving three-dimensional figures in seventh grade.