generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
multiply and divide positive rational numbers fluently
summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates
graph points in all four quadrants using ordered pairs of rational numbers
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers
interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots
generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties
write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
convert units within a measurement system, including the use of proportions and unit rates
add, subtract, multiply, and divide integers fluently
generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money
identify independent and dependent quantities from tables and graphs
order a set of rational numbers arising from mathematical and real-world contexts
extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle
summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution
model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
locate, compare, and order integers and rational numbers using a number line
compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships
compare the features and costs of a checking account and a debit card offered by different local financial institutions
solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models
give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients
write an equation that represents the relationship between independent and dependent quantities from a table
represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers
write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers
represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots
compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income
determine if the given value(s) make(s) one-variable, one-step equations or inequalities true
classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
write corresponding real-world problems given one-variable, one-step equations or inequalities
represent ratios and percents with concrete models, fractions, and decimals
balance a check register that includes deposits, withdrawals, and transfers
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions
Track each student's skills and progress in your Mastery dashboards