classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

identify a number, its opposite, and its absolute value

locate, compare, and order integers and rational numbers using a number line

order a set of rational numbers arising from mathematical and real-world contexts

extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

represent integer operations with concrete models and connect the actions with the models to standardized algorithms

add, subtract, multiply, and divide integers fluently

multiply and divide positive rational numbers fluently

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

apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

represent ratios and percents with concrete models, fractions, and decimals

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

generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money;

convert units within a measurement system, including the use of proportions and unit rates

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

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

use equivalent fractions, decimals, and percents to show equal parts of the same whole

write an equation that represents the relationship between independent and dependent quantities from a table

identify independent and dependent quantities from tables and graphs; write an equation that represents the relationship between independent and dependent quantities from a table

represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

distinguish between expressions and equations verbally, numerically, and algebraically

determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations

generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

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

model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

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

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

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

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

write corresponding real-world problems given one-variable, one-step equations or inequalities

model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts

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

graph points in all four quadrants using ordered pairs of rational numbers

represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution

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

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

interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

distinguish between situations that yield data with and without variability

compare the features and costs of a checking account and a debit card offered by different local financial institutions

distinguish between debit cards and credit cards

balance a check register that includes deposits, withdrawals, and transfers

describe the information in a credit report and how long it is retained

describe the value of credit reports to borrowers and to lenders

explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study

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