**Grade 6** |

| Understand ratio concepts and use ratio reasoning to solve
problems. |

| Apply and extend previous understandings of multiplication and
division to divide fractions by fractions. |

| Compute fluently with multi-digit numbers and find common factors
and multiples. |

| Apply and extend previous understandings of numbers to the system
of rational numbers. |

| Apply and extend previous understandings of arithmetic to algebraic
expressions. |

| Reason about and solve one-variable equations and inequalities. |

| Represent and analyze quantitative relationships between
dependent and independent variables. |

| Solve real-world and mathematical problems involving area, surface
area, and volume. |

| Develop understanding of statistical variability. |

| Summarize and describe distributions. |

**Grade 7** |

| Analyze proportional relationships and use them to solve real-world
and mathematical problems. |

| Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers. |

| Use properties of operations to generate equivalent expressions. |

| Solve real-life and mathematical problems using numerical and
algebraic expressions and equations. |

| Draw, construct, and describe geometrical figures and describe the
relationships between them. |

| Solve real-life and mathematical problems involving angle measure,
area, surface area, and volume. |

| Use random sampling to draw inferences about a population. |

| Draw informal comparative inferences about two populations. |

| Investigate chance processes and develop, use, and evaluate
probability models. |

**Grade 8** |

| Know that there are numbers that are not rational, and approximate
them by rational numbers. |

| Work with radicals and integer exponents. |

| Understand the connections between proportional relationships,
lines, and linear equations. |

| Analyze and solve linear equations and pairs of simultaneous linear
equations. |

| Define, evaluate, and compare functions. |

| Use functions to model relationships between quantities. |

| Understand congruence and similarity using physical models, transparencies,
or geometry software. |

| Understand and apply the Pythagorean Theorem. |

| Solve real-world and mathematical problems involving volume of
cylinders, cones, and spheres. |

| Investigate patterns of association in bivariate data. |