Sixth-grade students develop an understanding of the concept of a ratio and use ratio reasoning to solve a variety of real-world and mathematical problems, including those involving unit pricing and constant speed. Students extend their understanding of operations with fractions to include dividing fractions by fractions. Sixth-graders compute fluently with multi-digit numbers and decimals and find the greatest common factor and least common multiples of certain of operations with whole numbers. Students expand their scope of numbers to the system of rational numbers, which includes negative rational numbers and integers. They locate rational numbers on a number line, add and subtract negative numbers, and graph points in all four quadrants of the coordinate plane. Students write expressions and equations with variables and apply the properties of operations to generate equivalent expressions. Students begin to think statistically as they summarize numerical data sets by quantitative measures of center and variability. They build upon the foundation of area to determine area and volume of more complex shapes.