In middle school math, students move from arithmetic to algebra in grades six through eight. Learning focuses on ratio and proportional reasoning applied to real-world problems and quantitative relationships, leading to the notion of functions by grade eight. By the end of grade six, students are expected to be fluent in multi-digit division and calculations with multi-digit decimals, ratios and proportional relationships, and early expressions and equations. By the end of 7th grade should understand ratios and proportional relationships and arithmetic of rational numbers. By the end of 8th grade eight, students are expected to be fluent in linear algebra and linear functions.