extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers

add, subtract, multiply, and divide rational numbers fluently

apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

calculate unit rates from rates in mathematical and real-world problems

​represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

determine the constant of proportionality (k = y/x) within mathematical and real-world problems

solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

convert between measurement systems, including the use of proportions and the use of unit rates

generalize the critical attributes of similarity, including ratios within and between similar shapes

describe π as the ratio of the circumference of a circle to its diameter

solve mathematical and real-world problems involving similar shape and scale drawings

​represent sample spaces for simple and compound events using lists and tree diagrams

make predictions and determine solutions using experimental data for simple and compound events

make predictions and determine solutions using theoretical probability for simple and compound events

find the probabilities of a simple event and its complement and describe the relationship between the two

solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents

solve problems using qualitative and quantitative predictions and comparisons from simple experiments

determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces

represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b

solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids

determine the circumference and area of circles

determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles

solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net

write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

represent solutions for one-variable, two-step equations and inequalities on number lines

write a corresponding real-world problem given a one-variable, two-step equation or inequality

model and solve one-variable, two-step equations and inequalities

determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

use data from a random sample to make inferences about a population

compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations

calculate the sales tax for a given purchase and calculate income tax for earned wages

identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget

create and organize a financial assets and liabilities record and construct a net worth statement

use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby

calculate and compare simple interest and compound interest earnings

analyze and compare monetary incentives, including sales, rebates, and coupons